A Review of Methods and Algorithms for Optimizing Construction Scheduling
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paper_title: Scheduling Construction Projects Using Evolutionary Algorithm

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This paper attempts to use evolutionary algorithms to solve the problem of minimizing construction project duration in deterministic conditions, with in-time changeable and limited accessibility of renewable resources (workforce, machines, and equipment). Particular construction processes (with various levels of complexity) must be conducted in the established technological order and can be executed with different technological and organizational variants (different contractors, technologies, and ways of using resources). Such a description of realization conditions allows the method to also be applied to solving more complex problems that occur in construction practice (e.g., scheduling resources for a whole company, not only for a single project). The method's versatility distinguishes it from other approaches presented in numerous publications. To assess the solutions generated by the evolutionary algorithm, the writers worked a heuristic algorithm (for the allocation of resources and the calculation of the shortest project duration). The results obtained by means of this methodology seem to be similar to outcomes of other comparable methodologies. The proposed methodology (the model and the computer system) may be of great significance to the construction industry. The paper contains some examples of the practical use of the evolutionary algorithm for project planning with time constraints.
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paper_title: A Pattern-Based Approach for Facilitating Schedule Generation and Cost Analysis in Bridge Construction Projects

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The paper presents a computational method to help in automating the generation of time schedules for bridge construction projects. The method is based on the simulation of the construction works, taking into account the available resources and the interdependencies between the individual tasks. The simulation is realized by means of the discrete-event based simulation software originally created for plant layout in the manufacturing industry. Since the fixed process chains provided there are too rigid to model the more spontaneous task sequences of construction projects, a constraint module that selects the next task dynamically has been incorporated. The input data of the constraint module is formed by work packages of atomic activities. The description of a work package comprises the building element affected, the required material, machine and manpower resources, as well as the technological pre-requisites of the task to be performed. These input data are created with the help of a 3D model-based application that enables to assign process patterns to individual building elements. A process pattern consists of a sequence of work packages for realizing standard bridge parts, thus describing a construction method which in turn represents a higher level of abstraction in the scheduling process. In the last step, the user specifies the available resources. The system uses all the given information to automatically create a proposal for the construction schedule, which may then be refined using standard scheduling software.
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paper_title: Genetic algorithms for multi-constraint scheduling: an application for the construction industry

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SUMMARY Reliable construction schedule is vital for effective co-ordination across supply chains and various trades at construction work face. According to the lean construction concept, reliability of the schedule can be enhanced through detection and satisfaction of all potential constraints prior to releasing operation assignments. However, it is difficult to implement this concept since current scheduling tools and techniques are fragmented and designed to deal with a limited set of construction constraints. This paper introduces a methodology termed ‘multi-constraint scheduling’ in which four major groups of construction constraints including physical, contract, resource, and information constraints are considered. A Genetic Algorithm (GA) has been developed and used for multi-constraint optimisation problem. Given multiple constraints such as activity dependency, limited working area, and resource and information readiness, the GA alters tasks’ priorities and construction methods so as to arrive at optimum or near optimum set of project duration, cost, and smooth resource profiles. This feature has been practically developed as an embedded macro in MS Project. Several experiments confirmed that GA can provide near optimum solutions within acceptable searching time (i.e. 5 minutes for 1.92E11 alternatives). Possible improvements to this research are further suggested in the paper.
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paper_title: Intelligent optimization for project scheduling of the first mining face in coal mining

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In this paper, the intelligent optimization methods including genetic algorithm (GA), particle swarm optimization (PSO) and modified particle swarm optimization (MPSO) are used in optimizing the project scheduling of the first mining face of the second region of the fifth Ping'an coal mine in China. The result of optimization provides essential information of management and decision-making for governors and builder. The process of optimization contains two parts: the first part is obtaining the time parameters of each process and the network graph of the first mining face in the second region by PERT (program evaluation and review technique) method based on the raw data. The other part is the second optimization to maximal NPV (net present value) based on the network graph. The starting dates of all processes are decision-making variables. The process order and time are the constraints. The optimization result shows that MPSO is better than GA and PSO and the optimized NPV is 14,974,000 RMB more than the original plan.
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paper_title: Incorporating Practicability into Genetic Algorithm-Based Time-Cost Optimization

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Optimization problems in construction scheduling, such as time-cost optimization, can be effectively solved using genetic algorithms (GAs). This paper presents an approach that makes GA-based time-cost optimization viable for real world problems. Practicability is incorporated through the integration of a project management system to the GA system. The approach takes advantage of the powerful scheduling functionality of the project management system in evaluating project completion dates during optimization. The approach ensures that all scheduling parameters, including activity relationships, lags, calendars, constraints, resources, and progress, are considered in determining the project completion date, thus allowing comprehensive and realistic evaluations to be made during optimization.
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paper_title: A two-phase GA model for resource-constrained project scheduling

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In construction scheduling, problems can arise when each activity could start at different time points and the resources needed by the activities are limited. Moreover, activities have required conditions to be met, such as precedence relationships, resource requirements, etc. To resolve these problems, a two-phase GA (genetic algorithm) model is proposed in this paper, in which both the effects of time-cost trade-off and resource scheduling are taken into account. A GA-based time-cost trade-off analysis is adopted to select the execution mode of each activity through the balance of time and cost, followed by utilization of a GA-based resource scheduling method to generate a feasible schedule which may satisfy all the project constraints. Finally, the model is demonstrated using an example project and a real project.
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paper_title: Planning and estimating in practice and the use of integrated computer models

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Abstract Research into IT applications in the construction industry has been going on for many years, most of this work took the form of system development aimed at assisting construction practitioners and aimed at improving processes in order to reduce the cost of building. Most of these developments tended to identify a problem in a sector of theindustry and focused on using a certain technology in IT to provide a solution. This was often done without a proper investigation into the suitability and the acceptability of the technology to the end users (construction practitioners). Furthermore, most of the work was too focused on solving problems in isolation and did not consider the overall organisational framework and structure of the industry. This paper discusses and presents the results of a survey conducted to investigate the planning and estimating work practices in the industry in order to establish the important issues for the development of an integrated planning and estimating computer model. The survey established the important issues for the acceptability of computer models, the technical aspect to be addressed and a better working practice for estimating and planning. The technical aspect on which the computer model was based is the optimisation of the time and cost of building and the best work practice used is the integration of estimating and planning.
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paper_title: SOFT LOGIC IN NETWORK ANALYSIS

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One of the most important functions of planning is to offset uncertainty and change. However, projects are often affected by external factors or constraints that can either facilitate progress or create delays in the project. Sometimes, logic changes can be inevitable. Therefore, special techniques are needed to provide a simple way of network updating in order to reflect the impact of logic change on project completion date and on the critical path. This paper addresses the problem of soft logic and discusses logic changes during the course of the work. An algorithmic procedure has been developed to handle the soft logic in network analysis. SOFTCPM is a microcomputer program created by the writers that deals with the soft logic in CPM networks. It has the capability of updating the CPM network logic when any unexpected event occurs that prevents working according to the scheduled activity sequence.
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paper_title: A Simple CPM Time-Cost Tradeoff Algorithm

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This article describes an algorithm for efficiently shortening the duration of a project when the expected project duration exceeds a predetermined limit. The problem consists of determining which activities to expedite and by what amount. The objective is to minimize the cost of the project. ::: ::: This algorithm is considerably less complex than the analytic methods currently available. Because of its inherent simplicity, the algorithm is ideally suited for hand computation and also is suitable for computer solution. Solutions derived by the algorithm were compared with linear programming results. These comparisons revealed that the algorithm solutions are either a equally good or b nearly the same as the solutions obtained by more complex analytic methods which require a computer. ::: ::: With this method the CPM time-cost tradeoff problem is solved without access to a computer, thereby making this planning tool available to managers who otherwise would find implementation impractical.
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paper_title: A new exact penalty function method for continuous inequality constrained optimization problems

