Inventory models with lateral transshipments: A review
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paper_title: A Redistribution Model with Set-Up Charge

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This paper considers the problem of redistributing stock among several user activities within the period between regular deliveries of new supplies to the system. The cost of redistribution is assumed to be proportional to the number of shipments among the activities. A procedure based on minimizing total redistribution and shortage costs within the period is given for determining the amounts (if any) to be shipped among activities.
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paper_title: Alternative Inventory and Distribution Policies of a Food Manufacturer

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Alternative distribution strategies for delivering to a retailer's regional depots are compared. These include supplying all the manufacturer's warehouses from the factory and allowing every possible lateral transshipment with partial stock rebalancing over different time periods. The principal alternative is to have a hierarchical system. Effects of making emergency transfers to deliberately delayed delivery vehicles are evaluated. A data stream of actual demands for a typical product is used and forecasts are made over different time periods for production planning, warehouse allocations and transshipments. The conclusions are examined for various production frequencies and levels of stock cover.
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paper_title: Cost-parametric analysis of lateral transshipment policies in two-echelon supply chains

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Abstract In this paper, we examine the cost effects of two lateral (intra-echelon) transshipment approaches in a two-echelon supply chain network, with a single supply source at the higher echelon and multiple retail locations at the lower, through a series of simulation experiments under different operating conditions. An important finding is that either of the proposed lateral shipment approaches is considerably superior to a policy of no such shipments, albeit at the expense of increased transportation activity. Further, an ad hoc emergency transshipment approach appears to be significantly more effective in terms of several important criteria, as compared to a more systematic transshipment technique based on stock level equalization.
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paper_title: An effective lateral transshipment policy to improve service level in the supply chain

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Abstract A new lateral transshipment policy, called service level adjustment (SLA), is proposed. SLA differs from previous policies by integrating emergency lateral transshipment with preventive lateral transshipment to efficiently respond to customer demands. Additionally, the proposed policy considers the service level to decide the quantity for lateral transshipment. Experiments simulating a two-echelon supply chain were conducted. The proposed policy has lower total costs than previous transshipment policies. Moreover, our policy more effectively responds to changes in demands, penalty cost, and ordering cost.
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paper_title: A two‐echelon inventory model with purchases, dispositions, shipments, returns and transshipments

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This paper presents a one-period two-echelon inventory model with one warehouse in the first echelon and n warehouses in the second echelon. At the beginning of the period the stock levels at all facilities are adjusted by purchasing or disposing of items at the first echelon, returning or shipping items between the echelons and transshipping items within the second echelon. During the period, demands (which may be negative) are placed on all warehouses in the second echelon and an attempt is made to satisfy shortages either by an expedited shipment from the first echelon to the second echelon or an expedited transshipment within the second echelon. The decision problem is to choose an initial stock level at the first echelon (by a purchase or a disposition) and an initial allocation so as to minimize the initial stock movement costs during the period plus inventory carrying costs and system shortage costs at the end of the period. ::: ::: ::: ::: It is shown that the objective function takes on one of four forms, depending on the relative magnitudes of the various shipping costs. All four forms of the objective function are derived and proven to be convex. ::: ::: ::: ::: Several applications of this general model are considered. We also consider multi-period extensions of the general model and an important special case is solved explicitly.
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paper_title: Redistribution of total stock over several user locations

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paper_title: Transshipments in a divergent 2-echelon system

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Consider a two-echelon inventory system consisting of a central depot (CD) supplying a number of retailers. Only the retailers face customer demand. Both the CD and every retailer adopt a periodic review echelon order-up-to policy, i.e., periodically an order is placed to raise the echelon inventory position to the order-up-to-level. At the CD incoming stock is allocated by using the Balanced Stock (BS) rationing policy. When the orders arrive at the retailers, an instantaneous rebalancing of the total echelon stock of the retailers takes place. This rebalancing is realized by lateral transshipments, assuming zero transshipment lead times. The used rebalancing policy is also a BS rationing policy.
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paper_title: Supply and Redistribution Rules for Two-Location Inventory Systems: One-Period Analysis

