Operating room planning and scheduling: A literature review
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paper_title: Surgical demand scheduling: a review.

paper_content:

Abstract ::: This article reviews the literature on scheduling of patient demand for surgery and outlines an approach to improving overall performance of hospital surgical suites. Reported scheduling systems are categorized into those that schedule patients in advance of the surgical date and those that schedule available patients on the day of surgery. Approaches to estimating surgical procedure times are also reviewed, and the article concludes with a discussion of the failure to implement the majority of reported scheduling schemes.
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paper_title: Scheduling subject to resource constraints: classification and complexity

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Abstract In deterministic sequencing and scheduling problems, jobs are to be processed on machines of limited capacity. We consider an extension of this class of problems, in which the jobs require the use of additional scarce resources during their execution. A classification scheme for resource constraints is proposed and the computational complexity of the extended problem class is investigated in terms of this classification. Models involving parallel machines, unit-time jobs and the maximum completion time criterion are studied in detail; other models are briefly discussed.
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paper_title: A Review of the Application of Mathematical Programming to Tactical and Strategic Health and Social Services Problems

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The paper first considers tactical allocation problems in the health service (particularly the hospital) field which have been tackled by the mathematical programming approach. Examples of such problem areas are those of hospital admissions scheduling, nurse staff assignment, menu planning and the location of hospitals. However, examples of the successful implementation of such models in the literature have only been found for the area of menu planning.
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paper_title: Where are the costs in perioperative care : analysis of hospital costs and charges for inpatient surgical care

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BackgroundMany health-care institutions are emphasizing cost reduction programs as a primary tool for managing profitability. The goal of this study was to elucidate the proportion of anesthesia costs relative to perioperative costs as determined by charges and actual costs.
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paper_title: Surgical process scheduling: a structured review.

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There is no generally accepted definition of surgical process scheduling available in the literature; nursing researchers, physicians, administrators, and management scientists each view scheduling differently. To overcome this communication problem, a number of authors have proposed conceptual frameworks for surgical process scheduling. These frameworks have unfortunately been either unsatisfactory or incomplete. In this paper, we describe a conceptual framework for surgical process scheduling and use it to classify the existing literature. Results from the review indicate that while operational aspects of advance and allocation scheduling are well understood, further research should be directed towards resolving scheduling issues at strategic and administrative levels. In addition, techniques for integrating operating room (OR) scheduling with other hospital operations are required.
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paper_title: Achieving operating room efficiency through process integration.

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As healthcare organizations look for ways to gain new efficiencies and reduce costs, they are examining surgical services with a critical eye. In many cases, the operating room (OR) was not included in enterprisewide reengineering efforts, thereby limiting the positive impact of those efforts. Healthcare organizations are recognizing that every point along the patient care continuum is interrelated. To truly maximize reengineering efforts, they need to integrate the entire process and information flow within the OR and across the enterprise.
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paper_title: The Aging Population and Its Impact on the Surgery Workforce

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The population is expanding and aging. According to the US Census Bureau, the domestic population will increase 7.9% by 2010, and 17.0% by 2020. The fastest growing segment of this population consists of individuals over the age of 65; their numbers are expected to increase 13.3% by 2010 and 53.2% by 2020. Two main factors are responsible for these forecasts. First, we are living longer; life expectancy has increased from 66.7 years for individuals born in 1946 to 76.1 years for those born in 1996.1 Second, the baby boomers (those born between 1946 and 1964) are a wave of population density that will begin to hit retirement age in 2011.2 ::: ::: Older individuals require more medical services relative to their younger counterparts. The National Hospital Discharge Survey (NHDS) reported that in 1999, patients aged 65 years or older comprised 12% of the population, but constituted 40% of hospital discharges and 48% of days of inpatient care.3 As the proportion of elderly patients in the population increases, the medical system will face new challenges. Will there be enough surgeons to meet the increased demand for surgical services? ::: ::: The last decade has been notable for a perception of balance with regard to the physician supply relative to demand. Against this calm background, we sought to isolate and predict the effect of the aging population on the use of surgical services and the need for surgeons. We hypothesized that the surgical workload will increase significantly over the next 2 decades due in large part to the aging of the US population. Toward evaluating this hypothesis, we employed an approach based upon historical patterns of care. Data from national surveys of medical and surgical services were used to establish a profile of age-specific rates of surgical use. This profile was then used to model the impact of forecasted population shifts on surgical work.
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paper_title: Project scheduling : a research handbook

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Scope and Relevance of Project Scheduling.- The Project Scheduling Process.- Classification of Project Scheduling Problems.- Temporal Analysis: The Basic Deterministic Case.- Temporal Analysis: Advanced Topics.- The Resource-Constrained Project Scheduling Problem.- Resource-Constrained Scheduling: Advanced Topics.- Project Scheduling with Multiple Activity Execution Modes.- Stochastic Project Scheduling.- Robust and Reactive Scheduling.
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paper_title: Capacity Management in Health Care Services: Review and Future Research Directions

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Health care has undergone a number of radical changes during the past five years. These include increased competition, fixed-rate reimbursement systems, declining hospital occupancy rates, and growth in health maintenance organizations and preferred provider organizations. Given these changes in the manner in which health care is provided, contracted, and paid for, it is appropriate to review the past research on capacity management and to determine its relevance to the changing industry. This paper provides a review, classification, and analysis of the literature on this topic. In addition, future research needs are discussed and specific problem areas not dealt with in the previous literature are targeted.
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paper_title: Managing uncertainty in orthopaedic trauma theatres

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Abstract The management of acute healthcare involves coping with a large uncertainty in demand. This uncertainty is a prevailing feature of orthopaedic care and many scarce resources are devoted to providing the contingent theatre time for orthopaedic trauma patients. However, given the variability and uncertainty in the demand much of the theatre time is not used. Simulation was used to explore the balance between maximising the utilisation of the theatre sessions, avoiding too many overruns and ensuring a reasonable quality of care in a typical hospital in the United Kingdom. The simulation was developed to examine a policy of including planned, elective patients within the trauma session: it appears that if patients are willing to accept a possibility of their treatment being cancelled, substantially greater throughputs can be achieved. A number of approximations were examined as an alternative to the full simulation: the simpler model offers reasonable accuracy and easier implementation.
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paper_title: Optimization of operating room allocation using linear programming techniques

paper_content:

Abstract Background New and innovative approaches must be used to rationally allocate scarce resources such as operating room time while simultaneously optimizing the associated financial return. In this article we use the technique of linear programming to optimize allocation of OR time among a group of surgeons based on professional fee generation. Study design For the period of December 1, 2000, to July 31, 2002, the following individualized data were obtained for the Division of General Surgery at Duke University Medical Center: allocated OR time (hours), case mix as determined by CPT codes, total OR time used, and normalized professional charges and receipts. Inpatient, outpatient, and emergency cases were included. The Solver linear programming routine in Microsoft Excel (Microsoft Corp.) was used to determine the optimal mix of surgical OR time allocation to maximize professional receipts. Results Our model of optimized OR allocation would maximize weekly professional revenues at $237,523, a potential increase of 15% over the historical value of $207,700 or an annualized increase of approximately $1.5 million. Conclusions Our results suggest that mathematical modeling techniques used in operations research, management science, or decision science may rationally optimize OR allocation to maximize revenue or to minimize costs. These techniques may optimize allocation of scarce resources in the context of the goals specific to individual academic departments of surgery.
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paper_title: A Norm Utilisation for Scarce Hospital Resources: Evidence from Operating Rooms in a Dutch University Hospital

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BACKGROUND ::: Utilisation of operating rooms is high on the agenda of hospital managers and researchers. Many efforts in the area of maximising the utilisation have been focussed on finding the holy grail of 100% utilisation. The utilisation that can be realised, however, depends on the patient mix and the willingness to accept the risk of working in overtime. ::: ::: ::: MATERIALS AND METHODS ::: This is a mathematical modelling study that investigates the association between the utilisation and the patient mix that is served and the risk of working in overtime. Prospectively, consecutively, and routinely collected data of an operating room department in a Dutch university hospital are used. Basic statistical principles are used to establish the relation between realistic utilisation rates, patient mixes, and accepted risk of overtime. ::: ::: ::: RESULTS ::: Accepting a low risk of overtime combined with a complex patient mix results a low utilisation rate. If the accepted risk of overtime is higher and the patient mix is less complex, the utilisation rate that can be reached is closer to 100%. ::: ::: ::: CONCLUSION ::: Because of the inherent variability of healthcare processes, the holy grail of 100% utilisation is unlikely to be found. The method proposed in this paper calculates a realistic benchmark utilisation that incorporates the patient mix characteristics and the willingness to accept risk of overtime.
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paper_title: Patient mix optimisation in hospital admission planning: a case study

paper_content:

Admissions planning decides on the number of patients admitted for a specialty each day, but also on the mix of patients admitted. Within a specialty different categories of patients can be distinguished on behalf of their requirement of resources. The type of resources required for an admission may involve beds, operating theatre capacity, nursing capacity and intensive care beds. The mix of patients is, therefore, an important decision variable for the hospital to manage the workload of the inflow of patients. In this paper we will consider the following planning problem: how can a hospital generate an admission profile for a specialty, given a target patient throughput and utilization of resources, while satisfying given restrictions? For this planning problem, we will develop an integer linear programming model, that has been tested in a pilot setting in a hospital. The paper includes an analysis of the planning problem, a description of the model developed, an application of a specialty orthopaedics, and a discussion of the results obtained.
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paper_title: Closing Emergency Operating Rooms Improves Efficiency

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Long waiting times for emergency operations increase a patient's risk of postoperative complications and morbidity. Reserving Operating Room (OR) capacity is a common technique to maximize the responsiveness of an OR in case of arrival of an emergency patient. This study determines the best way to reserve OR time for emergency surgery. In this study two approaches of reserving capacity were compared: (1) concentrating all reserved OR capacity in dedicated emergency ORs, and (2) evenly reserving capacity in all elective ORs. By using a discrete event simulation model the real situation was modelled. Main outcome measures were: (1) waiting time, (2) staff overtime, and (3) OR utilisation were evaluated for the two approaches. Results indicated that the policy of reserving capacity for emergency surgery in all elective ORs led to an improvement in waiting times for emergency surgery from 74 (±4.4) minutes to 8 (±0.5) min. Working in overtime was reduced by 20%, and overall OR utilisation can increase by around 3%. Emergency patients are operated upon more efficiently on elective Operating Rooms instead of a dedicated Emergency OR. The results of this study led to closing of the Emergency OR in the Erasmus MC (Rotterdam, The Netherlands).
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paper_title: Analyzing incentives and scheduling in a major metropolitan hospital operating room through simulation

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This paper discusses the application of simulation to analyze the value proposition and construction of an incentive program in an operating room (OR) environment. The model was further used to evaluate operational changes including scheduling processes within the OR and utilization rates in areas such as post anesthesia care unit (PACU) and the ambulatory surgery department (ASD). Lessons learned are presented on developing multiple simulation models from one application as well as issues regarding model transition to a client.
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paper_title: Sampling Error Can Significantly Affect Measured Hospital Financial Performance of Surgeons and Resulting Operating Room Time Allocations

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Hospitals with limited operating room (OR) hours, those with intensive care unit or ward beds that are always full, or those that have no incremental revenue for many patients need to choose which surgeons get the resources. Although such decisions are based on internal financial reports, whether the reports are statistically valid is not known. Random error may affect surgeons' measured financial performance and, thus, what cases the anesthesiologists get to do and which patients get to receive care. We tested whether one fiscal year of surgeon-specific financial data is sufficient for accurate financial accounting. We obtained accounting data for all outpatient or same-day-admit surgery cases during one fiscal year at an academic medical center. Linear programming was used to find the mix of surgeons' OR time allocations that would maximize the contribution margin or minimize variable costs. Confidence intervals were calculated on these end points by using Fieller's theorem and Monte-Carlo simulation. The 95% confidence intervals for increases in contribution margins or reductions in variable costs were 4.3% to 10.8% and 6.0% to 8.9%, respectively. As many as 22% of surgeons would have had OR time reduced because of sampling error. We recommend that physicians ask for and OR managers get confidence intervals of end points of financial analyses when making decisions based on them.
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paper_title: Creating an optimal operating room schedule.

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ABSTRACT • SCHEDULING IN THE OR suite is a particularly daunting task for many surgical services managers. • CREATING AN OPTIMAL OR schedule requires looking at constraining factors as well as historical data. • THIS ARTICLE presents one solution to creating an OR schedule that results in increased use of the OR suite and better profitability. AORN J 81 (January 2005) 580–588.
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paper_title: Calculating a Potential Increase in Hospital Margin for Elective Surgery by Changing Operating Room Time Allocations or Increasing Nursing Staffing to Permit Completion of More Cases: A Case Study

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UNLABELLED ::: Administrators routinely seek to increase contribution margin (revenue minus variable costs) to better cover fixed costs, provide indigent care, and meet other community service responsibilities. Hospitals with high operating room (OR) utilizations can allocate OR time for elective surgery to surgeons based partly on their contribution margins per hour of OR time. This applies particularly when OR caseload is limited by nursing recruitment. From a hospital's annual accounting data for elective cases, we calculated the following for each surgeon's patients: variable costs for the entire hospitalization or outpatient visit, revenues, hours of OR time, hours of regular ward time, and hours of intensive care unit (ICU) time. The contribution margin per hour of OR time varied more than 1000% among surgeons. Linear programming showed that reallocating OR time among surgeons could increase the overall hospital contribution margin for elective surgery by 7.1%. This was not achieved simply by taking OR time from surgeons with the smallest contribution margins per OR hour and giving it to the surgeons with the largest contribution margins per OR hour because different surgeons used differing amounts of hospital ward and ICU time. We conclude that to achieve substantive improvement in a hospital's perioperative financial performance despite restrictions on available OR, hospital ward, or ICU time, contribution margin per OR hour should be considered (perhaps along with OR utilization) when OR time is allocated. ::: ::: ::: IMPLICATIONS ::: For hospitals where elective surgery caseload is limited by nursing recruitment, to increase one surgeon's operating room time either another surgeon's time must be decreased, nurses need to be paid a premium for working longer hours, or higher-priced "traveling" nurses can be contracted. Linear programming was performed using Microsoft Excel to estimate the effect of each of these interventions on hospital contribution margin.
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paper_title: Consequences of running more operating theatres than anaesthetists to staff them: a stochastic simulation study

paper_content:

Background Numerous hospitals implement a ratio of one anaesthetist supervising non-medically-qualified anaesthetist practitioners in two or more operating theatres. However, the risk of requiring anaesthetists simultaneously in several theatres due to concurrent critical periods has not been evaluated. It was examined in this simulation study. Methods Using a Monte Carlo stochastic simulation model, we calculated the risk of a staffing failure (no anaesthetist available when one is needed), in different scenarios of scheduling, staffing ratio, and number of theatres. Results With a staffing ratio of 0.5 for a two-theatre suite, the simulated risk that at least one failure occurring during a working day varied from 87% if only short operations were performed to 40% if only long operations performed (65% for a 50:50 mixture of short and long operations). Staffing-failure risk was particularly high during the first hour of the workday, and decreased as the number of theatres increased. The decrease was greater for simulations with only long operations than those with only short operations (the risk for 10 theatres declined to 12% and 74%, respectively). With a staffing ratio of 0.33, the staffing-failure risk was markedly higher than for a 0.5 ratio. The availability of a floater for the whole suite to intervene during failure strongly lowered this risk. Conclusions Scheduling one anaesthetist for two or three theatres exposes patients and staff to high risk of failure. Adequate planning of long and short operations and the presence of a floating anaesthetist are efficient means to optimize site activity and assure safety.
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paper_title: Tactical Decision Making for Selective Expansion of Operating Room Resources Incorporating Financial Criteria and Uncertainty in Subspecialties' Future Workloads

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We considered the allocation of operating room (OR) time at facilities where the strategic decision had been made to increase the number of ORs. Allocation occurs in two stages: a long-term tactical stage followed by short-term operational stage. Tactical decisions, approximately 1 yr in advance, determine what specialized equipment and expertise will be needed. Tactical decisionsarebasedonestimatesoffutureORworkload for each subspecialty or surgeon. We show that groups of surgeons can be excluded from consideration at this tactical stage (e.g., surgeons who need intensive care bedsorthosewithbelowaveragecontributionmargins perORhour).Lowerandupperlimitsareestimatedfor the future demand of OR time by the remaining surgeons.Thus,initialORallocationscanbeaccomplished with only partial information on future OR workload. Once the new ORs open, operational decision-making based on OR efficiency is used to fill the OR time and adjust staffing. Surgeons who were not allocated additional time at the tactical stage are provided increased OR time through operational adjustments based on their actual workload. In a case study from a tertiary hospital, future demand estimates were needed for only 15% of surgeons,illustratingthepracticalityofthesemethodsfor use in tactical OR allocation decisions. (Anesth Analg 2005;100:1425–32)
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paper_title: Managing uncertainty in orthopaedic trauma theatres

paper_content:

Abstract The management of acute healthcare involves coping with a large uncertainty in demand. This uncertainty is a prevailing feature of orthopaedic care and many scarce resources are devoted to providing the contingent theatre time for orthopaedic trauma patients. However, given the variability and uncertainty in the demand much of the theatre time is not used. Simulation was used to explore the balance between maximising the utilisation of the theatre sessions, avoiding too many overruns and ensuring a reasonable quality of care in a typical hospital in the United Kingdom. The simulation was developed to examine a policy of including planned, elective patients within the trauma session: it appears that if patients are willing to accept a possibility of their treatment being cancelled, substantially greater throughputs can be achieved. A number of approximations were examined as an alternative to the full simulation: the simpler model offers reasonable accuracy and easier implementation.
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paper_title: Changing Allocations of Operating Room Time From a System Based on Historical Utilization to One Where the Aim is to Schedule as Many Surgical Cases as Possible

paper_content:

Many facilities allocate operating room (OR) time based on historical utilization of OR time. This assumes that there is a fixed amount of regularly scheduled OR time, called “block time”. This “Fixed Hours” system does not apply to many surgical suites in the US. Most facilities make OR time available for all its surgeons’ patients, even if cases are expected to finish after the end of block time. In this setting, OR time should be allocated to maximize OR efficiency, not historical utilization. Then, cases are scheduled either on “Any Workday” (i.e., date chosen by patient and surgeon) or within a reasonable time (e.g., “Four Weeks”). In this study, we used anesthesia billing data from two facilities to study statistical challenges in converting from a Fixed Hours to an Any Workday or Four Weeks patient scheduling system. We report relationships among the number of staffed ORs (i.e., first case of the day starts), length of the regularly scheduled OR workday, OR efficiency, OR staffing cost, and changes in services’ OR allocations. These relationships determine the expected changes in each service’s OR allocation, when a facility using Fixed Hours considers converting to the Any Workday or Four Weeks systems.
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paper_title: Surgical case scheduling as a generalized job shop scheduling problem

paper_content:

Surgical case scheduling allocates hospital resources to individual surgical cases and decides on the time to perform the surgeries. This task plays a decisive role in utilizing hospital resources efficiently while ensuring quality of care for patients. This paper proposes a new surgical case scheduling approach which uses a novel extension of the Job Shop scheduling problem called multi-mode blocking job shop (MMBJS). It formulates the MMBJS as a mixed integer linear programming (MILP) problem and discusses the use of the MMBJS model for scheduling elective and add-on cases. The model is illustrated by a detailed example, and preliminary computational experiments with the CPLEX solver on practical-sized instances are reported.
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paper_title: Booked inpatient admissions and hospital capacity: mathematical modelling study.