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In this paper, a computational approach based on a new exact penalty ::: function method is devised for solving a class of continuous ::: inequality constrained optimization problems. The continuous ::: inequality constraints are first approximated by smooth function in ::: integral form. Then, we construct a new exact penalty function, ::: where the summation of all these approximate smooth functions in ::: integral form, called the constraint violation, is appended to the ::: objective function. In this way, we obtain a sequence of approximate ::: unconstrained optimization problems. It is shown that if the value ::: of the penalty parameter is sufficiently large, then any local ::: minimizer of the corresponding unconstrained optimization problem is ::: a local minimizer of the original problem. For illustration, three ::: examples are solved using the proposed method. From the solutions ::: obtained, we observe that the values of their objective functions ::: are amongst the smallest when compared with those obtained by other ::: existing methods available in the literature. More importantly, our ::: method finds solution which satisfies the continuous inequality ::: constraints.
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paper_title: Project Scheduling Problems: A Survey

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A survey of project scheduling problems since 1973 limited to work done specifically in the project scheduling area (although several techniques developed for assembly line balancing and job‐shop scheduling can be applicable to project scheduling): the survey includes the work done on fundamental problems such as the resource‐constrained project scheduling problem (RCPSP); time/cost trade‐off problem (TCTP); and payment scheduling problem (PSP). Also discusses some recent research that integrates RCPSP with either TCTP or PSP, and PSP with TCTP. In spite of their practical relevance, very little work has been done on these combined problems to date. The future of the project scheduling literature appears to be developing in the direction of combining the fundamental problems and developing efficient exact and heuristic methods for the resulting problems.
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paper_title: Multi-Objective Optimization of Construction Schedules

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This paper focuses on the multi-objective deterministic and stochastic modelling and optimization of construction tasks scheduling. Of particular importance is a frequency need to satisfy conflicting optimization objectives such as the minimization of extra task performance cost and total performance time. Technological relationships between relevant construction tasks have been modelled using the deterministic and probabilistic precedence networks, while the construction resources have been modelled deterministically and stochastically using duration/productivity and resource/performance cost and performance time matrices. For the solution of the problem a mixed integer programming approach has been adopted, utilizing a computer algorithm containing elements heuristic methods.
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paper_title: Augmented heuristic algorithm for multi-skilled resource scheduling

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Conventional project scheduling is restricted to single-skilled resource assumption where each worker is assumed to have only one skill. This, in effect, contradicts real-world practice where workers may possess multiple skills and, on several occasions, are assigned to perform tasks for which they are not specialized. Past research has shown a simple process of heuristic approach for multi-skilled resource scheduling where a project is planned under the assumption that each resource can have more than one skill and resource substitution is allowed. Nevertheless, the approach has presented resource substitution step where an activity with higher priority can claim any resource regardless of its concurrent activities' resource requirements. Furthermore, the approach is subjected to all-or-nothing resource assignment concept where an activity cannot start and resources are not needed for that activity at all unless the required resources of that activity can be completely fulfilled. This research presents an alternative heuristic approach for multi-skilled resource scheduling in an attempt to improve the resource substitution approach. Augmented resource substitution rule and resource-driven task duration are presented to increase starting opportunity of activities on earlier time. Case studies are presented to illustrate the improved result of shorter project duration.
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paper_title: Project scheduling - Theory and practice

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The project scheduling problem involves the scheduling of project activities subject to precedence and/or resource constraints. Of obvious practical importance, it has been the subject of intensive research since the late fifties. A wide variety of commercialized project management software packages have been put to practical use. Despite all these efforts, numerous reports reveal that many projects escalate in time and budget and that many project scheduling procedures have not yet found their way to practical use. The objective of this paper is to confront project scheduling theory with project scheduling practice. We provide a generic hierarchical project planning and control framework that serves to position the various project planning procedures and discuss important research opportunities, the exploration of which may help to close the theory-practice gap.
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paper_title: Application of genetic algorithms to construction scheduling with or without resource constraints

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The difficulties encountered in scheduling construction projects with resource constraints are highlighted by means of a simplified bridge construction problem. A genetic algorithm applicable to projects with or without resource constraints is described. In this application, chromosomes are formed by genes consisting of the start days of the activities. This choice necessitated introducing two mathematical operators (datum operator and left compression operator) and emphasizing one genetic operator (fine mutation operator). A generalized evaluation of the fitness function is conducted. The algorithm is applied to the example problem. The results and the effects of some of the parameters are discussed.Key words: scheduling, genetic algorithms, construction management, computer application.
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paper_title: Current Float Techniques for Resources Scheduling

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This paper concerns resources scheduling using a simple heuristic model described as the “current float” model. Current sfloat is defined as the finish float available with respect to its latest finish time in the original network computations. The current float model allocates limited resources by giving priority to the activity that has the least current float. The current floats need be computed only for those activities that are engaged in a resource conflict. The “total float” models that were used previously required the tedious task of constructing and computing a status network every time an activity is postponed due to nonavailability of resources. The current float model avoids this and requires only the original network computations. The mathematical validity of the model is explained, and the paper presents proof that the output of this model is the same as that of the total float model. The physical significance of the model is also indicated. An application section is included to illustrate ...
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paper_title: Time/cost optimization using hybrid evolutionary algorithm in construction project scheduling

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Abstract This paper deals with construction project scheduling. In the literature on the subject one can find such scheduling methods as: the Linear Scheduling Model (LSM), Line of Balance (LOB) charts and CMP/PERT network planning. The methods take into account several objective functions: the least cost, the least time, limited resources, work priorities, etc., both in the deterministic and probabilistic approach. The paper presents an analysis of the time/cost relationship, performed using time coupling method TCM III. A modified hybrid evolutionary algorithm (HEA) developed by Bozejko and Wodecki (A Hybrid Evolutionary Algorithm for Some Discrete Optimization Problems. IEEE Computer Society, 325–331, 2005) was used for optimization.
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paper_title: A survey on the resource-constrained project scheduling problem

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In this paper, research on the resource-constrained project scheduling problem is classified according to specified objectives and constraints. Each classified area is extensively surveyed, and special emphasis is given to trends in recent research. Specific papers involving nonrenewable resource constraints and time/cost-based objectives are discussed in detail because they present models that are close representations of real-world problems. The difficulty of solving such complex models by optimization techniques is noted. For the purposes of this survey, a set of 78 optimally solved test problems from the literature and a second set of 110 benchmark problems have been subjected to analysis with some well-known dispatching rules and a scheduling algorithm that consists of a decision-making process utilizing the problem constraints as a base of selection. The computational results are reported and discussed in the text. Constructive scheduling algorithms that are directly based on the problem constraints...
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paper_title: Scheduling Construction Projects

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Introduction to Scheduling Task Definition: The Foundation of A Schedule Gantt Charts Logic Diagrams and Scheduling The Critical Path Method (CPM) Calculation of CPM Event and Task Times The Precedence Method (PM) Calculation of Precedence Method Task Times and Floats Program Evaluation Review Technique (PERT) Probabilistic Scheduling (Monte Carlo Method) Calendar Day Scheduling Updating the Schedule Expediting the Project Resource-Constrained Scheduling and Resource Leveling Cash Flow Analysis Based on Construction Schedules Applications of Computers to Scheduling The Scientific Cost Estimating Method Computer Programs for Scheduling Table of Random Numbers Index.
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paper_title: TIME-COST-QUALITY TRADE-OFF ANALYSIS FOR HIGHWAY CONSTRUCTION

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Many departments of transportation have recently started to utilize innovative contracting methods that provide new incentives for improving construction quality. These emerging contracts place an increasing pressure on decision makers in the construction industry to search for an optimal resource utilization plan that minimizes construction cost and time while maximizing its quality. This paper presents a multiobjective optimization model that supports decision makers in performing this challenging task. The model is designed to transform the traditional two-dimensional time-cost tradeoff analysis to an advanced three-dimensional time-cost-quality trade-off analysis. The model is developed as a multiobjective genetic algorithm to provide the capability of quantifying and considering quality in construction optimization. An application example is analyzed to illustrate the use of the model and demonstrate its capabilities in generating and visualizing optimal tradeoffs among construction time, cost, and quality.
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paper_title: Multimode Project Scheduling Based on Particle Swarm Optimization

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This paper introduces a methodology for solving the multimode resource-constrained project scheduling problem (MRCPSP) based on particle swarm optimization (PSO). The MRCPSP considers both renewable and nonrenewable resources that have not been addressed efficiently in the construction field. The framework of the PSO-based methodology is developed with the objective of minimizing project duration. A particle representation formulation is proposed to represent the potential solution to the MRCPSP in terms of priority combination and mode combination for activities. Each particle-represented solution should be checked against the nonrenewable resource infeasibility and will be handled by adjusting the mode combination. The feasible particle-represented solution is transformed to a schedule through a serial generation scheme. Experimental analyses are presented to investigate the performance of the proposed methodology. Comparisons with other methods show that the PSO method is equally efficient at solving the MRCPSP.
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paper_title: A resources scheduling decision support system for concurrent project management