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This paper considers a two-location stochastic inventory problem with periodic review. It is assumed that replenishment may be ordered only at times of periodic review but a provision is made for transfer of stock between the locations at predetermined times within the replenishment cycle. Problems of determining jointly optimal stockage and transfer rules according to the expected total cost criterion are investigated. Under certain regularity conditions, the optimality of a simple class of Base Stock Conserving BSC transfer rules is first established. The related optimal stockage rule is then characterized for the single period model of captive sales.
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paper_title: EFFECTIVENESS OF STOCK TRANSSHIPMENT UNDER VARIOUS DEMAND DISTRIBUTIONS AND NONNEGLIGIBLE TRANSSHIPMENT TIMES*

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This paper investigates the operational characteristics of a pooling group consisting of two stocking locations, supplied periodically by a central warehouse. The two locations may collaborate by moving inventory between them. The lateral transshipment times are shorter than the regular replenishment lead times, but they are not negligible. Several alternative types of ordering and transshipment policies are examined. Extensive experimentation by simulation leads to the conclusion that the benefits of risk pooling are substantial only when demand is highly variable. Moreover, the type and variability of the demand distributions are key determinants of the appropriate transshipment policy and pooling groups design.
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paper_title: Stock redistribution in two-echelon logistics systems

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Consider a two-echelon periodic-review network consisting of a warehouse W and retailers R1,…,R n . Between replenishments of the overall system, stocks at certain retailers may become unbalanced. Therefore we allow, at a cost, the possibility of a lateral supply between retailers. This constitutes a ‘redistribution’, horizontal shipments made one period before the next regular replenishment opportunity. A stochastic inventory model is presented for such a system whose multiple stock-keeping locations have nonidentical costs; this is a major difference between the research reported here and previous work on redistribution. We developed an algorithm for carrying out the redistribution, and prove that the result is near optimal. A combination of analytical and simulation results quantify the benefits (lower costs and decreased safety stock) to our redistribution model. The resulting cost and service are compared to those of the simple allocation model (no lateral transshipments). Our cost-minimisation model is also compared to the complete redistribution model of Jonsson and Silver,1 who minimised backorders.
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paper_title: The one‐period, N‐location distribution problem

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This paper studies the one-period, general network distribution problem with linear costs. The approach is to decompose the problem into a transportation problem that represents a stocking decision, and into decoupled newsboy problems that represent the realization of demand with the usual associated holding and shortage costs. This approach leads to a characterization of optimal policies in terms of the dual of the transportation problem. This method is not directly suitable for the solution for large problems, but the exact solution for small problems can be obtained. For the numerical solutions of large problems, the problem has been formulated as a linear program with column generation. This latter approach is quite robust in the sense that it is easily extended to incorporate capacity constraints and the multiproduct case.
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paper_title: Analysis of a Two-Echelon Inventory Control System with Complete Redistribution

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This paper examines a two-level distribution system consisting of a central warehouse CW supplying several branch warehouses BW's, which, in turn, supply normally-distributed customer demands in a periodic-review environment. The CW replenishes system inventory using a base-stock replenishment policy and a predetermined order cycle of H time periods; i.e., every H periods, the CW orders enough from an outside supplier to bring the systemwide inventory position to a certain level to be determined based on a given minimum level of customer service. Upon receipt of this order, the CW allocates it entirely to the BW's so as to minimize the expected total units short at the BW's. This simple allocation scheme, may, of course, lead to out-of-balance BW inventories towards the end of the CW's order cycle. Hence, redistribution during the cycle should be considered. The redistribution treated here is a complete redistribution of all BW inventories one period before the end of the order cycle. Approximate formulas are derived which allow for a comparison of the system-wide inventories appropriate to each of two allocation schemes: 1 the simple allocation scheme only; and 2 the simple allocation scheme with total redistribution one period before the end of the order cycle. Limited computational tests indicate the magnitude of the improvements possible with total redistribution, and the sensitivities of these improvements to model parameters.
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paper_title: The Multiperiod Multilocation Inventory Problem