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Abstract Objectives: To investigate the variability of patients9 length of stay in intensive care after cardiac surgery. To investigate potential interactions between such variability, booked admissions, and capacity requirements. Design: Mathematical modelling study using routinely collected data. Setting: A cardiac surgery department. Source of data: Hospital records of 7014 people entering intensive care after cardiac surgery. Main outcome measures: Length of stay in intensive care; capacity requirements of an intensive care unit for a hypothetical booked admission system. Results: Although the vast majority of patients (89.5%) had a length of stay in intensive care of ≤48 hours, there was considerable overall variability and the distribution of stays has a lengthy tail. A mathematical model of the operation of a hypothetical booking system indicates that such variability has a considerable impact on intensive care capacity requirements, indicating that a high degree of reserve capacity is required to avoid high rates of operation cancellation because of unavailability of suitable postoperative care. Conclusion: Despite the considerable enthusiasm for booked admissions systems, queuing theory suggests that caution is required when considering such systems for inpatient admissions. Such systems may well result in frequent operational difficulties if there is a high degree of variability in length of stay and where reserve capacity is limited. Both of these are common in the NHS. What is already known in this topic Booking systems for hospital admissions have considerable potential benefits for patients in terms of peace of mind and planning their lives, but these benefits are dependent on having a low cancellation rate What this study adds Variability in length of stay can have a major impact on hospital operation and capacity requirements. Operational research techniques can be used to explore this impact If variability in length of stay is substantial, as is common, then booked admission systems may require considerable reserve capacity if cancellation rates are to be kept low
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paper_title: ENDOSCOPIES SCHEDULING PROBLEM: A CASE STUDY

paper_content:

The efficient management of an operating theatre involves the problems of planning and scheduling, and this is the same case for endoscopy center. The research aims at building a feasible and efficient operating program within one week for an endoscopy unit composed of two specialized operating rooms, with an objective of both maximizing the utilization of operating rooms and minimizing their overtime cost. At the planning stage, a tactical planning model for one week is built and is solved by a column-generation based heuristic (CGBH) procedure. The solution of the planning stage assigns each operating room to a set of surgical cases on each day. Afterwards, a daily scheduling problem is built at the scheduling stage in order to finally schedule the surgical cases assigned at the planning stage. This daily scheduling model is firstly simplified by a group technology into an "open shop" model and then solved by the Gonzalez-Sahni algorithm. As a result, a final operating program is ob
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paper_title: Operating Theatre Scheduling Using Lagrangian Relaxation

paper_content:

This paper addresses the surgery operation scheduling problem. Two types of resources are considered, operating rooms and recovery beds. Each patient first visits an operating room for surgery operation and is transferred to a recovery room immediately after the surgery operation. The operating room needs to be cleaned after the surgery operation before starting another operation. The problem consists in assigning patients to operating rooms and recovery beds in order to minimize the sum over all patients of one defined function of their completion times. According to this, the problem is NP harp problem. A Lagrangian relaxation approach is proposed in this paper to determine a near optimal schedule and a tight lower bound. Numerical results will be presented to show the efficiency of the method.
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paper_title: Scheduling of cases in an ambulatory center.

paper_content:

Perhaps the most important thing for an anesthesiologist and OR manager to understand is that there are different systems for OR allocation and case scheduling. We referred to them as Fixed Hours, Any Workday, and Reasonable Time. This understanding makes the OR management literature clear and applicable to all staff members. Most ambulatory centers handle cases on the workday chosen by the patient and surgeon but strive to do the work each day as efficiently as possible. Precisely how to make OR allocation and case scheduling decisions to achieve these objectives have been worked out. Studies show that case scheduling decisions to enhance OR efficiency are practiced in many facilities. In contrast, OR allocation decisions tend to be different than what OR managers do in practice. This means that it is important to apply the statistical methods for allocating OR time.
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paper_title: Optimization of operating room allocation using linear programming techniques

paper_content:

Abstract Background New and innovative approaches must be used to rationally allocate scarce resources such as operating room time while simultaneously optimizing the associated financial return. In this article we use the technique of linear programming to optimize allocation of OR time among a group of surgeons based on professional fee generation. Study design For the period of December 1, 2000, to July 31, 2002, the following individualized data were obtained for the Division of General Surgery at Duke University Medical Center: allocated OR time (hours), case mix as determined by CPT codes, total OR time used, and normalized professional charges and receipts. Inpatient, outpatient, and emergency cases were included. The Solver linear programming routine in Microsoft Excel (Microsoft Corp.) was used to determine the optimal mix of surgical OR time allocation to maximize professional receipts. Results Our model of optimized OR allocation would maximize weekly professional revenues at $237,523, a potential increase of 15% over the historical value of $207,700 or an annualized increase of approximately $1.5 million. Conclusions Our results suggest that mathematical modeling techniques used in operations research, management science, or decision science may rationally optimize OR allocation to maximize revenue or to minimize costs. These techniques may optimize allocation of scarce resources in the context of the goals specific to individual academic departments of surgery.
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paper_title: Surgical block scheduling in a system of hospitals: an application to resource and wait list management in a British Columbia health authority.

paper_content:

Scheduling surgical specialties in a medical facility is a very complex process. The choice of schedules and resource availability impact directly on the number of patients treated by specialty, cancellations, wait times, and the overall performance of the system. In this paper we present a system-wide model developed to allow management to explore tradeoffs between OR availability, bed capacity, surgeons' booking privileges, and wait lists. We developed a mixed integer programming model to schedule surgical blocks for each specialty into ORs and applied it to the hospitals in a British Columbia Health Authority, considering OR time availability and post-surgical resource constraints. The results offer promising insights into resource optimization and wait list management, showing that without increasing post-surgical resources hospitals could handle more cases by scheduling specialties differently.
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paper_title: Impact of surgical sequencing on post anesthesia care unit staffing

paper_content:

This paper analyzes the impact of sequencing rules on the phase I post anesthesia care unit (PACU) staffing and over-utilized operating room (OR) time resulting from delays in PACU admission. The sequencing rules are applied to each surgeon's list of cases independently. Discrete event simulation shows the importance of having a sufficient number of PACU nurses. Sequencing rules have a large impact on the maximum number of patients receiving care in the PACU (i.e., peak of activity). Seven sequencing rules are tested, over a wide range of scenarios. The largest effect of sequencing was on the percentage of days with at least one delay in PACU admission. The best rules are those that smooth the flow of patients entering in the PACU (HIHD (Half Increase in OR time and Half Decrease in OR time) and MIX (MIX OR time)). We advise against using the LCF (Longest Cases First) and equivalent sequencing methods. They generate more over-utilized OR time, require more PACU nurses during the workday, and result in more days with at least one delay in PACU admission.
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paper_title: Evaluation of operating room suite efficiency in the Veterans Health Administration system by using data-envelopment analysis

paper_content:

Abstract Background Operating room (OR) activity transcends single ratios such as cases/room, but weighting multiple inputs and outputs may be arbitrary. Data-envelopment analysis (DEA) is a novel technique by which each facility is analyzed by the weightings that optimize its score. Methods We performed DEA analysis of 23 Veterans Health Administration annual OR activity; 87,180 cases were performed, 24 publications generated, and 560 trainee-years of education delivered, in 168 ORs over 166,377 hours by 1,384 full-time equivalents of surgical and anesthesia providers and 523 nonproviders. Results Varying analyzed parameters produced similar efficiency rankings, with individual differences suggesting possible inefficiencies. We characterized returns to scale for efficient sites, suggesting whether patient flow might be efficiently further increased through these sites. We matched inefficient sites to similar efficient sites for comparison and suggested resource alterations to increase efficiency. Conclusions Broader DEA application might characterize OR efficiency more informatively than conventional single-ratio rank ordering.
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paper_title: The operating theatre planning by the follow-up of the risk of no realization

paper_content:

Abstract In the French context of healthcare expenses control, the operating theatre, that represents 9% of hospital's annual budget, presents a stake of major priority. The realization of the operating theatre planning is the fruit of negotiation of different actors of the block such as surgeons, anesthetists, nurses, managerial staff, etc. whose constraints and interests are often different. In this context, a win–win situation for this partnership (all parties involved) requires a good and constructive negotiation. In this paper, we propose an operating theatre planning procedure that aims at mastering the risk of no realization (RNR) of the tentative plan while stabilizing the operating rooms’ utilization time. During the application of this planning, we achieve the follow-up of the RNR and according to its evolution the research of another planning will be proposed in order to reduce the risk level. Finally, we present results obtained by simulations that support the interest for implementing these procedures.
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paper_title: Using Computer Simulation in Operating Room Management: Impacts on Process Engineering and Performance

paper_content:

Operating rooms are regarded as the most costly hospital facilities. Due to rising costs and decreasing reimbursements, it is necessary to optimize the efficiency of the operating room suite. In this context several strategies have been proposed that optimize patient throughput by redesigning perioperative processes. The successful deployment of effective practices for continuous process improvements in operating rooms can require that operating room management sets targets and monitors improvements throughout all phases of process engineering. Simulation can be used to study the effects of process improvements through novel facilities, technologies and/or strategies. In this paper, we propose a conceptual framework to use computer simulations in different stages of business process management (BPM) lifecycle for operating room management. Additionally, we conduct simulation studies in different stages of the BPM lifecycle. The results of our studies provide evidence that simulation can provide effective decision support to drive performance in operating rooms in several phases of the BPM lifecycle
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paper_title: Use of linear programming to estimate impact of changes in a hospital's operating room time allocation on perioperative variable costs.

paper_content:

BACKGROUND ::: Administrators at hospitals with a fixed annual budget may want to focus surgical services on priority areas to ensure its community receives the best health services possible. However, many hospitals lack the detailed managerial accounting data needed to ensure that such a change does not increase operating costs. The authors used a detailed hospital cost database to investigate by how much a change in allocations of operating room (OR) time among surgeons can increase perioperative variable costs. ::: ::: ::: METHODS ::: The authors obtained financial data for all patients who underwent outpatient or same-day admit surgery during a year. Linear programming was used to determine by how much changing the mix of surgeons can increase total variable costs while maintaining the same total hours of OR time for elective cases. ::: ::: ::: RESULTS ::: Changing OR allocations among surgeons without changing total OR hours allocated will likely increase perioperative variable costs by less than 34%. If, in addition, intensive care unit hours for elective surgical cases are not increased, hospital ward occupancy is capped, and implant use is tracked and capped, perioperative costs will likely increase by less than 10%. These four variables predict 97% of the variance in total variable costs. ::: ::: ::: CONCLUSIONS ::: The authors showed that changing OR allocations among surgeons without changing total OR hours allocated can increase hospital perioperative variable costs by up to approximately one third. Thus, at hospitals with fixed or nearly fixed annual budgets, allocating OR time based on an OR-based statistic such as utilization can adversely affect the hospital financially. The OR manager can reduce the potential increase in costs by considering not just OR time, but also the resulting use of hospital beds and implants.
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paper_title: Patient mix optimisation in hospital admission planning: a case study

paper_content:

Admissions planning decides on the number of patients admitted for a specialty each day, but also on the mix of patients admitted. Within a specialty different categories of patients can be distinguished on behalf of their requirement of resources. The type of resources required for an admission may involve beds, operating theatre capacity, nursing capacity and intensive care beds. The mix of patients is, therefore, an important decision variable for the hospital to manage the workload of the inflow of patients. In this paper we will consider the following planning problem: how can a hospital generate an admission profile for a specialty, given a target patient throughput and utilization of resources, while satisfying given restrictions? For this planning problem, we will develop an integer linear programming model, that has been tested in a pilot setting in a hospital. The paper includes an analysis of the planning problem, a description of the model developed, an application of a specialty orthopaedics, and a discussion of the results obtained.
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paper_title: An observational study of surgeons' sequencing of cases and its impact on postanesthesia care unit and holding area staffing requirements at hospitals.

paper_content:

BACKGROUND: Staffing requirements in the operating room (OR) holding area and in the Phase I postanesthesia care unit (PACU) are influenced by the sequencing of each surgeon's list of cases in the same OR on the same day. METHODS: Case sequencing was studied using 201 consecutive workdays of data from a 10 OR hospital surgical suite. RESULTS: The surgeons differed significantly among themselves in their sequencing of cases and were also internally nonsystematic, based on case durations. The functional effect of this uncoordinated sequencing was for the surgical suite to behave overall as if there was random sequencing. The resulting PACU staffing requirements were the same as those of the best sequencing method identified in prior simulation studies. Although sequencing "Longest Cases First" performs poorly when all ORs have close to 8 h of cases, at the studied hospital it performed no worse than the other methods. The reason was that some ORs were much busier than others on the same day. The standard deviation among ORs in the hours of cases, including turnovers, was 3.2 h; large relative to the mean workload. Data from 33 other hospitals confirmed that this situation is commonplace. Additional studies showed that case sequencing also had minimal effects on the peak number of patients in the holding area. CONCLUSIONS: The uncoordinated decision-making of multiple surgeons working in different ORs can result in a sufficiently uniform rate of admission of patients into the PACU and holding that the independent sequencing of each surgeon's list of cases would not reduce the incidence of delays in admission or staffing requirements.
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paper_title: Scheduling hospital services: the efficacy of elective-surgery quotas

paper_content:

We take advantage of the advance-scheduling property for elective surgeries by exploring whether the use of a daily quota system with a 1-week or 2-week scheduling window would improve the performance of a typical intensive care unit (ICU) that serves patients coming from a number of different sources within the hospital. The exploration is carried out via a simulation model whose parameters are established from actual ICU data that were gathered over a 6-month period. It is shown that formally linking one controllable upstream process, namely the scheduling of elective surgeries through a quota system, to the downstream ICU admission process, can have beneficial effects throughout the hospital.
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paper_title: A Hierarchical Multiple Criteria Mathematical Programming Approach for Scheduling General Surgery Operations in Large Hospitals

paper_content:

Limited staff and equipment within surgical services require efficient use of these resources among multiple surgeon groups. In this study, a set of hierarchical multiple criteria mathematical programming models are developed to generate weekly operating room schedules. The goals considered in these models are maximum utilization of operating room capacity, balanced distribution of operations among surgeon groups in terms of operation days, lengths of operation times, and minimization of patient waiting times. Because of computational difficulty of this scheduling problem, the overall problem is broken down into manageable hierarchical stages: (1) selection of patients, (2) assignment of operations to surgeon groups, and (3) determination of operation dates and operating rooms. Developed models are tested on the data collected in College of Medicine Research Hospital at Cukurova University as well as on simulated data sets, using MPL optimization package.
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paper_title: Ambulatory Care and Orthopaedic Capacity Planning

paper_content:

Ambulatory Care facilities (often referred to as diagnosis and treatment centres) separate the routine elective activity from the uncertainty of complex inpatient and emergency treatment. Only routine patients with predictable outcomes should be treated in Ambulatory Care. Hence the centre should be able to plan its activities effectively. This paper considers the consequences for the remaining elective inpatient bed and theatre requirements. Computer models are used to simulate many years of activity in an orthopaedic department at a typical District General hospital.
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paper_title: A three-phase approach for operating theatre schedules

paper_content:

In this paper we develop a three-phase, hierarchical approach for the weekly scheduling of operating rooms. This approach has been implemented in one of the surgical departments of a public hospital located in Genova (Genoa), Italy. Our aim is to suggest an integrated way of facing surgical activity planning in order to improve overall operating theatre efficiency in terms of overtime and throughput as well as waiting list reduction, while improving department organization. In the first phase we solve a bin packing-like problem in order to select the number of sessions to be weekly scheduled for each ward; the proposed and original selection criterion is based upon an updated priority score taking into proper account both the waiting list of each ward and the reduction of residual ward demand. Then we use a blocked booking method for determining optimal time tables, denoted Master Surgical Schedule (MSS), by defining the assignment between wards and surgery rooms. Lastly, once the MSS has been determined we use the simulation software environment Witness 2004 in order to analyze different sequencings of surgical activities that arise when priority is given on the basis of a) the longest waiting time (LWT), b) the longest processing time (LPT) and c) the shortest processing time (SPT). The resulting simulation models also allow us to outline possible organizational improvements in surgical activity. The results of an extensive computational experimentation pertaining to the studied surgical department are here given and analyzed.
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paper_title: Comparison of two methods of operating theatre planning: Application in Belgian Hospital

paper_content:

Operating Theatre is the centre of the hospital management’s efforts. It constitutes the most expensive sector with more than 10% of the intended operating budget of the hospital. To reduce the costs while maintaining a good quality of care, one of the solutions is to improve the existent planning and scheduling methods by improving the services and surgical specialty coordination or finding the best estimation of surgical case durations. The other solution is to construct an effective surgical case plan and schedule. The operating theatre planning and scheduling is the two important steps, which aim to make a surgical case programming with an objective of obtaining a realizable and efficient surgical case schedule. This paper focuses on the first step, the operating theatre planning problem. Two planning methods are introduced and compared. Real data of a Belgian university hospital “Tivoli” are used for the experiments.
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paper_title: A Set Packing Approach for Scheduling Elective Surgical Procedures

paper_content:

The efficient scheduling of surgical procedures to operating rooms in a hospital is a complex problem due to limited resources (e.g. medical staff, equipment) and conflicting objectives (e.g. reduce running costs and increase staff and patient satisfaction). A novel approach for scheduling elective surgeries over a short-term horizon is proposed which takes explicit consideration of these aspects. The problem is formulated as a set packing problem and solved optimally through column generation and constraint branching. Good results were obtained for instances from the literature.
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paper_title: Tactical Operating Theatre Scheduling: Efficient Appointment Assignment

paper_content:

Finding an appointment for elective surgeries in hospitals is a task that has a direct impact on the optimization potential for offline and online daily surgery scheduling. A novel approach based on bin packing which takes into account limited resource availability (e.g. staff, equipment), its utilization, clinical priority, hospital bed distribution and surgery difficulty is proposed for this planning level. A solution procedure is presented that explores the specific structure of the model to find appointments for elective surgeries in real time. Tests performed with randomly generated data motivated by a mid size hospital suggest that the new approach yields high quality solutions.
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paper_title: Managing risk and expected financial return from selective expansion of operating room capacity: mean-variance analysis of a hospital's portfolio of surgeons.

paper_content:

Surgeons using the same amount of operating room (OR) time differ in their achieved hospital contribution margins (revenue minus variable costs) by >1000%. Thus, to improve the financial return from perioperative facilities, OR strategic decisions should selectively focus additional OR capacity and capital purchasing on a few surgeons or subspecialties. These decisions use estimates of each surgeon's and/or subspecialty's contribution margin per OR hour. The estimates are subject to uncertainty (e.g., from outliers). We account for the uncertainties by using mean-variance portfolio analysis (i.e., quadratic programming). This method characterizes the problem of selectively expanding OR capacity based on the expected financial return and risk of different portfolios of surgeons. The assessment reveals whether the choices, of which surgeons have their OR capacity expanded, are sensitive to the uncertainties in the surgeons' contribution margins per OR hour. Thus, mean-variance analysis reduces the chance of making strategic decisions based on spurious information. We also assess the financial benefit of using mean-variance portfolio analysis when the planned expansion of OR capacity is well diversified over at least several surgeons or subspecialties. Our results show that, in such circumstances, there may be little benefit from further changing the portfolio to reduce its financial risk.
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paper_title: Tactical increases in operating room block time based on financial data and market growth estimates from data envelopment analysis.

paper_content:

BACKGROUND ::: Data envelopment analysis (DEA) is an established technique that hospitals and anesthesia groups can use to understand their potential to grow different specialties of inpatient surgery. Often related decisions such as recruitment of new physicians are made promptly. A practical challenge in using DEA in practice for this application has been the time to obtain access to and preprocess discharge data from states. ::: ::: ::: METHODS ::: A case study is presented to show how results of DEA are linked to financial analysis for purposes of deciding which surgical specialties should be provided more resources and institutional support, including the allocation of additional operating room (OR) block time on a tactical (1 yr) time course. State discharge abstract databases were used to study how to perform and present the DEA using data from websites of the United States' (US) Healthcare Cost and Utilization Project (HCUPNet) and Census Bureau (American FactFinder). ::: ::: ::: RESULTS ::: DEA was performed without state discharge data by using census data with federal surgical rates adjusted for age and gender. Validity was assessed based on multiple criteria, including: satisfaction of statistical assumptions, face validity of results for hospitals, differentiation between efficient and inefficient hospitals on other measures of how much surgery is done, and correlation of estimates of each hospital's potential to grow the workload of each of eight specialties with estimates obtained using unrelated statistical methods. ::: ::: ::: CONCLUSIONS ::: A hospital can choose specialties to target for expanded OR capacity based on its financial data, its caseloads for specific specialties, the caseloads from hospitals previously examined, and surgical rates from federal census data.
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paper_title: Determining Optimum Operating Room Utilization

paper_content:

UNLABELLED ::: Economic considerations suggest that it is desirable to keep operating rooms fully used when staffed, but the optimum utilization of an operating room (OR) is not known. We created a simulation of an OR to define optimum utilization. We set operational goals of having cases start within 15 min of the scheduled time and of having the cases end no more than 15 min past the scheduled end of the day. Within these goals, a utilization of 85% to 90% is the highest that can be achieved without delay or running late. Increasing the variability of case duration decreases the utilization that can be achieved within these targets. ::: ::: ::: IMPLICATIONS ::: Using a simulated operating room (OR), the authors demonstrate that OR utilization higher than 85% to 90% leads to patient delays and staff overtime. Increased efficiency of an OR comes at a cost of patient convenience.
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paper_title: SPECIAL ARTICLE Enterprise-Wide Patient Scheduling Information Systems to Coordinate Surgical Clinic and Operating Room Scheduling Can Impair Operating Room Efficiency

paper_content:

SUBSTITUTED-4-FLUORO-1,4-DIAZONIABICYCLO[2.2.2]OCTANE SALTS AND THEIR APPLICATION AS FLUORINATING AGENTS The present invention relates to the preparation and uses of 1-substituted-4-fluoro-1,4-diazoniabicyclo[2.2.2]octane salts, specifically 1-hydroxyl-4-fluoro-1,4-diazoniabicyclo[2.2.2]octane salts as reagents for the introduction of fluorine in organic compounds.
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paper_title: Operating room utilization: information management systems.