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This paper proposes an integrated methodology for the management of (availability) constrained resources within a concurrent project management environment. The methodology incorporates six main components the projects interface management module, the impact matrix module, the projects grouping module, the projects prioritization module, the master projects scheduling module, and the resources assignment module all of which are integrated coherently, within the framework of a decision support system. The component which is delineated in this paper is the resources assignment module; the other modules are respectively the subject of future papers. The essence of such an integrated and coherent methodology is to enhance the centralization and efficient distribution of information on various concurrent projects parameters, such as projects priorities, projects completion times, their associated costs, and resources allocation patterns, etc. The proposed methodogy is applied in an actual industrial case study...
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paper_title: Optimizing Construction Time and Cost Using Ant Colony Optimization Approach

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Time and cost are the most important factors to be considered in every construction project. In order to maximize the return, both the client and contractor would strive to optimize the project duration and cost concurrently. Over the years, many research studies have been conducted to model the time–cost relationships, and the modeling techniques range from the heuristic methods and mathematical approaches to genetic algorithms. Despite that, previous studies often assumed the time being constant leaving the analyses based purely on a single objective—cost. Acknowledging the significance of time–cost optimization, an evolutionary-based optimization algorithm known as ant colony optimization is applied to solve the multiobjective time–cost optimization problems. In this paper, the basic mechanism of the proposed model is unveiled. Having developed a program in the Visual Basic platform, tests are conducted to compare the performance of the proposed model against other analytical methods previously used fo...
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paper_title: Evolutionary algorithms applied to project scheduling problems—a survey of the state-of-the-art

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Evolutionary algorithms, a form of meta-heuristic, have been successfully applied to a number of classes of complex combinatorial problems such as the well-studied travelling salesman problem, bin packing problems, etc. They have provided a method other than an exact solution that will, within a reasonable execution time, provide either optimal or near optimal results. In many cases near optimal results are acceptable and the additional resources that may be required to provide exact optimal results prove uneconomical. The class of project scheduling problems (PSP) exhibit a similar type of complexity to the previous mentioned problems, also being NP-hard, and therefore would benefit from solution via meta-heuristic rather than exhaustive search. Improvement to a project schedule in terms of total duration or resource utilisation can be of major financial advantage and therefore near optimal solution via evolutionary techniques should be considered highly applicable. In preparation for further research th...
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paper_title: A survey of variants and extensions of the resource-constrained project scheduling problem

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The resource-constrained project scheduling problem (RCPSP) consists of activities that must be scheduled subject to precedence and resource constraints such that the makespan is minimized. It has become a well-known standard problem in the context of project scheduling which has attracted numerous researchers who developed both exact and heuristic scheduling procedures. However, it is a rather basic model with assumptions that are too restrictive for many practical applications. Consequently, various extensions of the basic RCPSP have been developed. This paper gives an overview over these extensions. The extensions are classified according to the structure of the RCPSP. We summarize generalizations of the activity concept, of the precedence relations and of the resource constraints. Alternative objectives and approaches for scheduling multiple projects are discussed as well. In addition to popular variants and extensions such as multiple modes, minimal and maximal time lags, and net present value-based objectives, the paper also provides a survey of many less known concepts.
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paper_title: Permutation-Based Elitist Genetic Algorithm for Optimization of Large-Sized Resource-Constrained Project Scheduling

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The resource-constrained project scheduling problem (RCPSP) has received the attention of many researchers because its general model can be used in a wide variety of construction planning and scheduling applications. The exact procedures and priority-rule-based heuristics fail to search for the optimum solution to the RCPSP of large-sized project networks in a reasonable amount of time for successful application in practice. This paper presents a permutation-based elitist genetic algorithm for solving the problem in order to fulfill the lack of an efficient optimal solution algorithm for project networks with 60 activities or more as well as to overcome the drawback of the exact solution approaches for large-sized project networks. The proposed algorithm employs the elitist strategy to preserve the best individual solution for the next generation so the improved solution can be obtained. A random number generator that provides and examines precedence feasible individuals is developed. A serial schedule generation scheme for the permutation-based decoding is applied to generate a feasible solution to the problem. Computational experiments using a set of standard test problems are presented to demonstrate the performance and accuracy of the proposed algorithm.
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paper_title: Profit Optimization for Multiproject Scheduling Problems Considering Cash Flow

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This study investigates cash flow for profit optimization and handles scheduling problems in multiproject environment. By identifying the amount and timing of individual inflow or outflow at the end of each period, contractors can observe the cash flow at specific time points according to project progress. Since most companies handle multiple projects simultaneously, managing project finance becomes complicated and tough for contractors. Therefore, this study considers cash flow and the financial requirements of contractors working in a multiple-project environment and proposes a profit optimization model for multiproject scheduling problems using constraint programming. The current study also presents a hypothetical example involving three projects to illustrate capability of the proposed model and adopts various constraints, including credit limit (CL) and due dates, for scenario analysis. The analysis result demonstrates that setting CLs ensures smooth financial pressure by properly shifting activities, and assigning due dates for projects helps planners avoid project duration extension while maximizing overall project profit.
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paper_title: Optimization of construction time-cost trade-off analysis using genetic algorithms

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In the management of a construction project, the project duration can often be compressed by accelerating some of its activities at an additional expense. This is the so-called time-cost trade-off ...
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paper_title: SCHEDULING/COST OPTIMIZATION AND NEURAL DYNAMICS MODEL FOR CONSTRUCTION

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A general mathematical formulation is presented for scheduling of construction projects and applied to the problem of highway construction scheduling. Repetitive and nonrepetitive tasks, work continuity constraints, multiple-crew strategies, and the effects of varying job conditions on the performance of a crew can be modeled. An optimization formulation is presented for the construction project scheduling problem with the goal of minimizing the direct construction cost. The nonlinear optimization is then solved by the neural dynamics model developed recently by Adeli and Park. For any given construction duration, the model yields at the optimum construction schedule for minimum construction cost automatically. By varying the construction duration, one can solve the cost-duration trade-off problem and obtain the global optimum schedule and the corresponding minimum construction cost. The new construction scheduling model provides the capabilities of both the CPM and LSM approaches. In addition, it provides features desirable for repetitive projects such as highway construction and allows schedulers greater flexibility. It is particularly suitable for studying the effects of change order on the construction cost. This research provides the mathematical foundation for development of a new generation of more general, flexible, and accurate construction scheduling systems.
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paper_title: Heuristic scheduling of resource‐constrained, multiple‐mode and repetitive projects

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An alternative heuristic method for scheduling repetitive projects in which resources are limited and activities may be executed with multiple modes of resource demands associated with different durations is proposed. Unlike general heuristic methods that separately analyze each competing activity and schedule only one at a time, the proposed heuristic algorithm ranks possible combinations of activities every time and simultaneously schedules all activities in the selected combination leading to minimal project duration. All alternative combinations of activities in consideration of resource constraints, multiple modes and characteristics of the repetitive projects are determined through a permutation tree-based procedure. The heuristic method is implemented based on the corresponding framework. An example is presented to demonstrate the efficiency of the proposed heuristic method. The study is expected to provide an efficient heuristic methodology for solving the project scheduling problem.
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paper_title: Requirements identification for 4D constraintbased construction planning and control system

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2 Abstract: Construction planning and control are identified among the top potential areas needing improvements. A traditional technique known as the Critical Path Method (CPM) has been widely criticised in terms of its inability to cope with non- precedence constraints, difficulty to evaluate and communicate interdependencies, and inadequacy for work-face productions. Attempting to treat these deficiencies, substantial research efforts have resulted in a wide range of advancements including design of new planning and control methodologies and development of sophisticated computerised applications. However, these efforts have not effectively overcome all of the above CPM drawbacks and, therefore, have not yet provided a solution to the industry.
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paper_title: Critical-Path Planning and Scheduling: Mathematical Basis