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This paper studies the structure of optimal policies in general multiperiod, multilocation inventory problems with proportional costs. It is shown that the multiperiod problem has the same generic form in each period as a one-period problem Hence, properties of the one-period problem are inherited by the multiperiod formulation; in particular the form of the optimal policy can be characterized. In the special case of a Leontief system structure and for a somewhat more general class it is shown that base-stock policies are optimal for certain initial states. For the stationary problem some results are derived about the monotonicity of the sequence of base stock vectors.
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paper_title: The Impact of the Secondary Market on the Supply Chain

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This paper investigates the impacts of a secondary market where resellers can buy and sell excess inventories. We develop a two-period model with a single manufacturer and many resellers. At the beginning of the first period resellers order and receive products from the manufacturer, but at the beginning of the second period, they can trade inventories among themselves in the secondary market. We endogenously derive the optimal decisions for the resellers, along with the equilibrium market price of the secondary market. The secondary market creates two interdependent effects--a quantity effect (sales by the manufacturer) and an allocation effect (supply chain performance). The former is indeterminate; i.e., the total sales volume for the manufacturer may increase or decrease, depending on the critical fractile. The latter is always positive; i.e., the secondary market always improves allocative efficiency. The sum of the effects is also unclear--the welfare of the supply chain may or may not increase as a result of the secondary market. Lastly, we study potential strategies for the manufacturer to increase sales in the presence of the secondary market.
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paper_title: Optimal and heuristic algorithms for the multi-location dynamic transshipment problem with fixed transshipment costs

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We consider centrally controlled multi-location systems, which coordinate their replenishment strategies through the use of transshipments. In a dynamic deterministic demand environment the problem is characterized by several locations, each of which has known demand for a single product for each period in a given finite horizon. We consider replenishment, transshipment and inventory holding costs at each location, where the first two have location-dependent fixed, as well as linear components, and the third is linear and identical to all locations. We prove that the resulting dynamic transshipment problem is NP-hard, identify a special structure which is satisfied by an optimal solution and develop, based on this structure, an exponential time algorithm to solve the problem optimally. In addition, we develop a heuristic algorithm, based on partitioning the time horizon, which is capable of solving larger instances than the optimal solution. Our computational tests demonstrate that the heuristic performs extremely well.
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paper_title: Modelling replenishment and transshipment decisions in periodic review multilocation inventory systems

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Effective models of key operational decisions in multilocation inventory systems are important for a successful retail sector. This paper argues that much of the existing research in this area is not applicable to a highly competitive retail environment, particularly if periodic review replenishment policies are used. The paper develops a model of a periodic review multilocation inventory system that is suitable for this environment and investigates the characteristics of optimal replenishment and transshipment decisions. This motivates the development of three simple heuristic transshipment policies that are practical for systems with many locations. The results of a numerical study involving systems with five locations suggest that the performance of these heuristic policies is often close to optimal and can be considerably better than the performance of commonly used policies.
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paper_title: Transshipments: An emerging inventory recourse to achieve supply chain leagility

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Abstract Supply chain designs are constrained by the cost-service trade-off. Cost minimization typically leads to physically efficient or lean supply chains at the expense of customer responsiveness or agility. Recently, the concept of leagility has been introduced. Research on leagility, defined as the capability of concurrently deploying the lean and agile paradigms, hinges heavily on the identification of the decoupling point, which, in turn, is enabled by postponement. Postponement strategies, however, present a cross-functional challenge for implementation. As a tactical solution to achieve leagility without postponement, we introduce transshipments, which represent a common practice in multi-location inventory systems involving monitored movement of stock between locations at the same echelon level of the supply chain. Through a series of models, we establish how transshipments can be used to enhance both agility and leanness.
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paper_title: An index heuristic for transshipment decisions in multi-location inventory systems based on a pairwise decomposition