paper_content:

Purpose of reviewAdvances during the past year in operational decision making using information management systems data have been predominantly in better understanding of how to allocate operating room time based on operating room efficiency, not just operating room utilization.Recent findingsEach q
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paper_title: Operating room managers' use of integer programming for assigning block time to surgical groups: a case study.

paper_content:

UNLABELLED ::: A common problem at hospitals with fixed amounts of available operating room (OR) time (i.e., "block time") is determining an equitable method of distributing time to surgical groups. Typically, facilities determine a surgical group's share of available block time using formulas based on OR utilization, contribution margin, or some other performance metric. Once each group's share of time has been calculated, a method must be found for fitting each group's allocated OR time into the surgical master schedule. This involves assigning specific ORs on specific days of the week to specific surgical groups, usually with the objective of ensuring that the time assigned to each group is close to its target share. Unfortunately, the target allocated to a group is rarely expressible as a multiple of whole blocks. In this paper, we describe a hospital's experience using the mathematical technique of integer programming to solve the problem of developing a consistent schedule that minimizes the shortfall between each group's target and actual assignment of OR time. Schedule accuracy, the sum over all surgical groups of shortfalls divided by the total time available on the schedule, was 99.7% (SD 0.1%, n = 11). Simulations show the algorithm's accuracy can exceed 97% with > or =4 ORs. The method is a systematic and successful way to assign OR blocks to surgeons. ::: ::: ::: IMPLICATIONS ::: At hospitals with a fixed budget of operating room (OR) time, integer programming can be used by OR managers to decide which surgical group is to be allocated which OR on which day(s) of the week. In this case study, we describe the successful application of integer programming to this task, and discuss the applicability of the results to other hospitals.
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paper_title: How to release allocated operating room time to increase efficiency: predicting which surgical service will have the most underutilized operating room time.

paper_content:

At many facilities, surgeons and patients choose the day of surgery, cases are not turned away, and staffing is adjusted to maximize operating room (OR) efficiency. If a surgical service has already filled its allocated OR time, but has an additional case to schedule, then OR efficiency is increased by scheduling the new case into the OR time of a different service with much underutilized OR time. The latter service is said to be "releasing" its allocated OR time. In this study, we analyzed 3 years of scheduling data from a medium-sized and a large surgical suite. Theoretically, the service that should have its OR time released is the service expected to have the most underutilized OR time on the day of surgery (i.e., any future cases that may be scheduled into that service's time also need to be factored in). However, we show that OR efficiency is only slightly less when the service whose time is released is the service that has the most allocated but unscheduled (i.e., unfilled) OR time at the moment the new case is scheduled. In contrast, compromising by releasing the OR time of a service other than the one with the most allocated but unscheduled OR time markedly reduces OR efficiency. OR managers can use these results when releasing allocated OR time.
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paper_title: A stochastic model for operating room planning with elective and emergency demand for surgery

paper_content:

This paper describes a stochastic model for Operating Room (OR) planning with two types of demand for surgery: elective surgery and emergency surgery. Elective cases can be planned ahead and have a patient-related cost depending on the surgery date. Emergency cases arrive randomly and have to be performed on the day of arrival. The planning problem consists in assigning elective cases to different periods over a planning horizon in order to minimize the sum of elective patient related costs and overtime costs of operating rooms. A new stochastic mathematical programming model is first proposed. We then propose a Monte Carlo optimization method combining Monte Carlo simulation and Mixed Integer Programming. The solution of this method is proved to converge to a real optimum as the computation budget increases. Numerical results show that important gains can be realized by using a stochastic OR planning model.
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paper_title: Operating room efficiency and scheduling

paper_content:

Purpose of reviewThe review focuses on six papers published in 2004 that pertain to operating room (OR) efficiency.Recent findingsWhen to release OR time was much less important than was having the correct OR allocations in the first place. If OR time must be released, then this decision should be b
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paper_title: When to Release Allocated Operating Room Time to Increase Operating Room Efficiency

paper_content:

UNLABELLED ::: We studied when allocated, but unfilled, operating room (OR) time of surgical services should be released to maximize OR efficiency. OR time was allocated for two surgical suites based on OR efficiency. Then, we analyzed real OR schedules. We added new hypothetical cases lasting 1, 2, or 3 h into OR time of the service that had the largest difference between allocated and scheduled cases (i.e., the most unfilled OR time) 5 days before the day of surgery. The process was repeated using the updated OR schedule available the day before surgery. The pair-wise difference in resulting overutilized OR time was calculated for n = 754 days of data from each of the two surgical suites. We found that postponing the decision of which service gets the new case until early the day before surgery reduces overutilized OR time by <15 min per OR per day as compared to releasing the allocated OR time 5 days before surgery. These results show that when OR time is released has a negligible effect on OR efficiency. This is especially true for ambulatory surgery centers with brief cases or large surgical suites with specialty-specific OR teams. What matters much more is having the correct OR allocations and, if OR time needs to be released, making that decision based on the scheduled workload. ::: ::: ::: IMPLICATIONS ::: Provided operating room (OR) time is allocated and cases are scheduled based on maximizing OR efficiency, then whether OR time is released five days or one day before the day of surgery has a negligible effect on OR efficiency.
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paper_title: Hospital Operating Room Capacity Expansion

paper_content:

A large midwestern hospital is expecting an increase in surgical caseload. New operating room (OR) capacity can be had by building new ORs or extending the working hours in the current ORs. The choice among these options is complicated by the fact that patients, surgeons and surgical staff, and hospital administrators are all important stakeholders in the health service operation, and each has different priorities. This paper investigates the trade-offs among three performance criteria (wait to get on schedule, scheduled procedure start-time reliability, and hospital profits), which are of particular importance to the different constituencies. The objective is to determine how the hospital can best expand its capacity, acknowledging the key role that each constituency plays in that objective. En route, the paper presents supporting analysis for process improvements and suggestions for optimal participation-inducing staff contracts for extending OR hours of operation.
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paper_title: Operating Theatre Optimization : A Resource-Constrained Based Solving Approach

paper_content:

The operating theatre is considered as the bottleneck of the hospital and as one of the most resources consuming unit. Therefore its management is of primary interest : an efficient planning allows to use as better as possible the availability of the operating theatre and reduce human and financial working costs. This paper deals with operating theatre planning optimization. We present a mathematical model combining surgeries planning and scheduling over short time horizon, and by taking into account renewable and nonrenewable resources availabilities. This model gets its inspiration from project management and especially resource-constrained project scheduling problem (RCPSP). We also introduce a genetic algorithm approach to heuristically solve the problem. We base our approach on the multi-mode variation of the RCPSP to define the related crossover, mutation and selection operators allowing the global search to work effectively.
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paper_title: Mount Sinai Hospital Uses Integer Programming to Allocate Operating Room Time

paper_content:

In concentrating polymer solutions up to a desired specification level of residual solvents, encrustations can be prevented and the yield and the degree of purity can be increased, when the product is heated up under pressure, expanded through a restrictor element (3) with vapor formation into a first, preferably coiled flow pipe (7) and concentrated therein as far as possible, the mixture of vapors and polymer solution is whirled at an angle into a second flow pipe (9) in a sloping arrangement and fitted with self-cleaning elements (11, 12) and concentrated therein up to the desired level, and vapors and concentrate are separately discharged only downstream thereof.
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paper_title: A Sequential Bounding Approach for Optimal Appointment Scheduling

paper_content:

This study is concerned with the determination of optimal appointment times for a sequence of jobs with uncertain durations. Such appointment systems are used in many customer service applications to increase the utilization of resources, match workload to available capacity, and smooth the flow of customers. We show that the problem can be expressed as a two-stage stochastic linear program that includes the expected cost of customer waiting, server idling, and a cost of tardiness with respect to a chosen session length. We exploit the problem structure to derive upper bounds that are independent of job duration distribution type. These upper bounds are used in a variation of the standard L-shaped algorithm to obtain optimal solutions via successively finer partitions of the support of job durations. We present new analytical insights into the problem as well as a series of numerical experiments that illustrate properties of the optimal solution with respect to distribution type, cost structure, and number of jobs.
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paper_title: Optimization of surgery sequencing and scheduling decisions under uncertainty

paper_content:

Operating rooms (ORs) are simultaneously the largest cost center and greatest source of revenues for most hospitals. Due to significant uncertainty in surgery durations, scheduling of ORs can be very challenging. Longer than average surgery durations result in late starts not only for the next surgery in the schedule, but potentially for the rest of the surgeries in the day as well. Late starts also result in direct costs associated with overtime staffing when the last surgery of the day finishes later than the scheduled shift end time. In this article we describe a stochastic optimization model and some practical heuristics for computing OR schedules that hedge against the uncertainty in surgery durations. We focus on the simultaneous effects of sequencing surgeries and scheduling start times. We show that a simple sequencing rule based on surgery duration variance can be used to generate substantial reductions in total surgeon and OR team waiting, OR idling, and overtime costs. We illustrate this with results of a case study that uses real data to compare actual schedules at a particular hospital to those recommended by our model.
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paper_title: The use of Simulation to Determine Maximum Capacity in the Surgical Suite Operating Room

paper_content:

Utilizing ambulatory care units at optimal levels has become increasingly important to hospitals from both service and business perspectives. With the inherent variation in hospitals due to unique procedures and patients, performing capacity analysis through analytical models is difficult without making simplifying assumptions. Many hospitals calculate efficiency by comparing total operating room minutes available to total operating minutes used. This metric both fails to account for the required non-value added tasks between surgeries and the delicate balance necessary between having patients ready for surgery when an operating room becomes available, which can result in increased waiting times, and maximizing patient satisfaction. We present a general methodology for determining the maximum capacity within a surgical suite through the use of a discrete-event simulation model. This research is based on an actual hospital concerned with doctor/resource acquisition decisions, patient satisfaction improvements, and increased productivity.
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paper_title: Allocation of Surgeries to Operating Rooms by Goal Programing

paper_content:

High usage rate in a surgical suite is extremely important in meeting the increasing demand for health care services and reducing costs to improve quality of care. In this paper a goal programming model which can produce schedules that best serve the needs of the hospital, i.e., by minimizing idle time and overtime, and increasing satisfaction of surgeons, patients, and staff, is described. The approach involves sorting the requests for a particular day on the basis of block restrictions, room utilization, surgeon preferences and intensive care capabilities. The model is tested using the data obtained during field studies at Dokuz Eylul University Hospital. The model is also tested for alternative achievement functions to examine the model's ability to satisfy abstract goals.
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paper_title: The Impact on Revenue of Increasing Patient Volume at Surgical Suites with Relatively High Operating Room Utilization

paper_content:

MBA†Division of Management Consulting, Department of Anesthesia, University of Iowa, Iowa City, Iowa; *Department ofAnesthesia and Health Policy and Research, Stanford University, Stanford, California; †Department of Anesthesiology andFuqua School of Business, Duke University, Durham, North CarolinaWe previously studied hospitals in the United States ofAmerica that are losing money despite limiting the hoursthat operating room (OR) staff are available to care forpatients undergoing elective surgery. These hospitalsroutinelykeeputilizationrelativelyhightomaximizerev-enue. We tested, using discrete-event computer simula-tion, whether increasing patient volume while being re-imbursed less for each additional patient can reliablyachieve an increase in revenue when initial adjusted ORutilizationis90%.Wefoundthatincreasingthevolumeofreferred patients by the amount expected to fill the surgi-cal suite (100%/90%) would increase utilization by ,1%for a hospital surgical suite (with longer duration cases)and4%foranambulatorysurgerysuite(withshortcases).The increase in patient volume would result in longer pa-tient waiting times for surgery and more patients leavingthe surgical queue. With a 15% reduction in payment forthenewpatients,theincreaseinvolumemaynotincreaserevenue and can even decrease the contribution marginfor the hospital surgical suite. The implication is that forhospitalswitharelativelyhighORutilization,signingdis-counted contracts to increase patient volume by theamountexpectedto“fill”theORcanhavetheneteffectofdecreasing the contribution margin (i.e., profitability).(Anesth Analg 2001;92:1215–21)
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paper_title: Building cyclic master surgery schedules with leveled resulting bed occupancy

paper_content:

This paper proposes and evaluates a number of models for building surgery schedules with leveled resulting bed occupancy. The developed models involve two types of constraints. Demand constraints ensure that each surgeon (or surgical group) obtains a specific number of operating room blocks. Capacity constraints limit the available blocks on each day. Furthermore, the number of operated patients per block and the length of stay of each operated patient are dependent on the type of surgery. Both are considered stochastic, following a multinomial distribution. We develop a number of mixed integer programming based heuristics and a metaheuristic to minimize the expected total bed shortage and present computational results.
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paper_title: Scheduling Surgical Cases into Overflow Block Time— Computer Simulation of the Effects of Scheduling Strategies on Operating Room Labor Costs

paper_content:

“Overflow” block time is operating room (OR) time for a surgical group’s cases that cannot be completed in the regular block time allocated to each surgeon in the surgical group. Having such overflow block time increases OR utilization. The optimal way to schedule patients into a surgical group’s ov
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paper_title: Determining the Number of Beds in the Postanesthesia Care Unit: A Computer Simulation Flow Approach

paper_content:

UNLABELLED ::: Designing a new operating room (OR) suite is a difficult process owing to the number of caregivers involved and because decision-making managers try to minimize the direct and indirect costs of operating the OR suite. In this study, we devised a computer simulation flow model to calculate, first, the minimum number of beds required in the postanesthesia care unit (PACU). In a second step, we evaluated the relationship between the global performance of the OR suite in terms of OR scheduling and number of staffed PACU beds and porters. We designed a mathematical model of OR scheduling. We then developed a computer simulation flow model of the OR suite. Both models were connected; the first one performed the input flows, and the second simulated the OR suite running. The simulations performed examined the number of beds in the PACU in an ideal situation or in the case of reduction in the number of porters. We then analyzed the variation of number of beds occupied per hour in the PACU when the time spent by patients in the PACU or the number of porters varied. The results highlighted the strong impact of the number of porters on the OR suite performance and particularly on PACU performances. ::: ::: ::: IMPLICATIONS ::: Designing new operating room (OR) facilities implies many decisions on the number of ORs, postanesthesia care unit (PACU) beds, and on the staff of nurses and porters. To make these decisions, managers can use rules of thumb or recommendations. Our study highlights the interest of using flow simulation to validate these choices. In this case study we determine the number of PACU beds and porter staff and assess the impact of decreasing the number of porters on PACU bed requirements.
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paper_title: A branch-and-price approach for integrating nurse and surgery scheduling

paper_content:

A common problem at hospitals is the extreme variation in daily (even hourly) workload pressure for nurses. The operating room is considered to be the main engine and hence the main generator of variance in the hospital. The purpose of this paper is threefold. First of all, we present a concrete model that integrates both the nurse and the operating room scheduling process. Second, we show how the column generation technique approach, one of the most employed exact methods for solving nurse scheduling problems, can easily cope with this model extension. Third, by means of a large number of computational experiments we provide an idea of the cost saving opportunities and required solution times.
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paper_title: Visualizing the Demand for Various Resources as a Function of the Master Surgery Schedule: A Case Study

paper_content:

This paper presents a software system that visualizes the impact of the master surgery schedule on the demand for various resources throughout the rest of the hospital. The master surgery schedule can be seen as the engine that drives the hospital. Therefore, it is very important for decision makers to have a clear image on how the demand for resources is linked to the surgery schedule. The software presented in this paper enables schedulers to instantaneously view the impact of, e.g., an exchange of two block assignments in the master surgery schedule on the expected resource consumption pattern. A case study entailing a large Belgian surgery unit illustrates how the software can be used to assist in building better surgery schedules.
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paper_title: How to Schedule Elective Surgical Cases into Specific Operating Rooms to Maximize the Efficiency of Use of Operating Room Time

paper_content:

We considered elective case scheduling at hospitals and surgical centers at which surgeons and patients choose the day of surgery, cases are not turned away, and anesthesia and nursing staffing are adjusted to maximize the efficiency of use of operating room (OR) time. We investigated scheduling a new case into an OR by using two patient-scheduling rules: Earliest Start Time or Latest Start Time. By using several scenarios, we showed that the use of Earliest Start Time is rational economically at such facilities. Specifically, it maximizes OR efficiency when a service has nearly filled its regularly scheduled hours of OR time. However, Latest Start Time will perform better at balancing workload among services’ OR time. We then used historical case duration data from two facilities in computer simulations to investigate the effect of errors in predicting case durations on the performance of these two heuristics. The achievable incremental reduction in overtime by having perfect information on case duration versus using historical case durations was only a few minutes per OR. The differences between Earliest Start Time and Latest Start Time were also only a few minutes per OR. We conclude that for facilities at which the goals are, in order of importance, safety, patient and surgeon access to OR time, and then efficiency, few restrictions need to be placed on patient scheduling to achieve an efficient use of OR time. (Anesth Analg 2002;94:933–42)
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paper_title: Schedule the Short Procedure First to Improve OR Efficiency

paper_content:

ABSTRACT • OPERATING ROOM MANAGERS are hampered in their efforts to optimize OR efficiency by surgical procedures that last a longer or shorter time than scheduled. The lack of predictability is a result of inaccuracy in scheduling and variability in the duration of procedures. • SCHEDULING SHORT PROCEDURES before long procedures theoretically limits this variability. • MONTE CARLO SIMULATION of ORs scheduled with various combinations of short and long procedures supports this concept's validity. • RESULTS INDICATE that scheduling short procedures first can improve on-time performance and decrease staff member overtime expense without reducing surgical throughput. AORNJ 78 (October 2003) 651–657.
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paper_title: Optimisation Modelling of hospital operating room planning : analyzing strategies and problem settings

paper_content:

There is a growing proportion of elderly which increases the demand for health care. As a consequence health care costs are rising and the need for hospital resource planning seems urgent. Different aspects (often conflicting) such as patient demand, clinical need and political ambitions must be considered. In this paper we propose a model for analyzing a hospital surgical suite with focus on operating room planning. An optimization model is developed for patient operation scheduling and for key resource allocation. Medical examinations and treatments of patients are performed using a number of resources, similar to products being refined in a number of processes in a logistics chain. Optimal resource allocation, given different objectives according to patient perspective, staff perspective, costs etc. under different system settings (e.g. principles for operating room allocation and amount of stand-by personnel), is studied. Preliminary results are presented based on case studies from two Swedish hospitals.
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paper_title: The value of the dedicated orthopaedic trauma operating room.

paper_content:

Background:Trauma centers and orthopaedic surgeons have traditionally been faced with limited operating room (OR) availability for fracture surgery. Orthopaedic trauma cases are often waitlisted and done late at night. We investigated the feasibility of having an unbooked orthopaedic trauma OR to re
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paper_title: Scheduling patients in an ambulatory surgical center

paper_content:

This paper presents a deterministic approach to schedule patients in an ambulatory surgical center (ASC) such that the number of postanesthesia care unit nurses at the center is minimized. We formulate the patient scheduling problem as new variants of the no-wait, two-stage process shop scheduling problem and present computational complexity results for the new scheduling models. Also, we develop a tabu search-based heuristic algorithm to solve the patient scheduling problem. Our algorithm is shown to be very effective in finding near optimal schedules on a set of real data from a university hospital's ASC. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2003
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paper_title: Analysis via goal programming of the minimum achievable stay in surgical waiting lists

paper_content:

In this paper, a Goal Programming model is developed in order to study the possibility of decreasing the length of stay on the waiting list of a hospital that belongs to the Spanish Health Service. First, a problem is solved to determine the optimal planning for one year, so as to make the maximum waiting time decrease to six months (at present, some operations have a waiting list of more than a year). Afterwards, two other problems are solved in order to determine the impact that a further reduction of the waiting time (four months) would have on the requirements of extra resources for the hospital. The particular problem for the Trauma service is described in detail, but global results are shown and commented.
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paper_title: A goal programming approach to strategic resource allocation in acute care hospitals

paper_content:

Abstract This paper describes a methodology for allocating resources in hospitals. The methodology uses two linear goal-programming models. One model sets case mix and volume for physicians, while holding service costs fixed; the other translates case mix decisions into a commensurate set of practice changes for physicians. The models allow decision makers to set case mix and case costs in such a way that the institution is able to break even, while preserving physician income and minimizing disturbance to practice. The models also permit investigation of trade-offs between case mix and physician practice parameters. Results are presented from a decision-making scenario facing the surgical division of Toronto's Mount Sinai Hospital after the announcement of a 3-year, 18% reduction in funding.
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paper_title: Patient mix optimization in tactical cardiothoracic surgery planning: a case study

paper_content:

Cardiothoracic surgery planning involves different resources such as operating theatre (OT) time, medium care beds, intensive care beds and nursing staff. Within cardiothoracic surgery different categories of patients can be distinguished with respect to their requirements of resources. The mix of patients is, therefore, an important aspect of decision making for the hospital to manage the use of these resources. A master OT schedule is used at the tactical level of planning for deriving the weekly OT plan. It defines for each day of a week the number of OT hours available and the number of patients operated from each patient category. We develop a model for this tactical level planning problem, the core of which is a mixed integer linear program. The model is used to evaluate scenarios for surgery planning at tactical as well as strategic levels, demonstrating the potential of integer programming for providing recommendations for change.
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paper_title: Operating Room Managerial Decision-Making on the Day of Surgery With and Without Computer Recommendations and Status Displays

paper_content:

BACKGROUND: There are three basic types of decision aids to facilitate operating room (OR) management decision-making on the day of surgery. Decision makers can rely on passive status displays (e.g., big screens or whiteboards), active status displays (e.g., text pager notification), and/or command displays (e.g., text recommendations about what to do). METHODS: Anesthesiologists, OR nurses, and housekeepers were given nine simulated scenarios (vignettes) involving multiple ORs to study their decision-making. Participants were randomized to one of four groups, all with an updated paper OR schedule: with/without command display and with/without passive status display. RESULTS: Participants making decisions without command displays performed no better than random chance in terms of increasing the predictability of work hours, reducing over-utilized OR time, and increasing OR efficiency. Status displays had no effect on these end-points, whereas command displays improved the quality of decisions. In the scenarios for which the command displays provided recommendations that adversely affected safety, participants appropriately ignored advice. CONCLUSIONS: Anesthesia providers and nursing staff made decisions that increased clinical work per unit time in each OR, even when doing so resulted in an increase in over-utilized OR time, higher staffing costs, unpredictable work hours, and/or mandatory overtime. Organizational culture and socialization during clinical training may be a cause. Command displays showed promise in mitigating this tendency. Additional investigations are in our companion paper.
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paper_title: Strategies to reduce delays in admission into a postanesthesia care unit from operating rooms

paper_content:

The authors performed a systematic review of strategies to reduce delays in admission into PACUs from ORs. The purpose of this article was to evaluate for managers how to choose interventions based on effectiveness and practicality. The authors discuss optimization methods that can be used to sequence consecutive cases in the same OR, by the same surgeon, on the same day, based on the objective of reducing delays in PACU admission due to the unavailability of unfilled PACU beds. Although effective, such methods can be impractical because of large organizational change required and limited equipment or personnel availability. When all physical beds are not full, PACU nurse staffing can be adjusted. Statistical methods can be used to ensure that nursing schedules closely match the times that minimize delays in PACU admission. These methods are effective and practical. Explicit criteria can be applied to assist in deciding when to assign other qualified nurses to the PACU, when to ask PACU nurses to work late, and/or when to make a decision on the day before surgery to add more PACU nurses for the next day (if available). The latter would be based on statistical forecasts of the timing of patients' admissions into the PACU. Whether or not all physical beds are full, the risk of delays in PACU admission is relatively insensitive to economically feasible reductions in PACU length of stay. Such interventions should be considered only if statistical analysis, performed by using computer simulation, has established that reducing PACU length of stay will reduce delays in admission at a manager's facility.
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paper_title: An operating theatre planning and scheduling problem in the case of a "block scheduling" strategy

paper_content:

Operating theatre is always the most important and expensive sector of the hospital, and its surgical process management problem is always regarded as the kernel. In this paper, we focus on one of the surgical process management problems: block scheduling problem. An efficient weekly operating program is built for an operating theatre through two phases: at first the operating theatre weekly planning problem is solved with a heuristic procedure based on column generation procedure; then the operating theatre daily scheduling problem, based on the results from the first phase, is solved with a hybrid genetic algorithm. In the end, the proposed problem is tested and validated with randomly generated data, and then the numerical results are provided.
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paper_title: A Hierarchical Multiple Criteria Mathematical Programming Approach for Scheduling General Surgery Operations in Large Hospitals

paper_content:

Limited staff and equipment within surgical services require efficient use of these resources among multiple surgeon groups. In this study, a set of hierarchical multiple criteria mathematical programming models are developed to generate weekly operating room schedules. The goals considered in these models are maximum utilization of operating room capacity, balanced distribution of operations among surgeon groups in terms of operation days, lengths of operation times, and minimization of patient waiting times. Because of computational difficulty of this scheduling problem, the overall problem is broken down into manageable hierarchical stages: (1) selection of patients, (2) assignment of operations to surgeon groups, and (3) determination of operation dates and operating rooms. Developed models are tested on the data collected in College of Medicine Research Hospital at Cukurova University as well as on simulated data sets, using MPL optimization package.
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paper_title: A three-phase approach for operating theatre schedules

paper_content:

In this paper we develop a three-phase, hierarchical approach for the weekly scheduling of operating rooms. This approach has been implemented in one of the surgical departments of a public hospital located in Genova (Genoa), Italy. Our aim is to suggest an integrated way of facing surgical activity planning in order to improve overall operating theatre efficiency in terms of overtime and throughput as well as waiting list reduction, while improving department organization. In the first phase we solve a bin packing-like problem in order to select the number of sessions to be weekly scheduled for each ward; the proposed and original selection criterion is based upon an updated priority score taking into proper account both the waiting list of each ward and the reduction of residual ward demand. Then we use a blocked booking method for determining optimal time tables, denoted Master Surgical Schedule (MSS), by defining the assignment between wards and surgery rooms. Lastly, once the MSS has been determined we use the simulation software environment Witness 2004 in order to analyze different sequencings of surgical activities that arise when priority is given on the basis of a) the longest waiting time (LWT), b) the longest processing time (LPT) and c) the shortest processing time (SPT). The resulting simulation models also allow us to outline possible organizational improvements in surgical activity. The results of an extensive computational experimentation pertaining to the studied surgical department are here given and analyzed.
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paper_title: SPECIAL ARTICLE Enterprise-Wide Patient Scheduling Information Systems to Coordinate Surgical Clinic and Operating Room Scheduling Can Impair Operating Room Efficiency

paper_content:

SUBSTITUTED-4-FLUORO-1,4-DIAZONIABICYCLO[2.2.2]OCTANE SALTS AND THEIR APPLICATION AS FLUORINATING AGENTS The present invention relates to the preparation and uses of 1-substituted-4-fluoro-1,4-diazoniabicyclo[2.2.2]octane salts, specifically 1-hydroxyl-4-fluoro-1,4-diazoniabicyclo[2.2.2]octane salts as reagents for the introduction of fluorine in organic compounds.
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paper_title: Operating room managers' use of integer programming for assigning block time to surgical groups: a case study.

paper_content:

UNLABELLED ::: A common problem at hospitals with fixed amounts of available operating room (OR) time (i.e., "block time") is determining an equitable method of distributing time to surgical groups. Typically, facilities determine a surgical group's share of available block time using formulas based on OR utilization, contribution margin, or some other performance metric. Once each group's share of time has been calculated, a method must be found for fitting each group's allocated OR time into the surgical master schedule. This involves assigning specific ORs on specific days of the week to specific surgical groups, usually with the objective of ensuring that the time assigned to each group is close to its target share. Unfortunately, the target allocated to a group is rarely expressible as a multiple of whole blocks. In this paper, we describe a hospital's experience using the mathematical technique of integer programming to solve the problem of developing a consistent schedule that minimizes the shortfall between each group's target and actual assignment of OR time. Schedule accuracy, the sum over all surgical groups of shortfalls divided by the total time available on the schedule, was 99.7% (SD 0.1%, n = 11). Simulations show the algorithm's accuracy can exceed 97% with > or =4 ORs. The method is a systematic and successful way to assign OR blocks to surgeons. ::: ::: ::: IMPLICATIONS ::: At hospitals with a fixed budget of operating room (OR) time, integer programming can be used by OR managers to decide which surgical group is to be allocated which OR on which day(s) of the week. In this case study, we describe the successful application of integer programming to this task, and discuss the applicability of the results to other hospitals.
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paper_title: Mount Sinai Hospital Uses Integer Programming to Allocate Operating Room Time

paper_content:

In concentrating polymer solutions up to a desired specification level of residual solvents, encrustations can be prevented and the yield and the degree of purity can be increased, when the product is heated up under pressure, expanded through a restrictor element (3) with vapor formation into a first, preferably coiled flow pipe (7) and concentrated therein as far as possible, the mixture of vapors and polymer solution is whirled at an angle into a second flow pipe (9) in a sloping arrangement and fitted with self-cleaning elements (11, 12) and concentrated therein up to the desired level, and vapors and concentrate are separately discharged only downstream thereof.
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paper_title: Optimisation Modelling of hospital operating room planning : analyzing strategies and problem settings

paper_content:

There is a growing proportion of elderly which increases the demand for health care. As a consequence health care costs are rising and the need for hospital resource planning seems urgent. Different aspects (often conflicting) such as patient demand, clinical need and political ambitions must be considered. In this paper we propose a model for analyzing a hospital surgical suite with focus on operating room planning. An optimization model is developed for patient operation scheduling and for key resource allocation. Medical examinations and treatments of patients are performed using a number of resources, similar to products being refined in a number of processes in a logistics chain. Optimal resource allocation, given different objectives according to patient perspective, staff perspective, costs etc. under different system settings (e.g. principles for operating room allocation and amount of stand-by personnel), is studied. Preliminary results are presented based on case studies from two Swedish hospitals.
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paper_title: Surgical case scheduling as a generalized job shop scheduling problem

paper_content:

Surgical case scheduling allocates hospital resources to individual surgical cases and decides on the time to perform the surgeries. This task plays a decisive role in utilizing hospital resources efficiently while ensuring quality of care for patients. This paper proposes a new surgical case scheduling approach which uses a novel extension of the Job Shop scheduling problem called multi-mode blocking job shop (MMBJS). It formulates the MMBJS as a mixed integer linear programming (MILP) problem and discusses the use of the MMBJS model for scheduling elective and add-on cases. The model is illustrated by a detailed example, and preliminary computational experiments with the CPLEX solver on practical-sized instances are reported.
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paper_title: Data Structures, Algorithms, & Software Principles in C

paper_content:

(All chapters, except Chapter 1, begin with an Introduction and Motivation.) 1. Preparing for the Journey. Where Are We Going? Blending Mathematics, Science, and Engineering. The Search for Enduring Principles in Computer Science. Principles of Software System Structure. Efficiency and Tradeoffs. Software Engineering Principles. Our Approach to Mathematics. Some Notes on Programming Notation. Preview of Coming Attractions. 2. Linked Data Representations. What are Pointers? The Basic Intuition. Pointers in C-The Rudiments. Pointer Diagramming Notation. Linear Linked Lists. Other Linked Data Structures. 3. Introduction to Recursion. Thinking Recursively. Common Pitfall-Infinite Regresses. Quantitative Aspects of Recursive Algorithms. 4. Modularity and Data Abstraction. The Structure of C Modules. Priority Queues-An Abstract Data Type. A Pocket Calculator Interface. How to Hide Data Representations. Modularity and Information Hiding in Program Design. 5. Introduction to Software Engineering Concepts. Top-Down Programming By Stepwise Refinement. Proving Programs Correct. Transforming and Optimizing Programs. Testing Programs. The Philosophy of Measurement and Tuning. Software Reuse and Bottom-up Programming. Program Structuring and Documentation. 6. Introduction to Analysis of Algorithms. What Do We Use for a Yardstick? The Intuition Behind O-Notation. O-Notation-Definition and Manipulation. Analyzing Simple Algorithms. What O-Notation Doesn't Tell You. 7. Linear Data Structures-Stacks and Queues. Some Background on Stacks. ADTs for Stacks and Queues. Using the Stack ADT to Check for Balanced Parentheses. Using the Stack ADT to Evaluate Postfix Expressions. Implementing the Stack ADT. How C Implements Recursive Function Calls Using Stacks. Implementations of the Queue ADT. More Queue Applications. 8. Lists, Strings, and Dynamic Memory Allocation. Lists. Generalized Lists. Applications of Generalized Lists. Strings. Dynamic Memory Allocation. 9. Trees. Basic Concepts and Terminology. Binary Trees. A Sequential Binary Tree Representation. An Application-Heaps and Priority Queues. Traversing Binary Trees. Binary Search Trees. AVL Trees and Their Performance. Two-Three Trees. Tries. An Application-Huffman Codes. 10. Graphs. Basic Concepts and Terminology. Graph Representations. Graph Searching. Topological Ordering. Shortest Paths. Task Networks. Useful Background on Graphs. 11. Hashing and the Table ADT. The Table ADT. Introduction to Hashing by Simple Examples. Collisions, Load Factors, and Clusters. Algorithms for Hashing by Open Addressing. Choosing a Hash Function. Comparison of Searching Methods Using the Table ADT. 12. External Collections of Data. Characteristics of External Storage Devices. Techniques That Don't Work Well. Techniques That Work Well. Information Retrieval and Databases. 13. Sorting. Laying Some Groundwork. Priority Queue Sorting Methods. Divide-and-Conquer Methods. Methods That Insert Keys and Keep Them Sorted. O(n) Methods-Address Calculation Sorting. Other Methods. Comparison and Perspective. 14. Advanced Recursion. Recursion as a Descriptive Method. Using Recursion to Build a Parser. Translating from Infix to Postfix. Recursion and Program Verification. 15. Object-Oriented Programming. Exploring OOP Through Progressive Examples. Building Systems Using Object-Oriented Programming. Advantages and Disadvantages of Object-Oriented Programming. 16. Advanced Software Engineering Concepts. The Software Lifecycle. Software Productivity. Software Process Models. Appendix Math Reference and Tutorial. 0201591189T04062001
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paper_title: Operating Theatre Scheduling Using Lagrangian Relaxation

paper_content:

This paper addresses the surgery operation scheduling problem. Two types of resources are considered, operating rooms and recovery beds. Each patient first visits an operating room for surgery operation and is transferred to a recovery room immediately after the surgery operation. The operating room needs to be cleaned after the surgery operation before starting another operation. The problem consists in assigning patients to operating rooms and recovery beds in order to minimize the sum over all patients of one defined function of their completion times. According to this, the problem is NP harp problem. A Lagrangian relaxation approach is proposed in this paper to determine a near optimal schedule and a tight lower bound. Numerical results will be presented to show the efficiency of the method.
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paper_title: Surgical block scheduling in a system of hospitals: an application to resource and wait list management in a British Columbia health authority.

paper_content:

Scheduling surgical specialties in a medical facility is a very complex process. The choice of schedules and resource availability impact directly on the number of patients treated by specialty, cancellations, wait times, and the overall performance of the system. In this paper we present a system-wide model developed to allow management to explore tradeoffs between OR availability, bed capacity, surgeons' booking privileges, and wait lists. We developed a mixed integer programming model to schedule surgical blocks for each specialty into ORs and applied it to the hospitals in a British Columbia Health Authority, considering OR time availability and post-surgical resource constraints. The results offer promising insights into resource optimization and wait list management, showing that without increasing post-surgical resources hospitals could handle more cases by scheduling specialties differently.
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paper_title: Evaluation of operating room suite efficiency in the Veterans Health Administration system by using data-envelopment analysis

paper_content:

Abstract Background Operating room (OR) activity transcends single ratios such as cases/room, but weighting multiple inputs and outputs may be arbitrary. Data-envelopment analysis (DEA) is a novel technique by which each facility is analyzed by the weightings that optimize its score. Methods We performed DEA analysis of 23 Veterans Health Administration annual OR activity; 87,180 cases were performed, 24 publications generated, and 560 trainee-years of education delivered, in 168 ORs over 166,377 hours by 1,384 full-time equivalents of surgical and anesthesia providers and 523 nonproviders. Results Varying analyzed parameters produced similar efficiency rankings, with individual differences suggesting possible inefficiencies. We characterized returns to scale for efficient sites, suggesting whether patient flow might be efficiently further increased through these sites. We matched inefficient sites to similar efficient sites for comparison and suggested resource alterations to increase efficiency. Conclusions Broader DEA application might characterize OR efficiency more informatively than conventional single-ratio rank ordering.
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paper_title: A Hierarchical Multiple Criteria Mathematical Programming Approach for Scheduling General Surgery Operations in Large Hospitals

paper_content:

Limited staff and equipment within surgical services require efficient use of these resources among multiple surgeon groups. In this study, a set of hierarchical multiple criteria mathematical programming models are developed to generate weekly operating room schedules. The goals considered in these models are maximum utilization of operating room capacity, balanced distribution of operations among surgeon groups in terms of operation days, lengths of operation times, and minimization of patient waiting times. Because of computational difficulty of this scheduling problem, the overall problem is broken down into manageable hierarchical stages: (1) selection of patients, (2) assignment of operations to surgeon groups, and (3) determination of operation dates and operating rooms. Developed models are tested on the data collected in College of Medicine Research Hospital at Cukurova University as well as on simulated data sets, using MPL optimization package.
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paper_title: A Set Packing Approach for Scheduling Elective Surgical Procedures

paper_content:

The efficient scheduling of surgical procedures to operating rooms in a hospital is a complex problem due to limited resources (e.g. medical staff, equipment) and conflicting objectives (e.g. reduce running costs and increase staff and patient satisfaction). A novel approach for scheduling elective surgeries over a short-term horizon is proposed which takes explicit consideration of these aspects. The problem is formulated as a set packing problem and solved optimally through column generation and constraint branching. Good results were obtained for instances from the literature.
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paper_title: Tactical Operating Theatre Scheduling: Efficient Appointment Assignment

paper_content:

Finding an appointment for elective surgeries in hospitals is a task that has a direct impact on the optimization potential for offline and online daily surgery scheduling. A novel approach based on bin packing which takes into account limited resource availability (e.g. staff, equipment), its utilization, clinical priority, hospital bed distribution and surgery difficulty is proposed for this planning level. A solution procedure is presented that explores the specific structure of the model to find appointments for elective surgeries in real time. Tests performed with randomly generated data motivated by a mid size hospital suggest that the new approach yields high quality solutions.
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paper_title: Tactical increases in operating room block time based on financial data and market growth estimates from data envelopment analysis.

paper_content:

BACKGROUND ::: Data envelopment analysis (DEA) is an established technique that hospitals and anesthesia groups can use to understand their potential to grow different specialties of inpatient surgery. Often related decisions such as recruitment of new physicians are made promptly. A practical challenge in using DEA in practice for this application has been the time to obtain access to and preprocess discharge data from states. ::: ::: ::: METHODS ::: A case study is presented to show how results of DEA are linked to financial analysis for purposes of deciding which surgical specialties should be provided more resources and institutional support, including the allocation of additional operating room (OR) block time on a tactical (1 yr) time course. State discharge abstract databases were used to study how to perform and present the DEA using data from websites of the United States' (US) Healthcare Cost and Utilization Project (HCUPNet) and Census Bureau (American FactFinder). ::: ::: ::: RESULTS ::: DEA was performed without state discharge data by using census data with federal surgical rates adjusted for age and gender. Validity was assessed based on multiple criteria, including: satisfaction of statistical assumptions, face validity of results for hospitals, differentiation between efficient and inefficient hospitals on other measures of how much surgery is done, and correlation of estimates of each hospital's potential to grow the workload of each of eight specialties with estimates obtained using unrelated statistical methods. ::: ::: ::: CONCLUSIONS ::: A hospital can choose specialties to target for expanded OR capacity based on its financial data, its caseloads for specific specialties, the caseloads from hospitals previously examined, and surgical rates from federal census data.
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paper_title: A stochastic model for operating room planning with elective and emergency demand for surgery

paper_content:

This paper describes a stochastic model for Operating Room (OR) planning with two types of demand for surgery: elective surgery and emergency surgery. Elective cases can be planned ahead and have a patient-related cost depending on the surgery date. Emergency cases arrive randomly and have to be performed on the day of arrival. The planning problem consists in assigning elective cases to different periods over a planning horizon in order to minimize the sum of elective patient related costs and overtime costs of operating rooms. A new stochastic mathematical programming model is first proposed. We then propose a Monte Carlo optimization method combining Monte Carlo simulation and Mixed Integer Programming. The solution of this method is proved to converge to a real optimum as the computation budget increases. Numerical results show that important gains can be realized by using a stochastic OR planning model.
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paper_title: Operating Theatre Optimization : A Resource-Constrained Based Solving Approach

paper_content:

The operating theatre is considered as the bottleneck of the hospital and as one of the most resources consuming unit. Therefore its management is of primary interest : an efficient planning allows to use as better as possible the availability of the operating theatre and reduce human and financial working costs. This paper deals with operating theatre planning optimization. We present a mathematical model combining surgeries planning and scheduling over short time horizon, and by taking into account renewable and nonrenewable resources availabilities. This model gets its inspiration from project management and especially resource-constrained project scheduling problem (RCPSP). We also introduce a genetic algorithm approach to heuristically solve the problem. We base our approach on the multi-mode variation of the RCPSP to define the related crossover, mutation and selection operators allowing the global search to work effectively.
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paper_title: A Sequential Bounding Approach for Optimal Appointment Scheduling

paper_content:

This study is concerned with the determination of optimal appointment times for a sequence of jobs with uncertain durations. Such appointment systems are used in many customer service applications to increase the utilization of resources, match workload to available capacity, and smooth the flow of customers. We show that the problem can be expressed as a two-stage stochastic linear program that includes the expected cost of customer waiting, server idling, and a cost of tardiness with respect to a chosen session length. We exploit the problem structure to derive upper bounds that are independent of job duration distribution type. These upper bounds are used in a variation of the standard L-shaped algorithm to obtain optimal solutions via successively finer partitions of the support of job durations. We present new analytical insights into the problem as well as a series of numerical experiments that illustrate properties of the optimal solution with respect to distribution type, cost structure, and number of jobs.
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paper_title: OPERATING THEATRE PLANNING

paper_content:

N patients must be planned in an operating theatre over a medium term horizon (one or two weeks). This operating theatre is composed of several operating rooms and of one recovery room where several beds are available. Each patient needs a particular surgical procedure, which defines the human (surgeon) and material (equipment) resources to use and the intervention duration. Additive characteristics must be taken into account: hospitalisation date, intervention deadline, etc. The patient satisfaction and resource efficiency are sought. These two criteria are, respectively, modelled by hospitalisation costs, i.e. the patient stay duration, and the overtime costs, i.e. the resource overloads. We propose to solve this problem in two steps. First, an operating theatre planning is defined. It consists in assigning patients to operating rooms over the horizon. Second, each loaded operating room is scheduled individually in order to synchronise the various human and material resources used. This paper focuses on the first step, i.e. the operating theatre planning, which defines a general assignment problem, i.e. a NP hard problem. In order to solve heuristically this problem, an assignment model with resource capacity and time-window additive constraints is proposed. Integrating most of the constraints in the cost objective function, an extension of the Hungarian method has been developed to calculate the operating theatre planning. This primal–dual heuristic has been successfully experimented on a wide range of problem test data.
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paper_title: Robust surgery loading

paper_content:

We consider the robust surgery loading problem for a hospital’s operating theatre department, which concerns assigning surgeries and sufficient planned slack to operating room days. The objective is to maximize capacity utilization and minimize the risk of overtime, and thus cancelled patients. This research was performed in collaboration with the Erasmus MC, a large academic hospital in the Netherlands, which has also provided historical data for the experiments. We propose various constructive heuristics and local search methods that use statistical information on surgery durations to exploit the portfolio effect, and thereby to minimize the required slack. We demonstrate that our approach frees a lot of operating room capacity, which may be used to perform additional surgeries. Furthermore, we show that by combining advanced optimization techniques with extensive historical statistical records on surgery durations can significantly improve the operating room department utilization.
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paper_title: Determining the Number of Beds in the Postanesthesia Care Unit: A Computer Simulation Flow Approach

paper_content:

UNLABELLED ::: Designing a new operating room (OR) suite is a difficult process owing to the number of caregivers involved and because decision-making managers try to minimize the direct and indirect costs of operating the OR suite. In this study, we devised a computer simulation flow model to calculate, first, the minimum number of beds required in the postanesthesia care unit (PACU). In a second step, we evaluated the relationship between the global performance of the OR suite in terms of OR scheduling and number of staffed PACU beds and porters. We designed a mathematical model of OR scheduling. We then developed a computer simulation flow model of the OR suite. Both models were connected; the first one performed the input flows, and the second simulated the OR suite running. The simulations performed examined the number of beds in the PACU in an ideal situation or in the case of reduction in the number of porters. We then analyzed the variation of number of beds occupied per hour in the PACU when the time spent by patients in the PACU or the number of porters varied. The results highlighted the strong impact of the number of porters on the OR suite performance and particularly on PACU performances. ::: ::: ::: IMPLICATIONS ::: Designing new operating room (OR) facilities implies many decisions on the number of ORs, postanesthesia care unit (PACU) beds, and on the staff of nurses and porters. To make these decisions, managers can use rules of thumb or recommendations. Our study highlights the interest of using flow simulation to validate these choices. In this case study we determine the number of PACU beds and porter staff and assess the impact of decreasing the number of porters on PACU bed requirements.
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paper_title: A branch-and-price approach for integrating nurse and surgery scheduling

paper_content:

A common problem at hospitals is the extreme variation in daily (even hourly) workload pressure for nurses. The operating room is considered to be the main engine and hence the main generator of variance in the hospital. The purpose of this paper is threefold. First of all, we present a concrete model that integrates both the nurse and the operating room scheduling process. Second, we show how the column generation technique approach, one of the most employed exact methods for solving nurse scheduling problems, can easily cope with this model extension. Third, by means of a large number of computational experiments we provide an idea of the cost saving opportunities and required solution times.
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paper_title: Optimisation Modelling of hospital operating room planning : analyzing strategies and problem settings

paper_content:

There is a growing proportion of elderly which increases the demand for health care. As a consequence health care costs are rising and the need for hospital resource planning seems urgent. Different aspects (often conflicting) such as patient demand, clinical need and political ambitions must be considered. In this paper we propose a model for analyzing a hospital surgical suite with focus on operating room planning. An optimization model is developed for patient operation scheduling and for key resource allocation. Medical examinations and treatments of patients are performed using a number of resources, similar to products being refined in a number of processes in a logistics chain. Optimal resource allocation, given different objectives according to patient perspective, staff perspective, costs etc. under different system settings (e.g. principles for operating room allocation and amount of stand-by personnel), is studied. Preliminary results are presented based on case studies from two Swedish hospitals.
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paper_title: The value of the dedicated orthopaedic trauma operating room.

paper_content:

Background:Trauma centers and orthopaedic surgeons have traditionally been faced with limited operating room (OR) availability for fracture surgery. Orthopaedic trauma cases are often waitlisted and done late at night. We investigated the feasibility of having an unbooked orthopaedic trauma OR to re
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paper_title: Scheduling patients in an ambulatory surgical center

paper_content:

This paper presents a deterministic approach to schedule patients in an ambulatory surgical center (ASC) such that the number of postanesthesia care unit nurses at the center is minimized. We formulate the patient scheduling problem as new variants of the no-wait, two-stage process shop scheduling problem and present computational complexity results for the new scheduling models. Also, we develop a tabu search-based heuristic algorithm to solve the patient scheduling problem. Our algorithm is shown to be very effective in finding near optimal schedules on a set of real data from a university hospital's ASC. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2003
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paper_title: Sampling Error Can Significantly Affect Measured Hospital Financial Performance of Surgeons and Resulting Operating Room Time Allocations

paper_content:

Hospitals with limited operating room (OR) hours, those with intensive care unit or ward beds that are always full, or those that have no incremental revenue for many patients need to choose which surgeons get the resources. Although such decisions are based on internal financial reports, whether the reports are statistically valid is not known. Random error may affect surgeons' measured financial performance and, thus, what cases the anesthesiologists get to do and which patients get to receive care. We tested whether one fiscal year of surgeon-specific financial data is sufficient for accurate financial accounting. We obtained accounting data for all outpatient or same-day-admit surgery cases during one fiscal year at an academic medical center. Linear programming was used to find the mix of surgeons' OR time allocations that would maximize the contribution margin or minimize variable costs. Confidence intervals were calculated on these end points by using Fieller's theorem and Monte-Carlo simulation. The 95% confidence intervals for increases in contribution margins or reductions in variable costs were 4.3% to 10.8% and 6.0% to 8.9%, respectively. As many as 22% of surgeons would have had OR time reduced because of sampling error. We recommend that physicians ask for and OR managers get confidence intervals of end points of financial analyses when making decisions based on them.
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paper_title: Management of surgical waiting lists through a Possibilistic Linear Multiobjective Programming problem

paper_content:

This study attempts to apply a management science technique to improve the efficiency of Hospital Administration. We aim to design the performance of the surgical services at a Public Hospital that allows the Decision-Maker to plan surgical scheduling over one year in order to reduce waiting lists. Real decision problems usually involve several objectives that have parameters which are often given by the decision maker in an imprecise way. It is possible to handle these kinds of problems through multiple criteria models in terms of possibility theory. Here we apply a Possibilistic Linear Multiobjective Programming method, developed by the authors, for solving a hospital management problem using a Fuzzy Compromise Programming approach.
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paper_title: Consequences of running more operating theatres than anaesthetists to staff them: a stochastic simulation study

paper_content:

Background Numerous hospitals implement a ratio of one anaesthetist supervising non-medically-qualified anaesthetist practitioners in two or more operating theatres. However, the risk of requiring anaesthetists simultaneously in several theatres due to concurrent critical periods has not been evaluated. It was examined in this simulation study. Methods Using a Monte Carlo stochastic simulation model, we calculated the risk of a staffing failure (no anaesthetist available when one is needed), in different scenarios of scheduling, staffing ratio, and number of theatres. Results With a staffing ratio of 0.5 for a two-theatre suite, the simulated risk that at least one failure occurring during a working day varied from 87% if only short operations were performed to 40% if only long operations performed (65% for a 50:50 mixture of short and long operations). Staffing-failure risk was particularly high during the first hour of the workday, and decreased as the number of theatres increased. The decrease was greater for simulations with only long operations than those with only short operations (the risk for 10 theatres declined to 12% and 74%, respectively). With a staffing ratio of 0.33, the staffing-failure risk was markedly higher than for a 0.5 ratio. The availability of a floater for the whole suite to intervene during failure strongly lowered this risk. Conclusions Scheduling one anaesthetist for two or three theatres exposes patients and staff to high risk of failure. Adequate planning of long and short operations and the presence of a floating anaesthetist are efficient means to optimize site activity and assure safety.
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paper_title: Tactical Decision Making for Selective Expansion of Operating Room Resources Incorporating Financial Criteria and Uncertainty in Subspecialties' Future Workloads

paper_content:

We considered the allocation of operating room (OR) time at facilities where the strategic decision had been made to increase the number of ORs. Allocation occurs in two stages: a long-term tactical stage followed by short-term operational stage. Tactical decisions, approximately 1 yr in advance, determine what specialized equipment and expertise will be needed. Tactical decisionsarebasedonestimatesoffutureORworkload for each subspecialty or surgeon. We show that groups of surgeons can be excluded from consideration at this tactical stage (e.g., surgeons who need intensive care bedsorthosewithbelowaveragecontributionmargins perORhour).Lowerandupperlimitsareestimatedfor the future demand of OR time by the remaining surgeons.Thus,initialORallocationscanbeaccomplished with only partial information on future OR workload. Once the new ORs open, operational decision-making based on OR efficiency is used to fill the OR time and adjust staffing. Surgeons who were not allocated additional time at the tactical stage are provided increased OR time through operational adjustments based on their actual workload. In a case study from a tertiary hospital, future demand estimates were needed for only 15% of surgeons,illustratingthepracticalityofthesemethodsfor use in tactical OR allocation decisions. (Anesth Analg 2005;100:1425–32)
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paper_title: Managing uncertainty in orthopaedic trauma theatres

paper_content:

Abstract The management of acute healthcare involves coping with a large uncertainty in demand. This uncertainty is a prevailing feature of orthopaedic care and many scarce resources are devoted to providing the contingent theatre time for orthopaedic trauma patients. However, given the variability and uncertainty in the demand much of the theatre time is not used. Simulation was used to explore the balance between maximising the utilisation of the theatre sessions, avoiding too many overruns and ensuring a reasonable quality of care in a typical hospital in the United Kingdom. The simulation was developed to examine a policy of including planned, elective patients within the trauma session: it appears that if patients are willing to accept a possibility of their treatment being cancelled, substantially greater throughputs can be achieved. A number of approximations were examined as an alternative to the full simulation: the simpler model offers reasonable accuracy and easier implementation.
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paper_title: ENDOSCOPIES SCHEDULING PROBLEM: A CASE STUDY

paper_content:

The efficient management of an operating theatre involves the problems of planning and scheduling, and this is the same case for endoscopy center. The research aims at building a feasible and efficient operating program within one week for an endoscopy unit composed of two specialized operating rooms, with an objective of both maximizing the utilization of operating rooms and minimizing their overtime cost. At the planning stage, a tactical planning model for one week is built and is solved by a column-generation based heuristic (CGBH) procedure. The solution of the planning stage assigns each operating room to a set of surgical cases on each day. Afterwards, a daily scheduling problem is built at the scheduling stage in order to finally schedule the surgical cases assigned at the planning stage. This daily scheduling model is firstly simplified by a group technology into an "open shop" model and then solved by the Gonzalez-Sahni algorithm. As a result, a final operating program is ob
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paper_title: Operating Theatre Scheduling Using Lagrangian Relaxation

paper_content:

This paper addresses the surgery operation scheduling problem. Two types of resources are considered, operating rooms and recovery beds. Each patient first visits an operating room for surgery operation and is transferred to a recovery room immediately after the surgery operation. The operating room needs to be cleaned after the surgery operation before starting another operation. The problem consists in assigning patients to operating rooms and recovery beds in order to minimize the sum over all patients of one defined function of their completion times. According to this, the problem is NP harp problem. A Lagrangian relaxation approach is proposed in this paper to determine a near optimal schedule and a tight lower bound. Numerical results will be presented to show the efficiency of the method.
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paper_title: A Norm Utilisation for Scarce Hospital Resources: Evidence from Operating Rooms in a Dutch University Hospital

paper_content:

BACKGROUND ::: Utilisation of operating rooms is high on the agenda of hospital managers and researchers. Many efforts in the area of maximising the utilisation have been focussed on finding the holy grail of 100% utilisation. The utilisation that can be realised, however, depends on the patient mix and the willingness to accept the risk of working in overtime. ::: ::: ::: MATERIALS AND METHODS ::: This is a mathematical modelling study that investigates the association between the utilisation and the patient mix that is served and the risk of working in overtime. Prospectively, consecutively, and routinely collected data of an operating room department in a Dutch university hospital are used. Basic statistical principles are used to establish the relation between realistic utilisation rates, patient mixes, and accepted risk of overtime. ::: ::: ::: RESULTS ::: Accepting a low risk of overtime combined with a complex patient mix results a low utilisation rate. If the accepted risk of overtime is higher and the patient mix is less complex, the utilisation rate that can be reached is closer to 100%. ::: ::: ::: CONCLUSION ::: Because of the inherent variability of healthcare processes, the holy grail of 100% utilisation is unlikely to be found. The method proposed in this paper calculates a realistic benchmark utilisation that incorporates the patient mix characteristics and the willingness to accept risk of overtime.
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paper_title: The operating theatre planning by the follow-up of the risk of no realization

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Abstract In the French context of healthcare expenses control, the operating theatre, that represents 9% of hospital's annual budget, presents a stake of major priority. The realization of the operating theatre planning is the fruit of negotiation of different actors of the block such as surgeons, anesthetists, nurses, managerial staff, etc. whose constraints and interests are often different. In this context, a win–win situation for this partnership (all parties involved) requires a good and constructive negotiation. In this paper, we propose an operating theatre planning procedure that aims at mastering the risk of no realization (RNR) of the tentative plan while stabilizing the operating rooms’ utilization time. During the application of this planning, we achieve the follow-up of the RNR and according to its evolution the research of another planning will be proposed in order to reduce the risk level. Finally, we present results obtained by simulations that support the interest for implementing these procedures.
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paper_title: Using Computer Simulation in Operating Room Management: Impacts on Process Engineering and Performance

paper_content:

Operating rooms are regarded as the most costly hospital facilities. Due to rising costs and decreasing reimbursements, it is necessary to optimize the efficiency of the operating room suite. In this context several strategies have been proposed that optimize patient throughput by redesigning perioperative processes. The successful deployment of effective practices for continuous process improvements in operating rooms can require that operating room management sets targets and monitors improvements throughout all phases of process engineering. Simulation can be used to study the effects of process improvements through novel facilities, technologies and/or strategies. In this paper, we propose a conceptual framework to use computer simulations in different stages of business process management (BPM) lifecycle for operating room management. Additionally, we conduct simulation studies in different stages of the BPM lifecycle. The results of our studies provide evidence that simulation can provide effective decision support to drive performance in operating rooms in several phases of the BPM lifecycle
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paper_title: A Hierarchical Multiple Criteria Mathematical Programming Approach for Scheduling General Surgery Operations in Large Hospitals

paper_content:

Limited staff and equipment within surgical services require efficient use of these resources among multiple surgeon groups. In this study, a set of hierarchical multiple criteria mathematical programming models are developed to generate weekly operating room schedules. The goals considered in these models are maximum utilization of operating room capacity, balanced distribution of operations among surgeon groups in terms of operation days, lengths of operation times, and minimization of patient waiting times. Because of computational difficulty of this scheduling problem, the overall problem is broken down into manageable hierarchical stages: (1) selection of patients, (2) assignment of operations to surgeon groups, and (3) determination of operation dates and operating rooms. Developed models are tested on the data collected in College of Medicine Research Hospital at Cukurova University as well as on simulated data sets, using MPL optimization package.
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paper_title: Ambulatory Care and Orthopaedic Capacity Planning

paper_content:

Ambulatory Care facilities (often referred to as diagnosis and treatment centres) separate the routine elective activity from the uncertainty of complex inpatient and emergency treatment. Only routine patients with predictable outcomes should be treated in Ambulatory Care. Hence the centre should be able to plan its activities effectively. This paper considers the consequences for the remaining elective inpatient bed and theatre requirements. Computer models are used to simulate many years of activity in an orthopaedic department at a typical District General hospital.
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paper_title: A three-phase approach for operating theatre schedules

paper_content:

In this paper we develop a three-phase, hierarchical approach for the weekly scheduling of operating rooms. This approach has been implemented in one of the surgical departments of a public hospital located in Genova (Genoa), Italy. Our aim is to suggest an integrated way of facing surgical activity planning in order to improve overall operating theatre efficiency in terms of overtime and throughput as well as waiting list reduction, while improving department organization. In the first phase we solve a bin packing-like problem in order to select the number of sessions to be weekly scheduled for each ward; the proposed and original selection criterion is based upon an updated priority score taking into proper account both the waiting list of each ward and the reduction of residual ward demand. Then we use a blocked booking method for determining optimal time tables, denoted Master Surgical Schedule (MSS), by defining the assignment between wards and surgery rooms. Lastly, once the MSS has been determined we use the simulation software environment Witness 2004 in order to analyze different sequencings of surgical activities that arise when priority is given on the basis of a) the longest waiting time (LWT), b) the longest processing time (LPT) and c) the shortest processing time (SPT). The resulting simulation models also allow us to outline possible organizational improvements in surgical activity. The results of an extensive computational experimentation pertaining to the studied surgical department are here given and analyzed.
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paper_title: Comparison of two methods of operating theatre planning: Application in Belgian Hospital

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Operating Theatre is the centre of the hospital management’s efforts. It constitutes the most expensive sector with more than 10% of the intended operating budget of the hospital. To reduce the costs while maintaining a good quality of care, one of the solutions is to improve the existent planning and scheduling methods by improving the services and surgical specialty coordination or finding the best estimation of surgical case durations. The other solution is to construct an effective surgical case plan and schedule. The operating theatre planning and scheduling is the two important steps, which aim to make a surgical case programming with an objective of obtaining a realizable and efficient surgical case schedule. This paper focuses on the first step, the operating theatre planning problem. Two planning methods are introduced and compared. Real data of a Belgian university hospital “Tivoli” are used for the experiments.
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paper_title: A Set Packing Approach for Scheduling Elective Surgical Procedures

paper_content:

The efficient scheduling of surgical procedures to operating rooms in a hospital is a complex problem due to limited resources (e.g. medical staff, equipment) and conflicting objectives (e.g. reduce running costs and increase staff and patient satisfaction). A novel approach for scheduling elective surgeries over a short-term horizon is proposed which takes explicit consideration of these aspects. The problem is formulated as a set packing problem and solved optimally through column generation and constraint branching. Good results were obtained for instances from the literature.
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paper_title: Simulation of a Multiple Operating Room Surgical Suite

paper_content:

Outpatient surgery scheduling involves the coordination of several activities in an uncertain environment. Due to the very customized nature of surgical procedures there is significant uncertainty in the duration of activities related to the intake process, surgical procedure, and recovery process. Furthermore, there are multiple criteria which must be traded off when considering how to schedule surgical procedures including patient waiting, operating room (OR) team waiting, OR idling, and overtime for the surgical suite. Uncertainty combined with the need to tradeoff many criteria makes scheduling a complex task for OR managers. In this article we present a simulation model for a multiple OR surgical suite, describe some of the scheduling challenges, and illustrate how the model can be used as a decisions aid to improve strategic and operational decision making relating to the delivery of surgical services. All results presented are based on real data collected at Mayo Clinic in Rochester, MN.
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paper_title: Operating room managers' use of integer programming for assigning block time to surgical groups: a case study.