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This paper is concerned with establishing the mathematical basis of the Critical-Path Method---a new tool for planning, scheduling, and coordinating complex engineering-type projects. The essential ingredient of the technique is a mathematical model that incorporates sequence information, durations, and costs for each component of the project. It is a special parametric linear program that, via the primal-dual algorithm, may be solved efficiently by network flow methods. Analysis of the solutions of the model enables operating personnel to answer questions concerning labor needs, budget requirements, procurement and design limitations, the effects of delays, and communication difficulties.
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paper_title: SOFT LOGIC IN NETWORK ANALYSIS

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One of the most important functions of planning is to offset uncertainty and change. However, projects are often affected by external factors or constraints that can either facilitate progress or create delays in the project. Sometimes, logic changes can be inevitable. Therefore, special techniques are needed to provide a simple way of network updating in order to reflect the impact of logic change on project completion date and on the critical path. This paper addresses the problem of soft logic and discusses logic changes during the course of the work. An algorithmic procedure has been developed to handle the soft logic in network analysis. SOFTCPM is a microcomputer program created by the writers that deals with the soft logic in CPM networks. It has the capability of updating the CPM network logic when any unexpected event occurs that prevents working according to the scheduled activity sequence.
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paper_title: Constraint knowledge for construction scheduling

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The capabilities of network diagramming techniques (NDT) are restricted by limitations inherent in their representation of schedule constraints (typically expressed through precedent relationships between activities). This assertion suggests the selection of a richer representation as a departure point for extending the utility of planning and scheduling techniques. The authors suggest that such a representation is provided by a system which employs a general model of a project's 'status' and which allows schedule constraints to be expressed as rules which refer to this status. This system offers the advantages of allowing the precedence of activities to be based on more than just the completion of other activities. It also provides an efficient knowledge-based approach to scheduling that can express the reasoning underlying scheduling actions which can be employed by future artificial intelligence (AI) planning. The authors discuss how constraints are represented and describes what types of constraints can be represented in both NDT and in the proposed system-called A Construction Planner (ACP). This is followed by a comparison of the schedule generation algorithms used in NDT and in ACP.
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paper_title: Resource-Activity Critical-Path Method for Construction Planning

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In this paper, a practical method is developed in an attempt to address the fundamental matters and limitations of existing methods for critical-path method (CPM) based resource scheduling, which are identified by reviewing the prior research in resource-constrained CPM scheduling and repetitive scheduling. The proposed method is called the resource-activity critical-path method (RACPM), in which (1) the dimension of resource in addition to activity and time is highlighted in project scheduling to seamlessly synchronize activity planning and resource planning; (2) the start/finish times and the floats are defined as resource-activity attributes based on the resource-technology combined precedence relationships; and (3) the resource critical issue that has long baffled the construction industry is clarified. The RACPM is applied to an example problem taken from the literature for illustrating the algorithm and comparing it with the existing method. A sample application of the proposed RACPM for planning a footbridge construction project is also given to demonstrate that practitioners can readily interpret and utilize a RACPM schedule by relating the RACPM to the classic CPM. The RACPM provides schedulers with a convenient vehicle for seamlessly integrating the technology/process perspective with the resource use perspective in construction planning. The effect on the project duration and activity floats of varied resource availability can be studied through running RACPM on different scenarios of resources. This potentially leads to an integrated scheduling and cost estimating process that will produce realistic schedules, estimates, and control budgets for construction.
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paper_title: Critical path methods in construction practice

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Critical Path Method Procedures and Terminology. The Network Diagram and Utility Data. Network Calculations I: Critical Paths and Floats. Network Calculations II: Simple Compression. Network Calculations III: Complex Compression and Decompression. Network Calculations IV: Scheduling and Resource Leveling. Practical Planning with Critical Path Methods. Project Control with Critical Path Methods. Financial Planning and Cost Control. Evaluation of Work Changes and Delays. Attitudes, Responsibilities, and Duties. Computer-Aided CPM. Selection of Technique. Integrated Project Development and Management. CPM, a Systems Concept. Appendices. Index.
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paper_title: Professional Construction Management

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This paper describes in part findings and conclusions of ASCE’s Task Committee on Management of Construction Projects. This paper presents definitions of “Professional Construction Management” and “Professional Construction Manager”, explains the reasoning behind them, then describes the responsibilities of the Professional Construction Manager and his requirements in the planning and execution phases of a project. Professional Construction Management differs from conventional design-construct and traditional separate contractor and designer approaches in that there are by definition three separate and distinct members of the team (owner, designer, and manager) and the Professional Construction Manager does not perform significant design or construction work with his own forces. Professional Construction Management is not necessarily better or worse than other methods of procuring constructed facilities. However, the three-party-team approach is certainly a viable alternative to more traditional methods in many applications as its increasing use will demonstrate.
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paper_title: Construction Time-Cost Trade-Off Analysis Using LP/IP Hybrid Method

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Construction planners must select appropriate resources, including crew size, equipment, methods, and technologies, to perform the tasks of a construction project. In general, there is a trade-off between time and cost to complete a task—the less expensive the resources, the longer it takes. Using critical-path-method techniques, the overall project cost can be reduced by using less expensive resources for noncritical activities without impacting the duration. Furthermore planners usually need to adjust the selection of resources in order to shorten or lengthen the project duration. Finding optimal decisions is difficult and time-consuming considering the numbers of permutations involved. For example, a critical-path-method network with only eight activities, each with two options, will have 256 (2\u8) alternatives. Exhaustive enumeration is not economically feasible even with very fast computers. This paper presents a new algorithm using linear and integer programming to efficiently obtain optimal resource selections that optimize time and cost of a construction project.
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paper_title: Scheduling of repetitive projects with cost optimization

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Existing dynamic programming formulations are capable of identifying, from a set of possible alternatives, the optimum crew size for each activity in a repetitive project. The optimization criterion of these formulations is, however, limited to the minimization of the overall duration of the project. While this may lead to the minimization of the indirect cost of the project, it does not guarantee its overall minimum cost. The objective of this paper is to present a model that incorporates cost as an important decision variable in the optimization process. The model utilizes dynamic programming and performs the solution in two stages: first a forward process to identify local minimum conditions, and then a backward process to ensure an overall minimum state. In the first stage, a process similar to that use in time-cost trade-off analysis is employed, and a simple scanning and selecting process is used in the second stage. An example project from the literature is analyzed in order to demonstrate the use of the model and its validity, and illustrate the significance of cost as a decision variable in the optimization process.
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paper_title: Assignment and Allocation Optimization of Partially Multiskilled Workforce

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Multiskilling is a workforce strategy that has been shown to reduce indirect labor costs, improve productivity, and reduce turnover. A multiskilled workforce is one in which the workers possess a range of skills that allow them to participate in more than one work process. In practice, they may work across craft boundaries. The success of multiskilling greatly relies on the foreman's ability to assign workers to appropriate tasks and to compose crews effectively. The foreman assigns tasks to workers according to their knowledge, capabilities, and experience on former projects. This research investigated the mechanics of allocating a multiskilled workforce and developed a linear programming model to help optimize the multiskilled workforce assignment and allocation process in a construction project, or between the projects of one company. It is concluded that the model will be most useful in conditions where full employment does not exist; however, it is also useful for short term allocation decisions. By running the model for various simulated scenarios, additional observations were made. For example, it is concluded that, for a capital project, the benefits of multiskilling are marginal beyond approximately a 20% concentration of multiskilled workers in a project workforce. Benefits to workers themselves become marginal after acquiring competency in two or three crafts. These observations have been confirmed by field experience. Extension of this model to allocation of multifunctional resources, such as construction equipment, should also be possible.
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paper_title: Applied Integer Programming: Modeling and Solution