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In multi-location inventory systems, transshipments are often used to improve customer service and reduce cost. Determining optimal transshipment policies for such systems involves a complex optimisation problem that is only tractable for systems with few locations. Consequently simple heuristic transshipment policies are often applied in practice. This paper develops an approximate solution method which applies decomposition to reduce a Markov decision process model of a multi-location inventory system into a number of models involving only two locations. The value functions from the subproblems are used to estimate the fair charge for the inventory provided in a transshipment. This estimate of the fair charge is used as the decision criterion in a heuristic transshipment policy for the multi-location system. A numerical study shows that the proposed heuristic can deliver considerable cost savings compared to the simple heuristics often used in practice.
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paper_title: The use of simple calibrations of individual locations in making transshipment decisions in a multi-location inventory network

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Demands occur at each location in a network of stock-holding retail outlets. Should a location run out of stock between successive replenishments, then subsequent demands may be met either by transshipping from another location in the network or by an emergency supply from a central depot. We deploy an approximate stochastic dynamic programming approach to develop a class of interpretable and implementable heuristics for making transshipment decisions (whether and from where to transship) which make use of simple calibrations of the candidate locations. The calibration for a location depends upon its current stock, the time to its next replenishment and the identity of the location needing stock. A numerical investigation shows strong performance of the proposed policies in comparison with standard industry practice (complete pooling, no pooling) and a recently proposed heuristic. It points to the possibility of substantial cost savings over current practice.
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paper_title: Approximate solutions for multi-location inventory systems with transshipments

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Abstract We consider a multiple retailer distribution system where emergency transshipments are permitted. The objective is to determine the effect of transshipments on ordering policies. For the identical cost situation a solution procedure based on the dynamic programming technique is developed to obtain approximate optimal ( s , S ) policies for the multi-location inventory systems with centralized ordering. This ( s , S ) ordering policy is then compared with a simplified policy that assumes free and instantaneous transshipments. The findings are that for a small number of stores and small transshipment costs, relative to the holding and stock-out costs, inventory policies may be obtained from a simplified model using zero transshipment costs but using transshipments as a means to solve emergency situations. If transshipment costs are equal or greater than the holding plus stock-out costs then a model without transshipments can be used. In general using transshipments seem to be a very cost effective way of reducing inventories for situations with a large number of stores where transshipment costs are small relative to the stock-out plus holding costs.
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paper_title: Pooling in multi-location periodic inventory distribution systems

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Risk pooling through lateral transshipment in inventory distribution systems is an effective means of improving customer service and reducing total system costs. The objective of this paper is to study the performance of an inventory system with one central warehouse and multiple retail outlets, collaborating in the case of imminent shortage by moving inventory between them. The analysis concentrates on the case of three outlets (stocking locations), which captures most of the characteristics and tradeoffs of multi-location systems with complete pooling. In addition to determining order-up-to quantities for the stocking locations, the decision maker must also specify the details of the transshipment policy when one or two locations face shortages. Simulation with a wide choice of model parameters leads to some very interesting and practically useful conclusions, including the following: (a) the benefits of risk pooling through transshipment are substantial and increase with the number of pooled locations; (b) the type of transshipment policy in case of shortages does not affect significantly the system's performance; and (c) it is preferable to form "balanced" pooling groups, consisting of locations that face similar demand.
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paper_title: A dynamic multi-location inventory model with contingents and redistribution of rest stock

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Abstract In this paper a multi-location inventory model with redistribution is considered for the discounted cost criterion. Periodically each location gets a fixed amount of a given product. At the beginning of a period it is possible to sell some product out of the system. At the end of a period the rest stock can be redistributed for decreasing system's cost. Unused product is lost as well as the unsatisfied demand. We investigate the existence and the properties of optimal selling and redistribution decisions. For the 2-location model we have solved two numerical examples.
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paper_title: The Multi-Location Transshipment Problem

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We consider a supply chain, which consists of several retailers and one supplier. The retailers, which possibly differ in their cost and demand parameters, may be coordinated through replenishment strategies and transshipments, that is, movement of a product among the locations at the same echelon level. We prove that in order to minimize the expected long-run average cost for this system, an optimal replenishment policy is for each retailer to follow an order-up-to S policy. Furthermore, we demonstrate how the values of the order-up-to quantities can be calculated using a sample-path-based optimization procedure. Given an order-up-to S policy, we show how to determine an optimal transshipment policy, using an LP/Network flow framework. Such a combined numerical approach allows us to study complex and large systems.
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paper_title: Pooling in two-location inventory systems with non-negligible replenishment lead times