paper_content:

UNLABELLED ::: A common problem at hospitals with fixed amounts of available operating room (OR) time (i.e., "block time") is determining an equitable method of distributing time to surgical groups. Typically, facilities determine a surgical group's share of available block time using formulas based on OR utilization, contribution margin, or some other performance metric. Once each group's share of time has been calculated, a method must be found for fitting each group's allocated OR time into the surgical master schedule. This involves assigning specific ORs on specific days of the week to specific surgical groups, usually with the objective of ensuring that the time assigned to each group is close to its target share. Unfortunately, the target allocated to a group is rarely expressible as a multiple of whole blocks. In this paper, we describe a hospital's experience using the mathematical technique of integer programming to solve the problem of developing a consistent schedule that minimizes the shortfall between each group's target and actual assignment of OR time. Schedule accuracy, the sum over all surgical groups of shortfalls divided by the total time available on the schedule, was 99.7% (SD 0.1%, n = 11). Simulations show the algorithm's accuracy can exceed 97% with > or =4 ORs. The method is a systematic and successful way to assign OR blocks to surgeons. ::: ::: ::: IMPLICATIONS ::: At hospitals with a fixed budget of operating room (OR) time, integer programming can be used by OR managers to decide which surgical group is to be allocated which OR on which day(s) of the week. In this case study, we describe the successful application of integer programming to this task, and discuss the applicability of the results to other hospitals.
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paper_title: How to release allocated operating room time to increase efficiency: predicting which surgical service will have the most underutilized operating room time.

paper_content:

At many facilities, surgeons and patients choose the day of surgery, cases are not turned away, and staffing is adjusted to maximize operating room (OR) efficiency. If a surgical service has already filled its allocated OR time, but has an additional case to schedule, then OR efficiency is increased by scheduling the new case into the OR time of a different service with much underutilized OR time. The latter service is said to be "releasing" its allocated OR time. In this study, we analyzed 3 years of scheduling data from a medium-sized and a large surgical suite. Theoretically, the service that should have its OR time released is the service expected to have the most underutilized OR time on the day of surgery (i.e., any future cases that may be scheduled into that service's time also need to be factored in). However, we show that OR efficiency is only slightly less when the service whose time is released is the service that has the most allocated but unscheduled (i.e., unfilled) OR time at the moment the new case is scheduled. In contrast, compromising by releasing the OR time of a service other than the one with the most allocated but unscheduled OR time markedly reduces OR efficiency. OR managers can use these results when releasing allocated OR time.
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paper_title: A stochastic model for operating room planning with elective and emergency demand for surgery

paper_content:

This paper describes a stochastic model for Operating Room (OR) planning with two types of demand for surgery: elective surgery and emergency surgery. Elective cases can be planned ahead and have a patient-related cost depending on the surgery date. Emergency cases arrive randomly and have to be performed on the day of arrival. The planning problem consists in assigning elective cases to different periods over a planning horizon in order to minimize the sum of elective patient related costs and overtime costs of operating rooms. A new stochastic mathematical programming model is first proposed. We then propose a Monte Carlo optimization method combining Monte Carlo simulation and Mixed Integer Programming. The solution of this method is proved to converge to a real optimum as the computation budget increases. Numerical results show that important gains can be realized by using a stochastic OR planning model.
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paper_title: When to Release Allocated Operating Room Time to Increase Operating Room Efficiency

paper_content:

UNLABELLED ::: We studied when allocated, but unfilled, operating room (OR) time of surgical services should be released to maximize OR efficiency. OR time was allocated for two surgical suites based on OR efficiency. Then, we analyzed real OR schedules. We added new hypothetical cases lasting 1, 2, or 3 h into OR time of the service that had the largest difference between allocated and scheduled cases (i.e., the most unfilled OR time) 5 days before the day of surgery. The process was repeated using the updated OR schedule available the day before surgery. The pair-wise difference in resulting overutilized OR time was calculated for n = 754 days of data from each of the two surgical suites. We found that postponing the decision of which service gets the new case until early the day before surgery reduces overutilized OR time by <15 min per OR per day as compared to releasing the allocated OR time 5 days before surgery. These results show that when OR time is released has a negligible effect on OR efficiency. This is especially true for ambulatory surgery centers with brief cases or large surgical suites with specialty-specific OR teams. What matters much more is having the correct OR allocations and, if OR time needs to be released, making that decision based on the scheduled workload. ::: ::: ::: IMPLICATIONS ::: Provided operating room (OR) time is allocated and cases are scheduled based on maximizing OR efficiency, then whether OR time is released five days or one day before the day of surgery has a negligible effect on OR efficiency.
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paper_title: Hospital Operating Room Capacity Expansion

paper_content:

A large midwestern hospital is expecting an increase in surgical caseload. New operating room (OR) capacity can be had by building new ORs or extending the working hours in the current ORs. The choice among these options is complicated by the fact that patients, surgeons and surgical staff, and hospital administrators are all important stakeholders in the health service operation, and each has different priorities. This paper investigates the trade-offs among three performance criteria (wait to get on schedule, scheduled procedure start-time reliability, and hospital profits), which are of particular importance to the different constituencies. The objective is to determine how the hospital can best expand its capacity, acknowledging the key role that each constituency plays in that objective. En route, the paper presents supporting analysis for process improvements and suggestions for optimal participation-inducing staff contracts for extending OR hours of operation.
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paper_title: Operating Theatre Optimization : A Resource-Constrained Based Solving Approach

paper_content:

The operating theatre is considered as the bottleneck of the hospital and as one of the most resources consuming unit. Therefore its management is of primary interest : an efficient planning allows to use as better as possible the availability of the operating theatre and reduce human and financial working costs. This paper deals with operating theatre planning optimization. We present a mathematical model combining surgeries planning and scheduling over short time horizon, and by taking into account renewable and nonrenewable resources availabilities. This model gets its inspiration from project management and especially resource-constrained project scheduling problem (RCPSP). We also introduce a genetic algorithm approach to heuristically solve the problem. We base our approach on the multi-mode variation of the RCPSP to define the related crossover, mutation and selection operators allowing the global search to work effectively.
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paper_title: Mount Sinai Hospital Uses Integer Programming to Allocate Operating Room Time

paper_content:

In concentrating polymer solutions up to a desired specification level of residual solvents, encrustations can be prevented and the yield and the degree of purity can be increased, when the product is heated up under pressure, expanded through a restrictor element (3) with vapor formation into a first, preferably coiled flow pipe (7) and concentrated therein as far as possible, the mixture of vapors and polymer solution is whirled at an angle into a second flow pipe (9) in a sloping arrangement and fitted with self-cleaning elements (11, 12) and concentrated therein up to the desired level, and vapors and concentrate are separately discharged only downstream thereof.
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paper_title: A Sequential Bounding Approach for Optimal Appointment Scheduling

paper_content:

This study is concerned with the determination of optimal appointment times for a sequence of jobs with uncertain durations. Such appointment systems are used in many customer service applications to increase the utilization of resources, match workload to available capacity, and smooth the flow of customers. We show that the problem can be expressed as a two-stage stochastic linear program that includes the expected cost of customer waiting, server idling, and a cost of tardiness with respect to a chosen session length. We exploit the problem structure to derive upper bounds that are independent of job duration distribution type. These upper bounds are used in a variation of the standard L-shaped algorithm to obtain optimal solutions via successively finer partitions of the support of job durations. We present new analytical insights into the problem as well as a series of numerical experiments that illustrate properties of the optimal solution with respect to distribution type, cost structure, and number of jobs.
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paper_title: Optimization of surgery sequencing and scheduling decisions under uncertainty

paper_content:

Operating rooms (ORs) are simultaneously the largest cost center and greatest source of revenues for most hospitals. Due to significant uncertainty in surgery durations, scheduling of ORs can be very challenging. Longer than average surgery durations result in late starts not only for the next surgery in the schedule, but potentially for the rest of the surgeries in the day as well. Late starts also result in direct costs associated with overtime staffing when the last surgery of the day finishes later than the scheduled shift end time. In this article we describe a stochastic optimization model and some practical heuristics for computing OR schedules that hedge against the uncertainty in surgery durations. We focus on the simultaneous effects of sequencing surgeries and scheduling start times. We show that a simple sequencing rule based on surgery duration variance can be used to generate substantial reductions in total surgeon and OR team waiting, OR idling, and overtime costs. We illustrate this with results of a case study that uses real data to compare actual schedules at a particular hospital to those recommended by our model.
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paper_title: The use of Simulation to Determine Maximum Capacity in the Surgical Suite Operating Room

paper_content:

Utilizing ambulatory care units at optimal levels has become increasingly important to hospitals from both service and business perspectives. With the inherent variation in hospitals due to unique procedures and patients, performing capacity analysis through analytical models is difficult without making simplifying assumptions. Many hospitals calculate efficiency by comparing total operating room minutes available to total operating minutes used. This metric both fails to account for the required non-value added tasks between surgeries and the delicate balance necessary between having patients ready for surgery when an operating room becomes available, which can result in increased waiting times, and maximizing patient satisfaction. We present a general methodology for determining the maximum capacity within a surgical suite through the use of a discrete-event simulation model. This research is based on an actual hospital concerned with doctor/resource acquisition decisions, patient satisfaction improvements, and increased productivity.
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paper_title: OPERATING THEATRE PLANNING

paper_content:

N patients must be planned in an operating theatre over a medium term horizon (one or two weeks). This operating theatre is composed of several operating rooms and of one recovery room where several beds are available. Each patient needs a particular surgical procedure, which defines the human (surgeon) and material (equipment) resources to use and the intervention duration. Additive characteristics must be taken into account: hospitalisation date, intervention deadline, etc. The patient satisfaction and resource efficiency are sought. These two criteria are, respectively, modelled by hospitalisation costs, i.e. the patient stay duration, and the overtime costs, i.e. the resource overloads. We propose to solve this problem in two steps. First, an operating theatre planning is defined. It consists in assigning patients to operating rooms over the horizon. Second, each loaded operating room is scheduled individually in order to synchronise the various human and material resources used. This paper focuses on the first step, i.e. the operating theatre planning, which defines a general assignment problem, i.e. a NP hard problem. In order to solve heuristically this problem, an assignment model with resource capacity and time-window additive constraints is proposed. Integrating most of the constraints in the cost objective function, an extension of the Hungarian method has been developed to calculate the operating theatre planning. This primal–dual heuristic has been successfully experimented on a wide range of problem test data.
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paper_title: Allocation of Surgeries to Operating Rooms by Goal Programing

paper_content:

High usage rate in a surgical suite is extremely important in meeting the increasing demand for health care services and reducing costs to improve quality of care. In this paper a goal programming model which can produce schedules that best serve the needs of the hospital, i.e., by minimizing idle time and overtime, and increasing satisfaction of surgeons, patients, and staff, is described. The approach involves sorting the requests for a particular day on the basis of block restrictions, room utilization, surgeon preferences and intensive care capabilities. The model is tested using the data obtained during field studies at Dokuz Eylul University Hospital. The model is also tested for alternative achievement functions to examine the model's ability to satisfy abstract goals.
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paper_title: Building cyclic master surgery schedules with leveled resulting bed occupancy

paper_content:

This paper proposes and evaluates a number of models for building surgery schedules with leveled resulting bed occupancy. The developed models involve two types of constraints. Demand constraints ensure that each surgeon (or surgical group) obtains a specific number of operating room blocks. Capacity constraints limit the available blocks on each day. Furthermore, the number of operated patients per block and the length of stay of each operated patient are dependent on the type of surgery. Both are considered stochastic, following a multinomial distribution. We develop a number of mixed integer programming based heuristics and a metaheuristic to minimize the expected total bed shortage and present computational results.
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paper_title: Scheduling Surgical Cases into Overflow Block Time— Computer Simulation of the Effects of Scheduling Strategies on Operating Room Labor Costs

paper_content:

“Overflow” block time is operating room (OR) time for a surgical group’s cases that cannot be completed in the regular block time allocated to each surgeon in the surgical group. Having such overflow block time increases OR utilization. The optimal way to schedule patients into a surgical group’s ov
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paper_title: Robust surgery loading

paper_content:

We consider the robust surgery loading problem for a hospital’s operating theatre department, which concerns assigning surgeries and sufficient planned slack to operating room days. The objective is to maximize capacity utilization and minimize the risk of overtime, and thus cancelled patients. This research was performed in collaboration with the Erasmus MC, a large academic hospital in the Netherlands, which has also provided historical data for the experiments. We propose various constructive heuristics and local search methods that use statistical information on surgery durations to exploit the portfolio effect, and thereby to minimize the required slack. We demonstrate that our approach frees a lot of operating room capacity, which may be used to perform additional surgeries. Furthermore, we show that by combining advanced optimization techniques with extensive historical statistical records on surgery durations can significantly improve the operating room department utilization.
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paper_title: Determining the Number of Beds in the Postanesthesia Care Unit: A Computer Simulation Flow Approach

paper_content:

UNLABELLED ::: Designing a new operating room (OR) suite is a difficult process owing to the number of caregivers involved and because decision-making managers try to minimize the direct and indirect costs of operating the OR suite. In this study, we devised a computer simulation flow model to calculate, first, the minimum number of beds required in the postanesthesia care unit (PACU). In a second step, we evaluated the relationship between the global performance of the OR suite in terms of OR scheduling and number of staffed PACU beds and porters. We designed a mathematical model of OR scheduling. We then developed a computer simulation flow model of the OR suite. Both models were connected; the first one performed the input flows, and the second simulated the OR suite running. The simulations performed examined the number of beds in the PACU in an ideal situation or in the case of reduction in the number of porters. We then analyzed the variation of number of beds occupied per hour in the PACU when the time spent by patients in the PACU or the number of porters varied. The results highlighted the strong impact of the number of porters on the OR suite performance and particularly on PACU performances. ::: ::: ::: IMPLICATIONS ::: Designing new operating room (OR) facilities implies many decisions on the number of ORs, postanesthesia care unit (PACU) beds, and on the staff of nurses and porters. To make these decisions, managers can use rules of thumb or recommendations. Our study highlights the interest of using flow simulation to validate these choices. In this case study we determine the number of PACU beds and porter staff and assess the impact of decreasing the number of porters on PACU bed requirements.
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paper_title: A branch-and-price approach for integrating nurse and surgery scheduling

paper_content:

A common problem at hospitals is the extreme variation in daily (even hourly) workload pressure for nurses. The operating room is considered to be the main engine and hence the main generator of variance in the hospital. The purpose of this paper is threefold. First of all, we present a concrete model that integrates both the nurse and the operating room scheduling process. Second, we show how the column generation technique approach, one of the most employed exact methods for solving nurse scheduling problems, can easily cope with this model extension. Third, by means of a large number of computational experiments we provide an idea of the cost saving opportunities and required solution times.
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paper_title: How to Schedule Elective Surgical Cases into Specific Operating Rooms to Maximize the Efficiency of Use of Operating Room Time

paper_content:

We considered elective case scheduling at hospitals and surgical centers at which surgeons and patients choose the day of surgery, cases are not turned away, and anesthesia and nursing staffing are adjusted to maximize the efficiency of use of operating room (OR) time. We investigated scheduling a new case into an OR by using two patient-scheduling rules: Earliest Start Time or Latest Start Time. By using several scenarios, we showed that the use of Earliest Start Time is rational economically at such facilities. Specifically, it maximizes OR efficiency when a service has nearly filled its regularly scheduled hours of OR time. However, Latest Start Time will perform better at balancing workload among services’ OR time. We then used historical case duration data from two facilities in computer simulations to investigate the effect of errors in predicting case durations on the performance of these two heuristics. The achievable incremental reduction in overtime by having perfect information on case duration versus using historical case durations was only a few minutes per OR. The differences between Earliest Start Time and Latest Start Time were also only a few minutes per OR. We conclude that for facilities at which the goals are, in order of importance, safety, patient and surgeon access to OR time, and then efficiency, few restrictions need to be placed on patient scheduling to achieve an efficient use of OR time. (Anesth Analg 2002;94:933–42)
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paper_title: Schedule the Short Procedure First to Improve OR Efficiency

paper_content:

ABSTRACT • OPERATING ROOM MANAGERS are hampered in their efforts to optimize OR efficiency by surgical procedures that last a longer or shorter time than scheduled. The lack of predictability is a result of inaccuracy in scheduling and variability in the duration of procedures. • SCHEDULING SHORT PROCEDURES before long procedures theoretically limits this variability. • MONTE CARLO SIMULATION of ORs scheduled with various combinations of short and long procedures supports this concept's validity. • RESULTS INDICATE that scheduling short procedures first can improve on-time performance and decrease staff member overtime expense without reducing surgical throughput. AORNJ 78 (October 2003) 651–657.
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paper_title: Encyclopedia of Operations Research and Management Science

paper_content:

The goal of the Encyclopedia of Operations Research and Management Science is to provide decision makers and problem solvers in business, industry, government and academia with a comprehensive overview of the wide range of ideas, methodologies, and synergistic forces that combine to form the pre-eminent decision-aiding fields of operations research and management science (OR/MS). The Second Edition is a further extension of this goal - which through addressing and solving a wide range of problems - OR/MS methodologies continue to flourish and grow. This is a field that is used extensively throughout the applied sciences, and, because of this, the new edition has added topics in the following areas: Analytic Network Process; Call Centers; Certainty Equivalence; Comb. Optimization by Simulated CE; Computational Organization; Constraint Programming; Data Mining; Degeneracy Graphs; Economic Order Q Extensions; Educational Issues in B-Schools; Electronic Commerce; Financial Markets; Global Climate Change; Hidden Markov Models; History of Early British OR; Implementation for Public Sector; Info Tech Benefits; Interactive Multi-Objective Math. Programming; Knapsacks with Nonlinearities; Little's Law in Distribution Form; Military Ops Other than War; Multivariate Quality Control; Perturbation Analysis; Simulation Metamodeling; Simulation Optimization; Supply Chain Management; Theory of Constraints; Timetabling. The intended audience of the Encyclopedia of Operations Research and Management Science is technically diverse and wide; it includes anyone concerned with the science, techniques, and ideas of how one makes decisions. As this audience encompasses many professions, educational backgrounds and skills, we were attentive to the form, format and scope of the articles. Thus, the articles are designed to serve as initial sources of information for all such readers, with special emphasis on the needs of students. Each article provides a background or history of the topic, describes relevant applications, overviews present and future trends, and lists seminal and current references. To allow for variety in exposition, the authors were instructed to present their material from both research and applied perspectives. The Encyclopedia has been organized into specific topics that collectively encompass the foundations, applications, and emerging elements of this ever-changing field. We also wanted to establish the close associations that OR/MS has maintained with other scientific endeavors, with special emphasis on its symbiotic relationships to computer science, information processing, and mathematics. Based on our broad view of OR/MS, we commissioned 228 major expository articles and complemented them by numerous entries: descriptions, discussions, definitions, and abbreviations. The connections between topics are highlighted by an entry's final `See' statement, as appropriate. Each topical article provides a background or history of the topic, describes relevant applications, overviews present and future trends, and lists seminal and current references. Of significant importance is that each contributed topic has been authored by a leading authoritative researcher on that particular topic.
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paper_title: Scheduling patients in an ambulatory surgical center

paper_content:

This paper presents a deterministic approach to schedule patients in an ambulatory surgical center (ASC) such that the number of postanesthesia care unit nurses at the center is minimized. We formulate the patient scheduling problem as new variants of the no-wait, two-stage process shop scheduling problem and present computational complexity results for the new scheduling models. Also, we develop a tabu search-based heuristic algorithm to solve the patient scheduling problem. Our algorithm is shown to be very effective in finding near optimal schedules on a set of real data from a university hospital's ASC. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2003
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paper_title: The impact of service-specific staffing, case scheduling, turnovers, and first-case starts on anesthesia group and operating room productivity: a tutorial using data from an Australian hospital.

paper_content:

BACKGROUND ::: In this tutorial, we consider the impact of operating room (OR) management on anesthesia group and OR labor productivity and costs. Most of the tutorial focuses on the steps required for each facility to refine its OR allocations using its own data collected during patient care. ::: ::: ::: METHODS ::: Data from a hospital in Australia are used throughout to illustrate the methods. OR allocation is a two-stage process. During the initial tactical stage of allocating OR time, OR capacity ("block time") is adjusted. For operational decision-making on a shorter-term basis, the existing workload can be considered fixed. Staffing is matched to that workload based on maximizing the efficiency of use of OR time. ::: ::: ::: RESULTS ::: Scheduling cases and making decisions on the day of surgery to increase OR efficiency are worthwhile interventions to increase anesthesia group productivity. However, by far, the most important step is the appropriate refinement of OR allocations (i.e., planning service-specific staffing) 2-3 mo before the day of surgery. ::: ::: ::: CONCLUSIONS ::: Reducing surgical and/or turnover times and delays in first-case-of-the-day starts generally provides small reductions in OR labor costs. Results vary widely because they are highly sensitive both to the OR allocations (i.e., staffing) and to the appropriateness of those OR allocations.
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paper_title: Strategies to reduce delays in admission into a postanesthesia care unit from operating rooms

paper_content:

The authors performed a systematic review of strategies to reduce delays in admission into PACUs from ORs. The purpose of this article was to evaluate for managers how to choose interventions based on effectiveness and practicality. The authors discuss optimization methods that can be used to sequence consecutive cases in the same OR, by the same surgeon, on the same day, based on the objective of reducing delays in PACU admission due to the unavailability of unfilled PACU beds. Although effective, such methods can be impractical because of large organizational change required and limited equipment or personnel availability. When all physical beds are not full, PACU nurse staffing can be adjusted. Statistical methods can be used to ensure that nursing schedules closely match the times that minimize delays in PACU admission. These methods are effective and practical. Explicit criteria can be applied to assist in deciding when to assign other qualified nurses to the PACU, when to ask PACU nurses to work late, and/or when to make a decision on the day before surgery to add more PACU nurses for the next day (if available). The latter would be based on statistical forecasts of the timing of patients' admissions into the PACU. Whether or not all physical beds are full, the risk of delays in PACU admission is relatively insensitive to economically feasible reductions in PACU length of stay. Such interventions should be considered only if statistical analysis, performed by using computer simulation, has established that reducing PACU length of stay will reduce delays in admission at a manager's facility.
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paper_title: Solving surgical cases assignment problem by a branch-and-price approach ☆

paper_content:

In this paper, we study a surgical cases assignment problem (SCAP) of assigning a set of surgical cases to several multifunctional operating rooms with an objective of minimizing total operating cost. Firstly, we formulate this problem as an integer problem and then reformulate the integer program by using Dantzig–Wolf decomposition as a set partitioning problem. Based on this set partitioning formulation, a so-called branch-and-price exact solution algorithm, combining Branch-and-Bound procedure with column generation (CG) method, is designed for the proposed problem where each node is the linear relaxation problem of a set partitioning problem. This linear relaxation problem is solved by a CG approach in which each column represents a plan for one operating room and is generated by solving a sub-problem (SP) of single operating room planning problem. The computational results indicate that the decomposition approach is promising and capable of solving large problems.
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paper_title: An operating theatre planning and scheduling problem in the case of a "block scheduling" strategy

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Operating theatre is always the most important and expensive sector of the hospital, and its surgical process management problem is always regarded as the kernel. In this paper, we focus on one of the surgical process management problems: block scheduling problem. An efficient weekly operating program is built for an operating theatre through two phases: at first the operating theatre weekly planning problem is solved with a heuristic procedure based on column generation procedure; then the operating theatre daily scheduling problem, based on the results from the first phase, is solved with a hybrid genetic algorithm. In the end, the proposed problem is tested and validated with randomly generated data, and then the numerical results are provided.
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paper_title: Sampling Error Can Significantly Affect Measured Hospital Financial Performance of Surgeons and Resulting Operating Room Time Allocations

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Hospitals with limited operating room (OR) hours, those with intensive care unit or ward beds that are always full, or those that have no incremental revenue for many patients need to choose which surgeons get the resources. Although such decisions are based on internal financial reports, whether the reports are statistically valid is not known. Random error may affect surgeons' measured financial performance and, thus, what cases the anesthesiologists get to do and which patients get to receive care. We tested whether one fiscal year of surgeon-specific financial data is sufficient for accurate financial accounting. We obtained accounting data for all outpatient or same-day-admit surgery cases during one fiscal year at an academic medical center. Linear programming was used to find the mix of surgeons' OR time allocations that would maximize the contribution margin or minimize variable costs. Confidence intervals were calculated on these end points by using Fieller's theorem and Monte-Carlo simulation. The 95% confidence intervals for increases in contribution margins or reductions in variable costs were 4.3% to 10.8% and 6.0% to 8.9%, respectively. As many as 22% of surgeons would have had OR time reduced because of sampling error. We recommend that physicians ask for and OR managers get confidence intervals of end points of financial analyses when making decisions based on them.
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paper_title: Management of surgical waiting lists through a Possibilistic Linear Multiobjective Programming problem

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This study attempts to apply a management science technique to improve the efficiency of Hospital Administration. We aim to design the performance of the surgical services at a Public Hospital that allows the Decision-Maker to plan surgical scheduling over one year in order to reduce waiting lists. Real decision problems usually involve several objectives that have parameters which are often given by the decision maker in an imprecise way. It is possible to handle these kinds of problems through multiple criteria models in terms of possibility theory. Here we apply a Possibilistic Linear Multiobjective Programming method, developed by the authors, for solving a hospital management problem using a Fuzzy Compromise Programming approach.
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paper_title: Consequences of running more operating theatres than anaesthetists to staff them: a stochastic simulation study

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Background Numerous hospitals implement a ratio of one anaesthetist supervising non-medically-qualified anaesthetist practitioners in two or more operating theatres. However, the risk of requiring anaesthetists simultaneously in several theatres due to concurrent critical periods has not been evaluated. It was examined in this simulation study. Methods Using a Monte Carlo stochastic simulation model, we calculated the risk of a staffing failure (no anaesthetist available when one is needed), in different scenarios of scheduling, staffing ratio, and number of theatres. Results With a staffing ratio of 0.5 for a two-theatre suite, the simulated risk that at least one failure occurring during a working day varied from 87% if only short operations were performed to 40% if only long operations performed (65% for a 50:50 mixture of short and long operations). Staffing-failure risk was particularly high during the first hour of the workday, and decreased as the number of theatres increased. The decrease was greater for simulations with only long operations than those with only short operations (the risk for 10 theatres declined to 12% and 74%, respectively). With a staffing ratio of 0.33, the staffing-failure risk was markedly higher than for a 0.5 ratio. The availability of a floater for the whole suite to intervene during failure strongly lowered this risk. Conclusions Scheduling one anaesthetist for two or three theatres exposes patients and staff to high risk of failure. Adequate planning of long and short operations and the presence of a floating anaesthetist are efficient means to optimize site activity and assure safety.
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paper_title: Managing uncertainty in orthopaedic trauma theatres

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Abstract The management of acute healthcare involves coping with a large uncertainty in demand. This uncertainty is a prevailing feature of orthopaedic care and many scarce resources are devoted to providing the contingent theatre time for orthopaedic trauma patients. However, given the variability and uncertainty in the demand much of the theatre time is not used. Simulation was used to explore the balance between maximising the utilisation of the theatre sessions, avoiding too many overruns and ensuring a reasonable quality of care in a typical hospital in the United Kingdom. The simulation was developed to examine a policy of including planned, elective patients within the trauma session: it appears that if patients are willing to accept a possibility of their treatment being cancelled, substantially greater throughputs can be achieved. A number of approximations were examined as an alternative to the full simulation: the simpler model offers reasonable accuracy and easier implementation.
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paper_title: Booked inpatient admissions and hospital capacity: mathematical modelling study.

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Abstract Objectives: To investigate the variability of patients9 length of stay in intensive care after cardiac surgery. To investigate potential interactions between such variability, booked admissions, and capacity requirements. Design: Mathematical modelling study using routinely collected data. Setting: A cardiac surgery department. Source of data: Hospital records of 7014 people entering intensive care after cardiac surgery. Main outcome measures: Length of stay in intensive care; capacity requirements of an intensive care unit for a hypothetical booked admission system. Results: Although the vast majority of patients (89.5%) had a length of stay in intensive care of ≤48 hours, there was considerable overall variability and the distribution of stays has a lengthy tail. A mathematical model of the operation of a hypothetical booking system indicates that such variability has a considerable impact on intensive care capacity requirements, indicating that a high degree of reserve capacity is required to avoid high rates of operation cancellation because of unavailability of suitable postoperative care. Conclusion: Despite the considerable enthusiasm for booked admissions systems, queuing theory suggests that caution is required when considering such systems for inpatient admissions. Such systems may well result in frequent operational difficulties if there is a high degree of variability in length of stay and where reserve capacity is limited. Both of these are common in the NHS. What is already known in this topic Booking systems for hospital admissions have considerable potential benefits for patients in terms of peace of mind and planning their lives, but these benefits are dependent on having a low cancellation rate What this study adds Variability in length of stay can have a major impact on hospital operation and capacity requirements. Operational research techniques can be used to explore this impact If variability in length of stay is substantial, as is common, then booked admission systems may require considerable reserve capacity if cancellation rates are to be kept low
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paper_title: A Norm Utilisation for Scarce Hospital Resources: Evidence from Operating Rooms in a Dutch University Hospital

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BACKGROUND ::: Utilisation of operating rooms is high on the agenda of hospital managers and researchers. Many efforts in the area of maximising the utilisation have been focussed on finding the holy grail of 100% utilisation. The utilisation that can be realised, however, depends on the patient mix and the willingness to accept the risk of working in overtime. ::: ::: ::: MATERIALS AND METHODS ::: This is a mathematical modelling study that investigates the association between the utilisation and the patient mix that is served and the risk of working in overtime. Prospectively, consecutively, and routinely collected data of an operating room department in a Dutch university hospital are used. Basic statistical principles are used to establish the relation between realistic utilisation rates, patient mixes, and accepted risk of overtime. ::: ::: ::: RESULTS ::: Accepting a low risk of overtime combined with a complex patient mix results a low utilisation rate. If the accepted risk of overtime is higher and the patient mix is less complex, the utilisation rate that can be reached is closer to 100%. ::: ::: ::: CONCLUSION ::: Because of the inherent variability of healthcare processes, the holy grail of 100% utilisation is unlikely to be found. The method proposed in this paper calculates a realistic benchmark utilisation that incorporates the patient mix characteristics and the willingness to accept risk of overtime.
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paper_title: Proactive and reactive strategies fot resource-constrained project scheduling with uncertain resource availabilities

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Research concerning project planning under uncertainty has primarily focused on the stochastic resource-constrained project scheduling problem (stochastic RCPSP), an extension of the basic RCPSP, in which the assumption of deterministic activity durations is dropped. In this paper, we introduce a new variant of the RCPSP, for which the uncertainty is modeled by means of resource availabilities that are subject to unforeseen breakdowns. Our objective is to build a robust schedule that meets the project deadline and minimizes the schedule instability cost, defined as the expected weighted sum of the absolute deviations between the planned and the actually realized activity starting times during project execution. We describe how stochastic resource breakdowns can be modeled, which reaction is recommended, when a resource infeasibility occurs due to a breakdown, and how one can protect the initial schedule from the adverse effects of potential breakdowns. An extensive computational experiment is used to show the relative performance of the proposed proactive and reactive strategies. It is shown that protection of the baseline schedule, coupled with intelligent schedule recovery, yields significant performance gains over the use of deterministic scheduling approaches in a stochastic setting.
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paper_title: Impact of surgical sequencing on post anesthesia care unit staffing

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This paper analyzes the impact of sequencing rules on the phase I post anesthesia care unit (PACU) staffing and over-utilized operating room (OR) time resulting from delays in PACU admission. The sequencing rules are applied to each surgeon's list of cases independently. Discrete event simulation shows the importance of having a sufficient number of PACU nurses. Sequencing rules have a large impact on the maximum number of patients receiving care in the PACU (i.e., peak of activity). Seven sequencing rules are tested, over a wide range of scenarios. The largest effect of sequencing was on the percentage of days with at least one delay in PACU admission. The best rules are those that smooth the flow of patients entering in the PACU (HIHD (Half Increase in OR time and Half Decrease in OR time) and MIX (MIX OR time)). We advise against using the LCF (Longest Cases First) and equivalent sequencing methods. They generate more over-utilized OR time, require more PACU nurses during the workday, and result in more days with at least one delay in PACU admission.
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paper_title: The operating theatre planning by the follow-up of the risk of no realization

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Abstract In the French context of healthcare expenses control, the operating theatre, that represents 9% of hospital's annual budget, presents a stake of major priority. The realization of the operating theatre planning is the fruit of negotiation of different actors of the block such as surgeons, anesthetists, nurses, managerial staff, etc. whose constraints and interests are often different. In this context, a win–win situation for this partnership (all parties involved) requires a good and constructive negotiation. In this paper, we propose an operating theatre planning procedure that aims at mastering the risk of no realization (RNR) of the tentative plan while stabilizing the operating rooms’ utilization time. During the application of this planning, we achieve the follow-up of the RNR and according to its evolution the research of another planning will be proposed in order to reduce the risk level. Finally, we present results obtained by simulations that support the interest for implementing these procedures.
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paper_title: Using Computer Simulation in Operating Room Management: Impacts on Process Engineering and Performance

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Operating rooms are regarded as the most costly hospital facilities. Due to rising costs and decreasing reimbursements, it is necessary to optimize the efficiency of the operating room suite. In this context several strategies have been proposed that optimize patient throughput by redesigning perioperative processes. The successful deployment of effective practices for continuous process improvements in operating rooms can require that operating room management sets targets and monitors improvements throughout all phases of process engineering. Simulation can be used to study the effects of process improvements through novel facilities, technologies and/or strategies. In this paper, we propose a conceptual framework to use computer simulations in different stages of business process management (BPM) lifecycle for operating room management. Additionally, we conduct simulation studies in different stages of the BPM lifecycle. The results of our studies provide evidence that simulation can provide effective decision support to drive performance in operating rooms in several phases of the BPM lifecycle
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paper_title: An observational study of surgeons' sequencing of cases and its impact on postanesthesia care unit and holding area staffing requirements at hospitals.

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BACKGROUND: Staffing requirements in the operating room (OR) holding area and in the Phase I postanesthesia care unit (PACU) are influenced by the sequencing of each surgeon's list of cases in the same OR on the same day. METHODS: Case sequencing was studied using 201 consecutive workdays of data from a 10 OR hospital surgical suite. RESULTS: The surgeons differed significantly among themselves in their sequencing of cases and were also internally nonsystematic, based on case durations. The functional effect of this uncoordinated sequencing was for the surgical suite to behave overall as if there was random sequencing. The resulting PACU staffing requirements were the same as those of the best sequencing method identified in prior simulation studies. Although sequencing "Longest Cases First" performs poorly when all ORs have close to 8 h of cases, at the studied hospital it performed no worse than the other methods. The reason was that some ORs were much busier than others on the same day. The standard deviation among ORs in the hours of cases, including turnovers, was 3.2 h; large relative to the mean workload. Data from 33 other hospitals confirmed that this situation is commonplace. Additional studies showed that case sequencing also had minimal effects on the peak number of patients in the holding area. CONCLUSIONS: The uncoordinated decision-making of multiple surgeons working in different ORs can result in a sufficiently uniform rate of admission of patients into the PACU and holding that the independent sequencing of each surgeon's list of cases would not reduce the incidence of delays in admission or staffing requirements.
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paper_title: Scheduling hospital services: the efficacy of elective-surgery quotas

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We take advantage of the advance-scheduling property for elective surgeries by exploring whether the use of a daily quota system with a 1-week or 2-week scheduling window would improve the performance of a typical intensive care unit (ICU) that serves patients coming from a number of different sources within the hospital. The exploration is carried out via a simulation model whose parameters are established from actual ICU data that were gathered over a 6-month period. It is shown that formally linking one controllable upstream process, namely the scheduling of elective surgeries through a quota system, to the downstream ICU admission process, can have beneficial effects throughout the hospital.
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paper_title: A three-phase approach for operating theatre schedules

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In this paper we develop a three-phase, hierarchical approach for the weekly scheduling of operating rooms. This approach has been implemented in one of the surgical departments of a public hospital located in Genova (Genoa), Italy. Our aim is to suggest an integrated way of facing surgical activity planning in order to improve overall operating theatre efficiency in terms of overtime and throughput as well as waiting list reduction, while improving department organization. In the first phase we solve a bin packing-like problem in order to select the number of sessions to be weekly scheduled for each ward; the proposed and original selection criterion is based upon an updated priority score taking into proper account both the waiting list of each ward and the reduction of residual ward demand. Then we use a blocked booking method for determining optimal time tables, denoted Master Surgical Schedule (MSS), by defining the assignment between wards and surgery rooms. Lastly, once the MSS has been determined we use the simulation software environment Witness 2004 in order to analyze different sequencings of surgical activities that arise when priority is given on the basis of a) the longest waiting time (LWT), b) the longest processing time (LPT) and c) the shortest processing time (SPT). The resulting simulation models also allow us to outline possible organizational improvements in surgical activity. The results of an extensive computational experimentation pertaining to the studied surgical department are here given and analyzed.
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paper_title: Simulation of a Multiple Operating Room Surgical Suite

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Outpatient surgery scheduling involves the coordination of several activities in an uncertain environment. Due to the very customized nature of surgical procedures there is significant uncertainty in the duration of activities related to the intake process, surgical procedure, and recovery process. Furthermore, there are multiple criteria which must be traded off when considering how to schedule surgical procedures including patient waiting, operating room (OR) team waiting, OR idling, and overtime for the surgical suite. Uncertainty combined with the need to tradeoff many criteria makes scheduling a complex task for OR managers. In this article we present a simulation model for a multiple OR surgical suite, describe some of the scheduling challenges, and illustrate how the model can be used as a decisions aid to improve strategic and operational decision making relating to the delivery of surgical services. All results presented are based on real data collected at Mayo Clinic in Rochester, MN.
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paper_title: Managing risk and expected financial return from selective expansion of operating room capacity: mean-variance analysis of a hospital's portfolio of surgeons.

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Surgeons using the same amount of operating room (OR) time differ in their achieved hospital contribution margins (revenue minus variable costs) by >1000%. Thus, to improve the financial return from perioperative facilities, OR strategic decisions should selectively focus additional OR capacity and capital purchasing on a few surgeons or subspecialties. These decisions use estimates of each surgeon's and/or subspecialty's contribution margin per OR hour. The estimates are subject to uncertainty (e.g., from outliers). We account for the uncertainties by using mean-variance portfolio analysis (i.e., quadratic programming). This method characterizes the problem of selectively expanding OR capacity based on the expected financial return and risk of different portfolios of surgeons. The assessment reveals whether the choices, of which surgeons have their OR capacity expanded, are sensitive to the uncertainties in the surgeons' contribution margins per OR hour. Thus, mean-variance analysis reduces the chance of making strategic decisions based on spurious information. We also assess the financial benefit of using mean-variance portfolio analysis when the planned expansion of OR capacity is well diversified over at least several surgeons or subspecialties. Our results show that, in such circumstances, there may be little benefit from further changing the portfolio to reduce its financial risk.
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paper_title: Determining Optimum Operating Room Utilization

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UNLABELLED ::: Economic considerations suggest that it is desirable to keep operating rooms fully used when staffed, but the optimum utilization of an operating room (OR) is not known. We created a simulation of an OR to define optimum utilization. We set operational goals of having cases start within 15 min of the scheduled time and of having the cases end no more than 15 min past the scheduled end of the day. Within these goals, a utilization of 85% to 90% is the highest that can be achieved without delay or running late. Increasing the variability of case duration decreases the utilization that can be achieved within these targets. ::: ::: ::: IMPLICATIONS ::: Using a simulated operating room (OR), the authors demonstrate that OR utilization higher than 85% to 90% leads to patient delays and staff overtime. Increased efficiency of an OR comes at a cost of patient convenience.
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paper_title: A stochastic model for operating room planning with elective and emergency demand for surgery

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This paper describes a stochastic model for Operating Room (OR) planning with two types of demand for surgery: elective surgery and emergency surgery. Elective cases can be planned ahead and have a patient-related cost depending on the surgery date. Emergency cases arrive randomly and have to be performed on the day of arrival. The planning problem consists in assigning elective cases to different periods over a planning horizon in order to minimize the sum of elective patient related costs and overtime costs of operating rooms. A new stochastic mathematical programming model is first proposed. We then propose a Monte Carlo optimization method combining Monte Carlo simulation and Mixed Integer Programming. The solution of this method is proved to converge to a real optimum as the computation budget increases. Numerical results show that important gains can be realized by using a stochastic OR planning model.
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paper_title: Hospital Operating Room Capacity Expansion

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A large midwestern hospital is expecting an increase in surgical caseload. New operating room (OR) capacity can be had by building new ORs or extending the working hours in the current ORs. The choice among these options is complicated by the fact that patients, surgeons and surgical staff, and hospital administrators are all important stakeholders in the health service operation, and each has different priorities. This paper investigates the trade-offs among three performance criteria (wait to get on schedule, scheduled procedure start-time reliability, and hospital profits), which are of particular importance to the different constituencies. The objective is to determine how the hospital can best expand its capacity, acknowledging the key role that each constituency plays in that objective. En route, the paper presents supporting analysis for process improvements and suggestions for optimal participation-inducing staff contracts for extending OR hours of operation.
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paper_title: A Sequential Bounding Approach for Optimal Appointment Scheduling