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PREFACE. PART I MODELING. 1 Introduction. 1.1 Integer Programming. 1.2 Standard Versus Nonstandard Forms. 1.3 Combinatorial Optimization Problems. 1.4 Successful Integer Programming Applications. 1.5 Text Organization and Chapter Preview. 1.6 Notes. 1.7 Exercises. 2 Modeling and Models. 2.1 Assumptions on Mixed Integer Programs. 2.2 Modeling Process. 2.3 Project Selection Problems. 2.4 Production Planning Problems. 2.5 Workforce/Staff Scheduling Problems. 2.6 Fixed-Charge Transportation and Distribution Problems. 2.7 Multicommodity Network Flow Problem. 2.8 Network Optimization Problems with Side Constraints. 2.9 Supply Chain Planning Problems. 2.10 Notes. 2.11 Exercises. 3 Transformation Using 0 1 Variables. 3.1 Transform Logical (Boolean) Expressions. 3.2 Transform Nonbinary to 0 1 Variable. 3.3 Transform Piecewise Linear Functions. 3.4 Transform 0 1 Polynomial Functions. 3.5 Transform Functions with Products of Binary and Continuous Variables: Bundle Pricing Problem. 3.6 Transform Nonsimultaneous Constraints. 3.7 Notes. 3.8 Exercises. 4 Better Formulation by Preprocessing. 4.1 Better Formulation. 4.2 Automatic Problem Preprocessing. 4.3 Tightening Bounds on Variables. 4.4 Preprocessing Pure 0 1 Integer Programs. 4.5 Decomposing a Problem into Independent Subproblems. 4.6 Scaling the Coefficient Matrix. 4.7 Notes. 4.8 Exercises. 5 Modeling Combinatorial Optimization Problems I. 5.1 Introduction. 5.2 Set Covering and Set Partitioning. 5.3 Matching Problem. 5.4 Cutting Stock Problem. 5.5 Comparisons for Above Problems. 5.6 Computational Complexity of COP. 5.7 Notes. 5.8 Exercises. 6 Modeling Combinatorial Optimization Problems II. 6.1 Importance of Traveling Salesman Problem. 6.2 Transformations to Traveling Salesman Problem. 6.3 Applications of TSP. 6.4 Formulating Asymmetric TSP. 6.5 Formulating Symmetric TSP. 6.6 Notes. 6.7 Exercises. PART II REVIEW OF LINEAR PROGRAMMING AND NETWORK FLOWS. 7 Linear Programming Fundamentals. 7.1 Review of Basic Linear Algebra. 7.2 Uses of Elementary Row Operations. 7.3 The Dual Linear Program. 7.4 Relationships Between Primal and Dual Solutions. 7.5 Notes. 7.6 Exercises. 8 Linear Programming: Geometric Concepts. 8.1 Geometric Solution. 8.2 Convex Sets. 8.3 Describing a Bounded Polyhedron. 8.4 Describing Unbounded Polyhedron. 8.5 Faces, Facets, and Dimension of a Polyhedron. 8.6 Describing a Polyhedron by Facets. 8.7 Correspondence Between Algebraic and Geometric Terms. 8.8 Notes. 8.9 Exercises. 9 Linear Programming: Solution Methods. 9.1 Linear Programs in Canonical Form. 9.2 Basic Feasible Solutions and Reduced Costs. 9.3 The Simplex Method. 9.4 Interpreting the Simplex Tableau. 9.5 Geometric Interpretation of the Simplex Method. 9.6 The Simplex Method for Upper Bounded Variables. 9.7 The Dual Simplex Method. 9.8 The Revised Simplex Method. 9.9 Notes. 9.10 Exercises. 10 Network Optimization Problems and Solutions. 10.1 Network Fundamentals. 10.2 A Class of Easy Network Problems. 10.3 Totally Unimodular Matrices. 10.4 The Network Simplex Method. 10.5 Solution via LINGO. 10.6 Notes. 10.7 Exercises. PART III SOLUTIONS. 11 Classical Solution Approaches. 11.1 Branch-and-Bound Approach. 11.2 Cutting Plane Approach. 11.3 Group Theoretic Approach. 11.4 Geometric Concepts. 11.5 Notes. 11.6 Exercises. 12 Branch-and-Cut Approach. 12.1 Introduction. 12.2 Valid Inequalities. 12.3 Cut Generating Techniques. 12.4 Cuts Generated from Sets Involving Pure Integer Variables. 12.5 Cuts Generated from Sets Involving Mixed Integer Variables. 12.6 Cuts Generated from 0 1 Knapsack Sets. 12.7 Cuts Generated from Sets Containing 0 1 Coefficients and 0 1 Variables. 12.8 Cuts Generated from Sets with Special Structures. 12.9 Notes. 12.10 Exercises. 13 Branch-and-Price Approach. 13.1 Concepts of Branch-and-Price. 13.2 Dantzig Wolfe Decomposition. 13.3 Generalized Assignment Problem. 13.4 GAP Example. 13.5 Other Application Areas. 13.6 Notes. 13.7 Exercises. 14 Solution via Heuristics, Relaxations, and Partitioning. 14.1 Introduction. 14.2 Overall Solution Strategy. 14.3 Primal Solution via Heuristics. 14.4 Dual Solution via Relaxation. 14.5 Lagrangian Dual. 14.6 Primal Dual Solution via Benders Partitioning. 14.7 Notes. 14.8 Exercises. 15 Solutions with Commercial Software. 15.1 Introduction. 15.2 Typical IP Software Components. 15.3 The AMPL Modeling Language. 15.4 LINGO Modeling Language. 15.5 MPL Modeling Language. REFERENCES. APPENDIX: ANSWERS TO SELECTED EXERCISES. INDEX.
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paper_title: Advances in Linear and Integer Programming

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List of contributors 1. Simplex Algorithms 2. Interior Point Methods 3. A Computational View of Interior Point Methods 4. Interior Point Algorithms for Network Flow Problems 5. Branch and Cut Algorithms 6. Interior Point Algorithms for Integer Programming 7. Computational Logic and Integer Programming
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paper_title: Finance-Based Scheduling of Construction Projects Using Integer Programming

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Construction scheduling is the process of devising schemes for sequencing activities. A realistic schedule fulfills actual concerns of users, thus minimizing the chances of schedule failure. The minimization of total project duration has been the concept underlying critical-path method/program evaluation and review technique (CPM/PERT) schedules. Subsequently, techniques including resource management and time-cost trade-off analysis were developed to customize CPM/PERT schedules to fulfill users' concerns regarding project resources, cost, and time. However, financing construction activities throughout the course of the project is another crucial concern that must be properly treated otherwise, nonrealistic schedules are to be anticipated. Unless contractors manage to procure adequate cash to keep construction work running on schedule, the pace of work will definitely be relaxed. Therefore, always keeping scheduled activities in balance with available cash is a potential contribution to producing realistic schedules. An integer-programming finance-based scheduling method is offered to produce financially feasible schedules that balance financing requirements of activities at any period with cash available in that same period. The proposed method offers 2-fold benefits of minimizing total project duration and fulfilling finance availability constraints.
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paper_title: Multiobjective Linear Programming Model for Scheduling Linear Repetitive Projects

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Linear repetitive construction projects require large amounts of resources which are used in a sequential manner and therefore effective resource management is very important both in terms of project cost and duration. Existing methodologies such as the critical path method and the repetitive scheduling method optimize the schedule with respect to a single factor, to achieve minimum duration or minimize resource work breaks, respectively. However real life scheduling decisions are more complicated and project managers must make decisions that address the various cost elements in a holistic way. To respond to this need, new methodologies that can be applied through the use of decision support systems should be developed. This paper introduces a multiobjective linear programming model for scheduling linear repetitive projects, which takes into consideration cost elements regarding the project's duration, the idle time of resources, and the delivery time of the project's units. The proposed model can be used to generate alternative schedules based on the relative magnitude and importance of the different cost elements. In this sense, it provides managers with the capability to consider alternative schedules besides those defined by minimum duration or maximizing work continuity of resources. The application of the model to a well known example in the literature demonstrates its use in providing explicatory analysis of the results.
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paper_title: Integer programming : theory and practice

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New Heuristics and Adaptive Memory Procedures for Boolean Optimization Problems, Lars M. Hvattum, Arne Lokketangen, and Fred Glover Convergent Lagrangian Methods for Separable Nonlinear Integer Programming: Objective Level-Cut and Domain-Cut Methods, Duan Li, Xiaoling Sun, and Jun Wang The Generalized Assignment Problem, Robert M. Nauss Decomposition in Integer Linear Programming, Ted K. Ralphs and Matthew V. Galati Airline Scheduling Models and Solution Algorithms for the Temporary Closure of Airports, Shangyao Yan and Chung-Gee Lin Determining an Optimal Fleet Mix and Schedules: Part I - Single Source and Destination, Hanif D. Sherali and Salem M. Al-Yakoob Determining an Optimal Fleet Mix and Schedules: Part II - Multiple Sources and Destinations, and the Option of Leasing Transshipment Depots, Hanif D. Sherali and Salem M. Al-Yakoob An Integer Programming Model for the Optimization of Data Cycle Maps, David Panton, Maria John, and Andrew Mason Application of Column-Generation Techniques to Retail Assortment Planning, Govind P. Daruka and Udatta S. Palekar Noncommercial Software for Mixed-Integer Linear Programming, Jeff T. Linderoth and Ted K. Ralphs
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paper_title: Multiobjective optimization in Linear Repetitive Project scheduling