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This paper deals with the analysis of two-location periodic review inventory systems with non-negligible replenishment lead times. Emergency transshipments are used in these systems as a recourse action to reduce the occurrence of shortages. A class of partial pooling policies is proposed for the control of transshipments. The cost performance of this class of policies is shown to be inferior to that of complete pooling. An approximate model and a heuristic algorithm are introduced to compute near-optimal stocking policy solutions. Comparisons with simulation results verify the satisfactory performance of the approximate model and algorithm. Numerical sensitivity analysis provides additional insight into the nature of optimal transshipment behavior.
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paper_title: The dynamic transshipment problem

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We investigate the strategy of transshipments in a dynamic deterministic demand environment over a finite planning horizon. This is the first time that transshipments are examined in a dynamic or deterministic setting. We consider a system of two locations which replenish their stock from a single supplier, and where transshipments between the locations are possible. Our model includes fixed (possibly joint) and variable replenishment costs, fixed and variable transshipment costs, as well as holding costs for each location and transshipment costs between locations. The problem is to determine how much to replenish and how much to transship each period; thus this work can be viewed as a synthesis of transshipment problems in a static stochastic setting and multilocation dynamic deterministic lot sizing problems. We provide interesting structural properties of optimal policies which enhance our understanding of the important issues which motivate transshipments and allow us to develop an efficient polynomial time algorithm for obtaining the optimal strategy. By exploring the reasons for using transshipments, we enable practitioners to envision the sources of savings from using this strategy and therefore motivate them to incorporate it into their replenishment strategies. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48:386–408, 2001
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paper_title: Lateral stock transshipments in a two-location inventory system with fixed and joint replenishment costs

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We address the problem of inventory management in a two-location inventory system, in which the transshipments are carried out as means of emergency or alternative supply after demand has been realized. This model differs from previous ones as regards its replenishment costs structure, in which nonnegligible fixed replenishment costs and a joint replenishment cost are considered. The single period planning horizon is analyzed, with the form and several properties of the optimal replenishment and transshipment policies developed, discussed and illustrated. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 525–547, 1999
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paper_title: Effects of Pooling on the Optimization and Service Levels of Two-Location Inventory Systems

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Abstract The study of inventory distribution systems with two locations and random demand is the subject of this paper. It is shown that under certain conditions a policy of complete pooling between the locations minimizes the expected costs for the system. A solution procedure is proposed for the derivation of the optimal parameters determining the ordering and lateral transshipmentrules. Relationships between the measures of service level before and after pooling are derived, and it is concluded that pooling always improves the service levels at both locations. Minimization of total costs'subject to service level constraints is also studied. Numerical examples serve to illustrate the analytical results. Handled by the Editor-In-Chief.
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paper_title: An Optimal Policy for a Two Depot Inventory Problem with Stock Transfer

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Multiple depot inventory systems with stock transfer are used by many companies especially when demand is high relative to storage capacity. The key issues in such systems are how many of each item to hold at each depot and what to do if there is a demand for an item at a depot that has none of that item in stock. This study was motivated by the inventory problem faced by a UK car part retailer that groups its depots into pairs. The company's policy for dealing with a demand at a depot that cannot be satisfied from local stock is to either transfer the item from the other depot in the group or to place an emergency order. The object of this paper is to characterise an optimal policy for this problem and to propose a method of calculating the parameters of such a policy.
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paper_title: Optimal Solutions in the Multi-location Inventory System with Transshipments

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We consider a single-period multi-location inventory system where inventory choices at each location are centrally coordinated. Transshipments are allowed as recourse actions in order to reduce the cost of shortage or surplus inventory after demands are realized. This problem has not been solved to optimality before for more than two locations with general cost parameters. In this paper we present a simple and intuitive model that enables us to characterize optimal inventory and transshipment policies for three and four locations as well. The insight gained from these analytical results leads us to examine the optimality conditions of a greedy transshipment policy. We show that this policy will be optimal for two and three locations. For the n location model we characterize the necessary and sufficient conditions on the cost structure for which the greedy transshipment policy will be optimal.
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paper_title: Optimal Policies for Transshipping Inventory in a Retail Network