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This study is concerned with the determination of optimal appointment times for a sequence of jobs with uncertain durations. Such appointment systems are used in many customer service applications to increase the utilization of resources, match workload to available capacity, and smooth the flow of customers. We show that the problem can be expressed as a two-stage stochastic linear program that includes the expected cost of customer waiting, server idling, and a cost of tardiness with respect to a chosen session length. We exploit the problem structure to derive upper bounds that are independent of job duration distribution type. These upper bounds are used in a variation of the standard L-shaped algorithm to obtain optimal solutions via successively finer partitions of the support of job durations. We present new analytical insights into the problem as well as a series of numerical experiments that illustrate properties of the optimal solution with respect to distribution type, cost structure, and number of jobs.
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paper_title: Optimization of surgery sequencing and scheduling decisions under uncertainty

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Operating rooms (ORs) are simultaneously the largest cost center and greatest source of revenues for most hospitals. Due to significant uncertainty in surgery durations, scheduling of ORs can be very challenging. Longer than average surgery durations result in late starts not only for the next surgery in the schedule, but potentially for the rest of the surgeries in the day as well. Late starts also result in direct costs associated with overtime staffing when the last surgery of the day finishes later than the scheduled shift end time. In this article we describe a stochastic optimization model and some practical heuristics for computing OR schedules that hedge against the uncertainty in surgery durations. We focus on the simultaneous effects of sequencing surgeries and scheduling start times. We show that a simple sequencing rule based on surgery duration variance can be used to generate substantial reductions in total surgeon and OR team waiting, OR idling, and overtime costs. We illustrate this with results of a case study that uses real data to compare actual schedules at a particular hospital to those recommended by our model.
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paper_title: A strategy to decide whether to move the last case of the day in an operating room to another empty operating room to decrease overtime labor costs.

paper_content:

We examined how to program an operating room (OR) information system to assist the OR manager in deciding whether to move the last case of the day in one OR to another OR that is empty to decrease overtime labor costs. We first developed a statistical strategy to predict whether moving the case would decrease overtime labor costs for first shift nurses and anesthesia providers. The strategy was based on using historical case duration data stored in a surgical services information system. Second, we estimated the incremental overtime labor costs achieved if our strategy was used for moving cases versus movement of cases by an OR manager who knew in advance exactly how long each case would last. We found that if our strategy was used to decide whether to move cases, then depending on parameter values, only 2.0 to 4.3 more min of overtime would be required per case than if the OR manager had perfect retrospective knowledge of case durations. The use of other information technologies to assist in the decision of whether to move a case, such as real-time patient tracking information systems, closed-circuit cameras, or graphical airport-style displays can, on average, reduce overtime by no more than only 2 to 4 min per case that can be moved.
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paper_title: The use of Simulation to Determine Maximum Capacity in the Surgical Suite Operating Room

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Utilizing ambulatory care units at optimal levels has become increasingly important to hospitals from both service and business perspectives. With the inherent variation in hospitals due to unique procedures and patients, performing capacity analysis through analytical models is difficult without making simplifying assumptions. Many hospitals calculate efficiency by comparing total operating room minutes available to total operating minutes used. This metric both fails to account for the required non-value added tasks between surgeries and the delicate balance necessary between having patients ready for surgery when an operating room becomes available, which can result in increased waiting times, and maximizing patient satisfaction. We present a general methodology for determining the maximum capacity within a surgical suite through the use of a discrete-event simulation model. This research is based on an actual hospital concerned with doctor/resource acquisition decisions, patient satisfaction improvements, and increased productivity.
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paper_title: Building cyclic master surgery schedules with leveled resulting bed occupancy

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This paper proposes and evaluates a number of models for building surgery schedules with leveled resulting bed occupancy. The developed models involve two types of constraints. Demand constraints ensure that each surgeon (or surgical group) obtains a specific number of operating room blocks. Capacity constraints limit the available blocks on each day. Furthermore, the number of operated patients per block and the length of stay of each operated patient are dependent on the type of surgery. Both are considered stochastic, following a multinomial distribution. We develop a number of mixed integer programming based heuristics and a metaheuristic to minimize the expected total bed shortage and present computational results.
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paper_title: Closing Emergency Operating Rooms Improves Efficiency

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Long waiting times for emergency operations increase a patient's risk of postoperative complications and morbidity. Reserving Operating Room (OR) capacity is a common technique to maximize the responsiveness of an OR in case of arrival of an emergency patient. This study determines the best way to reserve OR time for emergency surgery. In this study two approaches of reserving capacity were compared: (1) concentrating all reserved OR capacity in dedicated emergency ORs, and (2) evenly reserving capacity in all elective ORs. By using a discrete event simulation model the real situation was modelled. Main outcome measures were: (1) waiting time, (2) staff overtime, and (3) OR utilisation were evaluated for the two approaches. Results indicated that the policy of reserving capacity for emergency surgery in all elective ORs led to an improvement in waiting times for emergency surgery from 74 (±4.4) minutes to 8 (±0.5) min. Working in overtime was reduced by 20%, and overall OR utilisation can increase by around 3%. Emergency patients are operated upon more efficiently on elective Operating Rooms instead of a dedicated Emergency OR. The results of this study led to closing of the Emergency OR in the Erasmus MC (Rotterdam, The Netherlands).
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paper_title: Scheduling Surgical Cases into Overflow Block Time— Computer Simulation of the Effects of Scheduling Strategies on Operating Room Labor Costs

paper_content:

“Overflow” block time is operating room (OR) time for a surgical group’s cases that cannot be completed in the regular block time allocated to each surgeon in the surgical group. Having such overflow block time increases OR utilization. The optimal way to schedule patients into a surgical group’s ov
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paper_title: Robust surgery loading

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We consider the robust surgery loading problem for a hospital’s operating theatre department, which concerns assigning surgeries and sufficient planned slack to operating room days. The objective is to maximize capacity utilization and minimize the risk of overtime, and thus cancelled patients. This research was performed in collaboration with the Erasmus MC, a large academic hospital in the Netherlands, which has also provided historical data for the experiments. We propose various constructive heuristics and local search methods that use statistical information on surgery durations to exploit the portfolio effect, and thereby to minimize the required slack. We demonstrate that our approach frees a lot of operating room capacity, which may be used to perform additional surgeries. Furthermore, we show that by combining advanced optimization techniques with extensive historical statistical records on surgery durations can significantly improve the operating room department utilization.
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paper_title: Operating Room Utilization Alone Is Not an Accurate Metric for the Allocation of Operating Room Block Time to Individual Surgeons with Low Caseloads

paper_content:

Introduction Many surgical suites allocate operating room (OR) block time to individual surgeons. If block time is allocated to services/groups and yet the same surgeon invariably operates on the same weekday, for all practical purposes block time is being allocated to individual surgeons.Organizational conflict occurs when a surgeon with a relatively low OR utilization has his or her allocated block time reduced. The authors studied potential limitations affecting whether a facility can accurately estimate the average block time utilizations of individual surgeons performing low volumes of cases. Methods Discrete-event computer simulation. Results Neither 3 months nor 1 yr of historical data were enough to be able to identify surgeons who had persistently low average OR utilizations. For example, with 3 months of data, the widths of the 95% CIs for average OR utilization exceeded 10% for surgeons who had average raw utilizations of 83% or less. If during a 3-month period a surgeon's measured adjusted utilization is 65%, there is a 95% chance that the surgeon's average adjusted utilization is as low as 38% or as high as 83%. If two surgeons have measured adjusted utilizations of 65% and 80%, respectively, there is a 16% chance that they have the same average adjusted utilization. Average OR utilization can be estimated more precisely for surgeons performing more cases each week. Conclusions Average OR utilization probably cannot be estimated precisely for low-volume surgeons based on 3 months or 1 yr of historical OR utilization data. The authors recommend that at surgical suites trying to allocate OR time to individual low-volume surgeons, OR allocations be based on criteria other than only OR utilization (e.g., based on OR efficiency).
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paper_title: How to Schedule Elective Surgical Cases into Specific Operating Rooms to Maximize the Efficiency of Use of Operating Room Time

paper_content:

We considered elective case scheduling at hospitals and surgical centers at which surgeons and patients choose the day of surgery, cases are not turned away, and anesthesia and nursing staffing are adjusted to maximize the efficiency of use of operating room (OR) time. We investigated scheduling a new case into an OR by using two patient-scheduling rules: Earliest Start Time or Latest Start Time. By using several scenarios, we showed that the use of Earliest Start Time is rational economically at such facilities. Specifically, it maximizes OR efficiency when a service has nearly filled its regularly scheduled hours of OR time. However, Latest Start Time will perform better at balancing workload among services’ OR time. We then used historical case duration data from two facilities in computer simulations to investigate the effect of errors in predicting case durations on the performance of these two heuristics. The achievable incremental reduction in overtime by having perfect information on case duration versus using historical case durations was only a few minutes per OR. The differences between Earliest Start Time and Latest Start Time were also only a few minutes per OR. We conclude that for facilities at which the goals are, in order of importance, safety, patient and surgeon access to OR time, and then efficiency, few restrictions need to be placed on patient scheduling to achieve an efficient use of OR time. (Anesth Analg 2002;94:933–42)
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paper_title: Schedule the Short Procedure First to Improve OR Efficiency

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ABSTRACT • OPERATING ROOM MANAGERS are hampered in their efforts to optimize OR efficiency by surgical procedures that last a longer or shorter time than scheduled. The lack of predictability is a result of inaccuracy in scheduling and variability in the duration of procedures. • SCHEDULING SHORT PROCEDURES before long procedures theoretically limits this variability. • MONTE CARLO SIMULATION of ORs scheduled with various combinations of short and long procedures supports this concept's validity. • RESULTS INDICATE that scheduling short procedures first can improve on-time performance and decrease staff member overtime expense without reducing surgical throughput. AORNJ 78 (October 2003) 651–657.
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paper_title: The value of the dedicated orthopaedic trauma operating room.

paper_content:

Background:Trauma centers and orthopaedic surgeons have traditionally been faced with limited operating room (OR) availability for fracture surgery. Orthopaedic trauma cases are often waitlisted and done late at night. We investigated the feasibility of having an unbooked orthopaedic trauma OR to re
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paper_title: The impact of service-specific staffing, case scheduling, turnovers, and first-case starts on anesthesia group and operating room productivity: a tutorial using data from an Australian hospital.

paper_content:

BACKGROUND ::: In this tutorial, we consider the impact of operating room (OR) management on anesthesia group and OR labor productivity and costs. Most of the tutorial focuses on the steps required for each facility to refine its OR allocations using its own data collected during patient care. ::: ::: ::: METHODS ::: Data from a hospital in Australia are used throughout to illustrate the methods. OR allocation is a two-stage process. During the initial tactical stage of allocating OR time, OR capacity ("block time") is adjusted. For operational decision-making on a shorter-term basis, the existing workload can be considered fixed. Staffing is matched to that workload based on maximizing the efficiency of use of OR time. ::: ::: ::: RESULTS ::: Scheduling cases and making decisions on the day of surgery to increase OR efficiency are worthwhile interventions to increase anesthesia group productivity. However, by far, the most important step is the appropriate refinement of OR allocations (i.e., planning service-specific staffing) 2-3 mo before the day of surgery. ::: ::: ::: CONCLUSIONS ::: Reducing surgical and/or turnover times and delays in first-case-of-the-day starts generally provides small reductions in OR labor costs. Results vary widely because they are highly sensitive both to the OR allocations (i.e., staffing) and to the appropriateness of those OR allocations.
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paper_title: Improving operating room efficiency by applying bin-packing and portfolio techniques to surgical case scheduling.

paper_content:

BACKGROUND ::: An operating room (OR) department has adopted an efficient business model and subsequently investigated how efficiency could be further improved. The aim of this study is to show the efficiency improvement of lowering organizational barriers and applying advanced mathematical techniques. ::: ::: ::: METHODS ::: We applied advanced mathematical algorithms in combination with scenarios that model relaxation of various organizational barriers using prospectively collected data. The setting is the main inpatient OR department of a university hospital, which sets its surgical case schedules 2 wk in advance using a block planning method. The main outcome measures are the number of freed OR blocks and OR utilization. ::: ::: ::: RESULTS ::: Lowering organizational barriers and applying mathematical algorithms can yield a 4.5% point increase in OR utilization (95% confidence interval 4.0%-5.0%). This is obtained by reducing the total required OR time. ::: ::: ::: CONCLUSIONS ::: Efficient OR departments can further improve their efficiency. The paper shows that a radical cultural change that comprises the use of mathematical algorithms and lowering organizational barriers improves OR utilization.
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paper_title: Analyzing incentives and scheduling in a major metropolitan hospital operating room through simulation

paper_content:

This paper discusses the application of simulation to analyze the value proposition and construction of an incentive program in an operating room (OR) environment. The model was further used to evaluate operational changes including scheduling processes within the OR and utilization rates in areas such as post anesthesia care unit (PACU) and the ambulatory surgery department (ASD). Lessons learned are presented on developing multiple simulation models from one application as well as issues regarding model transition to a client.
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paper_title: Operating room management and strategies in Switzerland: results of a survey.

paper_content:

Background and objective: Operating room management structures and interrelationships both within the operating suite and with other departments in the hospital can be very complex. Several different professional and support groups are represented that often have infrastructures of their own that may compete or conflict with the management hierarchy in the operating room. Today, there is often little actual management of the operating suite as an entity. We surveyed current operating room management in Switzerland. Methods: A questionnaire was sent to the chief anaesthesiologists of all public hospitals in Switzerland. It asked for information about the structure, organization and management of operating rooms as well as respondents' opinions and expectations about management. Derived from both the literature and the results of the survey, a 'stages of excellence' model of best practice was developed. Results: The overall response rate was 70%. Most anaesthesiologists were unsatisfied with current management policies and structures in their operating rooms. Of the hospitals questioned, 40% did not have an information system at all for the operating rooms. The remaining 60% had an information system that allowed rough scheduling in 71%, but only a few had more sophisticated systems that enabled dynamic scheduling (19%), user-defined conflict checking (5%), administration of a subsequent patient transfer station (postanaesthesia care units, intensive medical care, intensive care units) (10%) or other more advanced uses. All hospitals questioned offered some type of ambulatory surgery in a 'hospital-integrated' manner (i.e. use of the same operating room for both in- and outpatient surgery), but none had implemented a more efficient system where outpatient surgery was performed in separate facilities. Conclusions: Current management of the operating room in Switzerland is far from best-practice standards.
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paper_title: A three-phase approach for operating theatre schedules

paper_content:

In this paper we develop a three-phase, hierarchical approach for the weekly scheduling of operating rooms. This approach has been implemented in one of the surgical departments of a public hospital located in Genova (Genoa), Italy. Our aim is to suggest an integrated way of facing surgical activity planning in order to improve overall operating theatre efficiency in terms of overtime and throughput as well as waiting list reduction, while improving department organization. In the first phase we solve a bin packing-like problem in order to select the number of sessions to be weekly scheduled for each ward; the proposed and original selection criterion is based upon an updated priority score taking into proper account both the waiting list of each ward and the reduction of residual ward demand. Then we use a blocked booking method for determining optimal time tables, denoted Master Surgical Schedule (MSS), by defining the assignment between wards and surgery rooms. Lastly, once the MSS has been determined we use the simulation software environment Witness 2004 in order to analyze different sequencings of surgical activities that arise when priority is given on the basis of a) the longest waiting time (LWT), b) the longest processing time (LPT) and c) the shortest processing time (SPT). The resulting simulation models also allow us to outline possible organizational improvements in surgical activity. The results of an extensive computational experimentation pertaining to the studied surgical department are here given and analyzed.
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paper_title: Operating room managers' use of integer programming for assigning block time to surgical groups: a case study.

paper_content:

UNLABELLED ::: A common problem at hospitals with fixed amounts of available operating room (OR) time (i.e., "block time") is determining an equitable method of distributing time to surgical groups. Typically, facilities determine a surgical group's share of available block time using formulas based on OR utilization, contribution margin, or some other performance metric. Once each group's share of time has been calculated, a method must be found for fitting each group's allocated OR time into the surgical master schedule. This involves assigning specific ORs on specific days of the week to specific surgical groups, usually with the objective of ensuring that the time assigned to each group is close to its target share. Unfortunately, the target allocated to a group is rarely expressible as a multiple of whole blocks. In this paper, we describe a hospital's experience using the mathematical technique of integer programming to solve the problem of developing a consistent schedule that minimizes the shortfall between each group's target and actual assignment of OR time. Schedule accuracy, the sum over all surgical groups of shortfalls divided by the total time available on the schedule, was 99.7% (SD 0.1%, n = 11). Simulations show the algorithm's accuracy can exceed 97% with > or =4 ORs. The method is a systematic and successful way to assign OR blocks to surgeons. ::: ::: ::: IMPLICATIONS ::: At hospitals with a fixed budget of operating room (OR) time, integer programming can be used by OR managers to decide which surgical group is to be allocated which OR on which day(s) of the week. In this case study, we describe the successful application of integer programming to this task, and discuss the applicability of the results to other hospitals.
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paper_title: Mount Sinai Hospital Uses Integer Programming to Allocate Operating Room Time

paper_content:

In concentrating polymer solutions up to a desired specification level of residual solvents, encrustations can be prevented and the yield and the degree of purity can be increased, when the product is heated up under pressure, expanded through a restrictor element (3) with vapor formation into a first, preferably coiled flow pipe (7) and concentrated therein as far as possible, the mixture of vapors and polymer solution is whirled at an angle into a second flow pipe (9) in a sloping arrangement and fitted with self-cleaning elements (11, 12) and concentrated therein up to the desired level, and vapors and concentrate are separately discharged only downstream thereof.
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paper_title: What is the role and contribution of models to management and research in the health services? A view from Europe

paper_content:

Abstract Modelling in different forms has long been regarded as a cornerstone of health OR as in other fields of application. Models are now tending to become a standard tool in health services management and research. What are the lessons we as operational researchers have learnt during this development? How can health care managers and health service researchers benefit from modelling — with or without OR-analysts to guide them between the pitfalls? After an introductory overview concerning the nature and objectives of modelling, examples will be given of modelling applications from different health service areas in order to illustrate the versatility of the method. Further, the choice of methods and models is discussed with special attention to the problems of interpretation and implementation of results. From this overview some conclusions are drawn with regards to advantages and disadvantages of modelling as tools for policy planning and decision-making in the health area. Finally some observations are made concercing the conditions for the future development in the field.
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paper_title: The value of the dedicated orthopaedic trauma operating room.

paper_content:

Background:Trauma centers and orthopaedic surgeons have traditionally been faced with limited operating room (OR) availability for fracture surgery. Orthopaedic trauma cases are often waitlisted and done late at night. We investigated the feasibility of having an unbooked orthopaedic trauma OR to re
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paper_title: A goal programming approach to strategic resource allocation in acute care hospitals

paper_content:

Abstract This paper describes a methodology for allocating resources in hospitals. The methodology uses two linear goal-programming models. One model sets case mix and volume for physicians, while holding service costs fixed; the other translates case mix decisions into a commensurate set of practice changes for physicians. The models allow decision makers to set case mix and case costs in such a way that the institution is able to break even, while preserving physician income and minimizing disturbance to practice. The models also permit investigation of trade-offs between case mix and physician practice parameters. Results are presented from a decision-making scenario facing the surgical division of Toronto's Mount Sinai Hospital after the announcement of a 3-year, 18% reduction in funding.
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Title: Operating Room Planning and Scheduling: A Literature Review

Section 1: Introduction
Description 1: Introduce the importance and challenges of managing operating rooms in hospitals, and outline the goals and structure of the review.

Section 2: Patient Characteristics
Description 2: Describe the classification of patients (elective and non-elective) and discuss different approaches to planning and scheduling for these categories.

Section 3: Performance Measures
Description 3: Summarize the various criteria used to evaluate the performance of planning and scheduling methods, such as waiting time, resource utilization, and financial criteria.

Section 4: Decision Level
Description 4: Discuss the different levels at which planning and scheduling decisions are made, and summarize the types of decisions considered in the literature.

Section 5: Type of Analysis
Description 5: Outline the various types of analytical methods used, including optimization, simulation, and scenario analysis, and describe how each method is applied to operating room planning and scheduling.

Section 6: Solution Technique
Description 6: Review the specific solution techniques that are applied in the literature, including mathematical programming, heuristics, and meta-heuristics.

Section 7: Uncertainty
Description 7: Examine how uncertainty is incorporated into planning and scheduling models, highlighting types of uncertainty such as arrival and duration variability.

Section 8: Applicability of Research
Description 8: Discuss the extent to which research findings have been tested and implemented in practice, and identify gaps between theory and practice.

Section 9: Conclusion
Description 9: Summarize the key findings of the review, highlight major trends, and suggest areas for future research.