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The Critical Path Method (CPM) and the Repetitive Scheduling Method (RSM) are the most often used tools for the planning, scheduling and control Linear Repetitive Projects (LRPs). CPM focuses mostly on project’s duration and critical activities, while RSM focuses on resource continuity. In this paper we present a linear programming approach to address the multi objective nature of decisions construction managers face in scheduling LRPs. The Multi Objective Linear Programming model (MOLP-LRP) is a parametric model that can optimize a schedule in terms of duration, work-breaks, unit completion time and respective costs, while at the same time the LP range sensitivity analysis can provide useful information regarding cost tradeoffs between delay, work-break and unit delivery costs. MOLPS-LRP can generate alternative schedules based on the relative magnitude and importance of different cost elements. In this sense it provides managers with the capability to consider alternative schedules besides those defined by minimum duration (CPM) or minimum resource work-breaks (RSM). Demonstrative results and analysis are provided through a well known in the literature case study example.
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paper_title: Resource Leveling of Linear Schedules Using Integer Linear Programming

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Since the early 1960s many techniques have been developed to plan and schedule linear construction projects. However, one, the critical path method (CPM), overshadowed the others. As a result, CPM developed into the powerful and effective tool that it is today. However, research has indicated that CPM is ineffective for linear construction. Linear construction projects are typified by activities that must be repeated in different locations such as highways, pipelines, and tunnels. Recently, there has been renewed interest in linear scheduling. Much of this interest has involved a technique called the linear scheduling method (LSM). Only recently has there been the ability to calculate the controlling activities of a linear schedule, independent of network analysis. Additional research needs to be done to develop some of the techniques available in CPM into comparable ones for linear scheduling. One of these techniques is resource leveling. This paper uses the vehicle of a highway construction project to present an integer linear programming formulation to level the resources of linear projects.
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paper_title: The LP/IP hybrid method for construction time-cost trade-off analysis

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Construction planners face the decisions of selecting appropriate resources, including crew sizes, equipment, methods and technologies, to perform the tasks of a construction project. In general, there is a trade-off between time and cost to complete a task - the less expensive the resources, the longer it takes. Using Critical Path Method (CPM) techniques, the overall project cost can be reduced by using less expensive resources for non-critical activities without impacting the duration. Furthermore, planners need to adjust the resource selections to shorten or lengthen the project duration. Finding the optimal decisions is difficult and time-consuming considering the numbers of permutations involved. For example, a CPM network with only eight activities, each with two options, will have 28 alternatives. For large problems, exhaustive enumeration is not economically feasible even with very fast computers. This paper presents a new algorithm using linear and integer programming to obtain optimal resource ...
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paper_title: A Simple CPM Time-Cost Tradeoff Algorithm

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This article describes an algorithm for efficiently shortening the duration of a project when the expected project duration exceeds a predetermined limit. The problem consists of determining which activities to expedite and by what amount. The objective is to minimize the cost of the project. ::: ::: This algorithm is considerably less complex than the analytic methods currently available. Because of its inherent simplicity, the algorithm is ideally suited for hand computation and also is suitable for computer solution. Solutions derived by the algorithm were compared with linear programming results. These comparisons revealed that the algorithm solutions are either a equally good or b nearly the same as the solutions obtained by more complex analytic methods which require a computer. ::: ::: With this method the CPM time-cost tradeoff problem is solved without access to a computer, thereby making this planning tool available to managers who otherwise would find implementation impractical.
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paper_title: Augmented heuristic algorithm for multi-skilled resource scheduling

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Conventional project scheduling is restricted to single-skilled resource assumption where each worker is assumed to have only one skill. This, in effect, contradicts real-world practice where workers may possess multiple skills and, on several occasions, are assigned to perform tasks for which they are not specialized. Past research has shown a simple process of heuristic approach for multi-skilled resource scheduling where a project is planned under the assumption that each resource can have more than one skill and resource substitution is allowed. Nevertheless, the approach has presented resource substitution step where an activity with higher priority can claim any resource regardless of its concurrent activities' resource requirements. Furthermore, the approach is subjected to all-or-nothing resource assignment concept where an activity cannot start and resources are not needed for that activity at all unless the required resources of that activity can be completely fulfilled. This research presents an alternative heuristic approach for multi-skilled resource scheduling in an attempt to improve the resource substitution approach. Augmented resource substitution rule and resource-driven task duration are presented to increase starting opportunity of activities on earlier time. Case studies are presented to illustrate the improved result of shorter project duration.
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paper_title: A Network Flow Computation for Project Cost Curves

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A network flow method is outlined for solving the linear programming problem of computing the least cost curve for a project composed of many individual jobs, where it is assumed that certain jobs must be finished before others can be started. Each job has an associated crash completion time and normal completion time, and the cost of doing the job varies linearly between these extreme times. Given that the entire project must be completed in a prescribed time interval, it is desired to find job times that minimize the total project cost. The~method solves this problem for all feasible time intervals.
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paper_title: Schedule compression using the direct stiffness method

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This paper presents a new method for critical path (CPM) scheduling that optimizes project duration in order to minimize the project total cost. In addition, the method could be used to produce constrained schedules that accommodate contractual completion dates of projects and their milestones. The proposed method is based on the well-known "direct stiffness method" for structural analysis. The method establishes a complete analogy between the structural analysis problem with imposed support settlement and that of project scheduling with imposed target completion date. The project CPM network is replaced by an equivalent structure. The equivalence conditions are established such that when the equivalent structure is compressed by an imposed displacement equal to the schedule compression, the sum of all member forces represents the additional cost required to achieve such compression. To enable a comparison with the currently used methods, an example application from the literature is analyzed using the pr...
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paper_title: Heuristic scheduling of resource‐constrained, multiple‐mode and repetitive projects

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An alternative heuristic method for scheduling repetitive projects in which resources are limited and activities may be executed with multiple modes of resource demands associated with different durations is proposed. Unlike general heuristic methods that separately analyze each competing activity and schedule only one at a time, the proposed heuristic algorithm ranks possible combinations of activities every time and simultaneously schedules all activities in the selected combination leading to minimal project duration. All alternative combinations of activities in consideration of resource constraints, multiple modes and characteristics of the repetitive projects are determined through a permutation tree-based procedure. The heuristic method is implemented based on the corresponding framework. An example is presented to demonstrate the efficiency of the proposed heuristic method. The study is expected to provide an efficient heuristic methodology for solving the project scheduling problem.
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paper_title: Genetic algorithms for multi-constraint scheduling: an application for the construction industry

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SUMMARY Reliable construction schedule is vital for effective co-ordination across supply chains and various trades at construction work face. According to the lean construction concept, reliability of the schedule can be enhanced through detection and satisfaction of all potential constraints prior to releasing operation assignments. However, it is difficult to implement this concept since current scheduling tools and techniques are fragmented and designed to deal with a limited set of construction constraints. This paper introduces a methodology termed ‘multi-constraint scheduling’ in which four major groups of construction constraints including physical, contract, resource, and information constraints are considered. A Genetic Algorithm (GA) has been developed and used for multi-constraint optimisation problem. Given multiple constraints such as activity dependency, limited working area, and resource and information readiness, the GA alters tasks’ priorities and construction methods so as to arrive at optimum or near optimum set of project duration, cost, and smooth resource profiles. This feature has been practically developed as an embedded macro in MS Project. Several experiments confirmed that GA can provide near optimum solutions within acceptable searching time (i.e. 5 minutes for 1.92E11 alternatives). Possible improvements to this research are further suggested in the paper.
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paper_title: GA-BASED MULTICRITERIA OPTIMAL MODEL FOR CONSTRUCTION SCHEDULING