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Motivated by recent reports of improved customer service facilitated by the use of transshipment to pool inventory, we develop a formal model that focuses on the role of transshipment in a system of n-retailers who stock a good. In addition, some stock may be kept at a warehouse. If a retailer faces a stockout, he makes an attempt to fill backorders by using a transshipment that may come either from the warehouse or from another retailer that has excess stock. We determine that the optimal transshipment policy is described by exactly one of five protocols, and that the choice among them can be made by evaluating a set of easily computable conditions. We also provide other structural results that help identify conditions under which a warehouse should be open: how this decision is influenced by the total number of retailers, and how this decision is related to the degree of correlation of demand between retailers.
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paper_title: Who Benefits from Transshipment? Exogenous vs. Endogenous Wholesale Prices

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This paper studies how transshipments affect manufacturers and retailers, considering both exogenous and endogenous wholesale prices. For a distribution system where a single manufacturer sells to multiple identical-cost retailers, we consider both the manufacturer being a price taker and the manufacturer being a price setter in a single-period setup under multivariate normal demand distribution. In the case of the manufacturer being a price taker, we provide several analytical results regarding the effects of key parameters on order quantities and profits. In the case of the manufacturer being a price setter, we characterize the Stackelberg game that arises, and provide several insights into how the game dynamics are affected by transshipments. Specifically, we find that risk pooling makes retailers' order quantities less sensitive to the wholesale price set by the manufacturer; hence, in general, the manufacturer benefits from retailers' transshipments by charging a higher wholesale price, while retailers are often worse off. The paper captures the effect of demand correlation and the effect of the number of retailers throughout, and it illustrates the findings by a numerical example. We also provide an interactive Web page for numerical experiments.
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paper_title: Cooperation between multiple news-vendors with transshipments

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We study a situation with n retailers, each of them facing a news-vendor problem, i.e., selling to customers over a finite period of time (product with a short life cycle, such as fashion). Groups of retailers might improve their expected joint profit by coordinating their orders, followed by transshipments after demand realization is known. We analyze these situations by defining a cooperative game, called a general news-vendor game, for such a situation with n retailers. We concentrate on whether it makes sense to cooperate by studying properties of general news-vendor games. Our main result states that general news-vendor games have non-empty cores.
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paper_title: A Three-Stage Model for a Decentralized Distribution System of Retailers

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We present and study a three-stage model of a decentralized distribution system consisting ofn retailers, each of whom faces a stochastic demand for an identical product. In the first stage, before the demand is realized, each retailer independently orders her initial inventory. In the second stage, after the demand is realized, each retailer decides how much of her residual supply/demand she wants to share with the other retailers. In the third stage, residual inventories are transshipped to meet residual demands, and an additional profit is allocated. Our model is an extension of the two-stage model of Anupindi et al. (ABZ) (2001), which implicitly assumes that all residuals enter the transshipment stage. We show, however, that allocation rules in the third stage based on dual solutions, which were used in the ABZ model, may induce the retailers to hold back some of their residual supply/demand. In general, we study the effect of implementing various allocations rules in the third stage on the values of the residual supply/demand the retailers are willing to share with others in the second stage, and the trade-off involved in achieving an optimal solution for the corresponding centralized system.
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paper_title: Existence of Coordinating Transshipment Prices in a Two-Location Inventory Model

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We consider a two-location production/inventory model where each location makes production decisions and is subject to uncertain capacity. Each location optimizes its own profits. Transshipment (at a cost) is allowed from one location to another. We focus on the question of whether one can globally set a pair of coordinating transshipment prices, i.e., payments that each party has to make to the other for the transshipped goods, that induce the local decision makers to make inventory and transshipment decisions that are globally optimal. A recent paper suggests, for a special case of our model, that there always exists a unique pair of coordinating transshipment prices. We demonstrate through a counterexample that this statement is not correct and derive sufficient and necessary conditions under which it would hold. We show that in some conditions, coordinating prices may exist for only a narrow range of problem parameters and explore conditions when this can happen. Finally, we study the effects of demand and capacity variability on the magnitude of coordinating transshipment prices.
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paper_title: A Two-Location Inventory Model with Transshipment and Local Decision Making