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Resources for construction activities are limited in the real construction world. To avoid the waste and shortage of resources on a construction jobsite, scheduling must include resource allocation. A multicriteria computational optimal scheduling model, which integrates the time/cost trade-off model, resource-limited model, and resource leveling model, is proposed. A searching technique using genetic algorithms (GAs) is adopted in the model. Furthermore, the nondominated solutions are found by the multiple attribute decision-making method, technique for order preference by similarity to ideal solution. The model can effectively provide the optimal combination of construction durations, resource amounts, minimum direct project costs, and minimum project duration under the constraint of limited resources.
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paper_title: Applying Pareto Ranking and Niche Formation to Genetic Algorithm-Based Multiobjective Time-Cost Optimization

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Time–cost optimization (TCO) is one of the greatest challenges in construction project planning and control, since the optimization of either time or cost, would usually be at the expense of the other. Although the TCO problem has been extensively examined, many research studies only focused on minimizing the total cost for an early completion. This does not necessarily convey any reward to the contractor. However, with the increasing popularity of alternative project delivery systems, clients and contractors are more concerned about the combined benefits and opportunities of early completion as well as cost savings. In this paper, a genetic algorithms ( GAs ) -driven multiobjective model for TCO is proposed. The model integrates the adaptive weight to balance the priority of each objective according to the performance of the previous “generation.” In addition, the model incorporates Pareto ranking as a selection criterion and the niche formation techniques to improve popularity diversity. Based on the pr...
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paper_title: Comparing Schedule Generation Schemes in Resource-Constrained Project Scheduling Using Elitist Genetic Algorithm

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An issue has arisen with regard to which of the schedule generation schemes will perform better for an arbitrary instance of the resource-constrained project scheduling problem (RCPSP), which is one of the most challenging areas in construction engineering and management. No general answer has been given to this issue due to the different mechanisms between the serial scheme and the parallel scheme. In an effort to address this issue, this paper compares the two schemes using a permutation-based Elitist genetic algorithm for the RCPSP. Computational experiments are presented with multiple standard problems. From the results of a paired difference experiment, the algorithm using the serial scheme provides better solutions than the one using the parallel scheme. The results also show that the algorithm with the parallel scheme takes longer to solve each problem than the one using the serial scheme.
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paper_title: Intelligent optimization for project scheduling of the first mining face in coal mining

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In this paper, the intelligent optimization methods including genetic algorithm (GA), particle swarm optimization (PSO) and modified particle swarm optimization (MPSO) are used in optimizing the project scheduling of the first mining face of the second region of the fifth Ping'an coal mine in China. The result of optimization provides essential information of management and decision-making for governors and builder. The process of optimization contains two parts: the first part is obtaining the time parameters of each process and the network graph of the first mining face in the second region by PERT (program evaluation and review technique) method based on the raw data. The other part is the second optimization to maximal NPV (net present value) based on the network graph. The starting dates of all processes are decision-making variables. The process order and time are the constraints. The optimization result shows that MPSO is better than GA and PSO and the optimized NPV is 14,974,000 RMB more than the original plan.
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paper_title: Construction Resource Scheduling with Genetic Algorithms

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A new approach for resource scheduling using genetic algorithms (GAs) is presented here. The methodology does not depend on any set of heuristic rules. Instead, its strength lies in the selection and recombination tasks of the GA to learn the domain of the specific project network. By this it is able to evolve improved schedules with respect to the objective function. Further, the model is general enough to encompass both resource leveling and limited resource allocation problems unlike existing methods, which are class-dependent. In this paper, the design and mechanisms of the model are described. Case studies with standard test problems are presented to demonstrate the performance of the GA-scheduler when compared against heuristic methods under various resource availability profiles. Results obtained with the proposed model do not indicate an exponential growth in the computational time required for larger problems.
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paper_title: USING IMPROVED GENETIC ALGORITHMS TO FACILITATE TIME-COST OPTIMIZATION

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Time-cost optimization problems in construction projects are characterized by the constraints on the time and cost requirements. Such problems are difficult to solve because they do not have unique solutions. Typically, if a project is running behind the scheduled plan, one option is to compress some activities on the critical path so that the target completion time can be met. As combinatorial optimization problems, time-cost optimization problems are suitable for applying genetic algorithms (GAs). However, basic GAs may involve very large computational costs. This paper presents several improvements to basic GAs and demonstrates how these improved GAs reduce computational costs and significantly increase the efficiency in searching for optimal solutions.
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paper_title: Comparison between Genetic Algorithms and Particle Swarm Optimization

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This paper compares two evolutionary computation paradigms: genetic algorithms and particle swarm optimization. The operators of each paradigm are reviewed, focusing on how each affects search behavior in the problem space. The goals of the paper are to provide additional insights into how each paradigm works, and to suggest ways in which performance might be improved by incorporating features from one paradigm into the other.
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paper_title: Nondominated Archiving Multicolony Ant Algorithm in Time-Cost Trade-Off Optimization

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Time–cost trade-off analysis is addressed as an important aspect of any construction project planning and control. Nonexistence of a unique solution makes the time–cost trade-off problems very difficult to tackle. As a combinatorial optimization problem one may apply heuristics or mathematical programming techniques to solve time–cost trade-off problems. In this paper, a new multicolony ant algorithm is developed and used to solve the time–cost multiobjective optimization problem. Pareto archiving together with innovative solution exchange strategy are introduced which are highly efficient in developing the Pareto front and set of nondominated solutions in a time–cost optimization problem. An 18-activity time–cost problem is used to evaluate the performance of the proposed algorithm. Results show that the proposed algorithm outperforms the well-known weighted method to develop the nondominated solutions in a combinatorial optimization problem. The paper is more relevant to researchers who are interested i...
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paper_title: Using Machine Learning and GA to Solve Time-Cost Trade-Off Problems

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Existing genetic algorithms (GA) based systems for solving time-cost trade-off problems suffer from two limitations. First, these systems require the user to manually craft the time-cost curves for formulating the objective functions. Second, these systems only deal with linear time-cost relationships. To overcome these limitations, this paper presents a computer system called MLGAS (Machine Learning and Genetic Algorithms based System), which integrates a machine learning method with GA. A quadratic template is introduced to capture the nonlinearity of time-cost relationships. The machine learning method automatically generates the quadratic time-cost curves from historical data and also measures the credibility of each quadratic time-cost curve. The quadratic curves are then used to formulate the objective function that can be solved by the GA. Several improvements are made to enhance the capacity of GA to prevent premature convergence. Comparisons of MLGAS with an experienced project manager indicate that MLGAS generates better solutions to nonlinear time-cost trade-off problems.
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paper_title: Optimization of Resource Allocation and Leveling Using Genetic Algorithms

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Resource allocation and leveling are among the top challenges in project management. Due to the complexity of projects, resource allocation and leveling have been dealt with as two distinct subproblems solved mainly using heuristic procedures that cannot guarantee optimum solutions. In this paper, improvements are proposed to resource allocation and leveling heuristics, and the Genetic Algorithms (GAs) technique is used to search for near-optimum solution, considering both aspects simultaneously. In the improved heuristics, random priorities are introduced into selected tasks and their impact on the schedule is monitored. The GA procedure then searches for an optimum set of tasks' priorities that produces shorter project duration and better-leveled resource profiles. One major advantage of the procedure is its simple applicability within commercial project management software systems to improve their performance. With a widely used system as an example, a macro program is written to automate the GA proced...
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paper_title: Use of Genetic Algorithms in Resource Scheduling of Construction Projects

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This paper presents an augmented Lagrangian genetic algorithm model for resource scheduling. The algorithm considers scheduling characteristics that were ignored in prior research. Previous resource scheduling formulations have primarily focused on project duration minimization. Furthermore, resource leveling and resource-constrained scheduling have traditionally been solved independently. The model presented here considers all precedence relationships, multiple crew strategies, total project cost minimization, and time-cost trade-off. In the new formulation, resource leveling and resource-constrained scheduling are performed simultaneously. The model presented uses the quadratic penalty function to transform the resource-scheduling problem to an unconstrained one. The algorithm is general and can be applied to a broad class of optimization problems. An illustrative example is presented to demonstrate the performance of the proposed method.
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paper_title: Multimode Project Scheduling Based on Particle Swarm Optimization

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This paper introduces a methodology for solving the multimode resource-constrained project scheduling problem (MRCPSP) based on particle swarm optimization (PSO). The MRCPSP considers both renewable and nonrenewable resources that have not been addressed efficiently in the construction field. The framework of the PSO-based methodology is developed with the objective of minimizing project duration. A particle representation formulation is proposed to represent the potential solution to the MRCPSP in terms of priority combination and mode combination for activities. Each particle-represented solution should be checked against the nonrenewable resource infeasibility and will be handled by adjusting the mode combination. The feasible particle-represented solution is transformed to a schedule through a serial generation scheme. Experimental analyses are presented to investigate the performance of the proposed methodology. Comparisons with other methods show that the PSO method is equally efficient at solving the MRCPSP.
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paper_title: Optimizing Construction Time and Cost Using Ant Colony Optimization Approach

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Time and cost are the most important factors to be considered in every construction project. In order to maximize the return, both the client and contractor would strive to optimize the project duration and cost concurrently. Over the years, many research studies have been conducted to model the time–cost relationships, and the modeling techniques range from the heuristic methods and mathematical approaches to genetic algorithms. Despite that, previous studies often assumed the time being constant leaving the analyses based purely on a single objective—cost. Acknowledging the significance of time–cost optimization, an evolutionary-based optimization algorithm known as ant colony optimization is applied to solve the multiobjective time–cost optimization problems. In this paper, the basic mechanism of the proposed model is unveiled. Having developed a program in the Visual Basic platform, tests are conducted to compare the performance of the proposed model against other analytical methods previously used fo...
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paper_title: Multi Objective Optimization of Time Cost Quality Quantity Using Multi Colony Ant Algorithm

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Research on a new metaheuristic for optimization is often initially focused on proof of concept applications. Time and cost are the most important factors to be considered in every construction project. Over the years, many research studies have been conducted to model the time-cost relationship. Construction planners often face the challenge of optimum resources utilization to compromise between different and usually conflicting aspects of projects. Time, cost and quality of project delivery are among the crucial aspects of each project. Ant colony optimization, which was introduced in the early 1990’s as a novel technique for solving hard combinational optimization problem, finds itself currently at this point of its life cycle. In this paper, new metaheuristic multi-colony ant algorithm is developed for the optimization of three objectives time-cost quality with quantity as a trade off problem. The model is also applied to two objectives time – cost trade off problem and the results are compared to those of the existing approaches.
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paper_title: Applying a Genetic Algorithm-Based Multiobjective Approach for Time-Cost Optimization

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Reducing both project cost and time (duration) is critical in a competitive environment. However, a trade-off between project time and cost is required. This in turn requires contracting organizations to carefully evaluate various approaches to attaining an optimal time-cost equilibrium. Although several analytical models have been developed for time-cost optimization (TCO), they mainly focus on projects where the contract duration is fixed. The optimization objective in those cases is therefore restricted to identifying the minimum total cost only. With the increasing popularity of alternative project delivery systems, clients and contractors are targeting the increased benefits and opportunities of seeking an earlier project completion. The multiobjective model for TCO proposed in this paper is powered by techniques using genetic algorithms (GAs). The proposed model integrates the adaptive weights derived from previous generations, and induces a search pressure toward an ideal point. The concept of the GA-based multiobjective TCO model is illustrated through a simple manual simulation, and the results indicate that the model could assist decision-makers in concurrently arriving at an optimal project duration and total cost.
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paper_title: Optimization of construction time-cost trade-off analysis using genetic algorithms

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In the management of a construction project, the project duration can often be compressed by accelerating some of its activities at an additional expense. This is the so-called time-cost trade-off ...
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paper_title: Hybrid of genetic algorithm and simulated annealing for multiple project scheduling with multiple resource constraints

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Since scheduling of multiple projects is a complex and time-consuming task, a large number of heuristic rules have been proposed by researchers for such problems. However, each of these rules is usually appropriate for only one specific type of problem. In view of this, a hybrid of genetic algorithm and simulated annealing (GA-SA Hybrid) is proposed in this paper for generic multi-project scheduling problems with multiple resource constraints. The proposed GA-SA Hybrid is compared to the modified simulated annealing method (MSA), which is more powerful than genetic algorithm (GA) and simulated annealing (SA). As both GA and SA are generic search methods, the GA-SA Hybrid is also a generic search method. The random-search feature of GA, SA and GA-SA Hybrid makes them applicable to almost all kinds of optimization problems. In general, these methods are more effective than most heuristic rules. Three test projects and three real projects are presented to show the advantage of the proposed GA-SA Hybrid method. It can be seen that GA-SA Hybrid has better performance than GA, SA, MSA, and some most popular heuristic methods.
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paper_title: A genetic algorithm-based method for scheduling repetitive construction projects

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This paper develops a new method for scheduling repetitive construction projects with several objectives such as project duration, project cost, or both of them. The method deals with constraints of precedence relationships between activities, and constraints of resource work continuity. The method considers different attributes of activities (such as activities which allow or do not allow interruptions), and different relationships between direct costs and durations for activities (such as linear, non-linear, continuous, or discrete relationship) to provide a satisfactory schedule. In order to minimize the mentioned objectives, the proposed method finds a set of suitable durations for activities by genetic algorithm, and then determines the suitable start times of these activities by a scheduling algorithm. The bridge construction example from literature is analyzed to validate the proposed method, and another example is also given to illustrate its new capability in project planning.
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paper_title: Using genetic algorithms to solve construction time-cost trade-off problems

paper_content:

Time-cost trade-off analysis is one of the most important aspects of construction project planning and control. There are trade-offs between time and cost to complete the activities of a project; in general, the less expensive the resources used, the longer it takes to complete an activity. Using critical path method (CPM), the overall project cost can be reduced by using less expensive resources for noncritical activities without impacting the project duration. Existing methods for time-cost trade-off analysis focus on using heuristics or mathematical programming. These methods, however, are not efficient enough to solve large-scale CPM networks (hundreds of activities or more). Analogous to natural selection and genetics in reproduction, genetic algorithms (GAs) have been successfully adopted to solve many science and engineering problems and have proven to be an efficient means for searching optimal solutions in a large problem domain. This paper presents: (1) an algorithm based on the principles of GAs for construction time-cost trade-off optimization; and (2) a computer program that can execute the algorithm efficiently.
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paper_title: A new exact penalty function method for continuous inequality constrained optimization problems

paper_content:

In this paper, a computational approach based on a new exact penalty ::: function method is devised for solving a class of continuous ::: inequality constrained optimization problems. The continuous ::: inequality constraints are first approximated by smooth function in ::: integral form. Then, we construct a new exact penalty function, ::: where the summation of all these approximate smooth functions in ::: integral form, called the constraint violation, is appended to the ::: objective function. In this way, we obtain a sequence of approximate ::: unconstrained optimization problems. It is shown that if the value ::: of the penalty parameter is sufficiently large, then any local ::: minimizer of the corresponding unconstrained optimization problem is ::: a local minimizer of the original problem. For illustration, three ::: examples are solved using the proposed method. From the solutions ::: obtained, we observe that the values of their objective functions ::: are amongst the smallest when compared with those obtained by other ::: existing methods available in the literature. More importantly, our ::: method finds solution which satisfies the continuous inequality ::: constraints.
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Title: A Review of Methods and Algorithms for Optimizing Construction Scheduling

Section 1: Introduction
Description 1: Provide an overview of construction scheduling, the complexities involved, the importance of resource selection, and the constraints that must be considered. Mention the evolution of methods and algorithms over the last 20 years.

Section 2: Solving CSO problems
Description 2: Discuss different methods for solving construction scheduling optimization (CSO) problems, classifying them into mathematical, heuristic, and metaheuristic methods.

Section 3: Mathematical methods
Description 3: Describe various mathematical methods including the Critical Path Method (CPM), Integer Programming (IP), Linear Programming (LP), and Dynamic Programming, along with their applications, advantages, and limitations in construction scheduling.

Section 4: Heuristic methods
Description 4: Communicate the principles of heuristic methods for construction scheduling, such as Fondahl's method, Structural model method, and Siemens approximation. Highlight their simplicity, problem dependency, and limitations.

Section 5: Metaheuristic method
Description 5: Explain metaheuristic methods such as Genetic Algorithm (GA), Ant Colony Optimization (ACO), and Particle Swarm Optimization (PSO). Provide detailed exploration of how these methods are inspired by natural processes and their application in CSO problems.

Section 6: Conclusion and future research
Description 6: Summarize the discussed methods and highlight the need for global optimality in solutions. Suggest directions for future research including multi-objective construction scheduling optimization covering time, cost, risk, and quality.