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In situations where a seller has surplus stock and another seller is stocked out, it may be desirable to transfer surplus stock from the former to the latter. We examine how the possibility of such transshipments between two independent locations affects the optimal inventory orders at each location. If each location aims to maximize its own profits--we call this local decision making--their inventory choices will not, in general, maximize joint profits. We find transshipment prices which induce the locations to choose inventory levels consistent with joint-profit maximization.
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paper_title: A General Framework for the Study of Decentralized Distribution Systems

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We develop a general framework for the analysis of decentralized distribution systems. We carry the analysis in terms of a simplified model which entailsN retailers who face stochastic demands and hold stocks locally and/or at one or more central locations. An exogenously specified fraction of any unsatisfied demand (demand greater than locally available stock) at a retailer could be satisfied using excess stocks at other retailers and/or stocks held at a central location. We consider inventory ordering and allocation decisions. The operational decisions of inventory and allocation of stocks and the financial decision of allocation of revenues/costs must be made in a way consistent with the individual incentives of the various independent retailers. We develop a "coopetitive" framework for the sequential decisions of inventory and allocation. We introduce the notion ofclaims that allows us to separate the ownership (with decision rights) and the location of inventories in the system. For the cooperative shipping and allocation decision, we use the concept of core and develop sufficient conditions for the existence of the core. For the inventory decision, we develop conditions for the existence of a pure strategy Nash Equilibrium. For this decentralized system, we show that there exists an allocation mechanism that achieves the first-best solution for inventory deployment and allocation. We develop conditions under which the first-best equilibrium will be unique. Our model can be easily generalized to include complicated ownership structures such as "super dealers," partnerships, "inventory speculators," and situations in retail e-commerce settings such as "click-through arrangements," separation of "demand generators," and "fulfillment houses," etc. It can also be applied to situations involving capacity allocations and product substitutions.
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paper_title: Metric: A Multi-Echelon Technique for Recoverable Item Control

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Metric is a mathematical model of a base-depot supply system in which item demand is compound Poisson with a mean value estimated by a Bayesian procedure. When a unit fails at base level there is a probability r that it can be repaired at the base according to an arbitrary probability distribution of repair time, and a probability 1 − r that it must be returned to the depot for repair according to some other arbitrary distribution. In the latter case the base levies a resupply request on depot. No lateral resupply between bases is considered in the model. For high-cost, low-demand items the appropriate policy is ( s − 1, s ), which means that items are not batched for repair or resupply requests. This problem has a simple analytic solution that is a function of the mean repair times rather than the repair time distributions. A practical and efficient computer program has been designed to show the cost-effectiveness tradeoff for a large group of recoverable items. In addition to minimizing expected backorders for any system investment, the program can evaluate any distribution of stock and it can compute the optimal redistribution of stock. No arbitrary estimates of backorder cost or holding cost are required.
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paper_title: An inventory model with returns and lateral transshipments

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In this paper, we propose a single-item inventory model with returns. The model allows lateral transshipment of returns from one inventory system to another. Each inventory system is under continuous review and an (r, Q) policy is employed as the inventory control. An approximated closed-form solution of the system steady-state probability distribution is derived when Q is large. The approximated inventory cost and replenishment cost can be written in terms of this distribution. We show that the rejection rate of returns is reduced significantly when transshipment of returns is allowed between the inventory systems.
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paper_title: Modeling lateral transshipments in multiechelon repairable-item inventory systems with finite repair channels

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This article concerns the problem of determining the optimal spare inventory level for a multiechelon repairable-item inventory system, which has several bases and a central depot. When an item fails, the failed item is replaced immediately if a spare is available at the base. If there is no spare item available at the base, it is requested as a lateral transshipment to another base that has a spare in stock. If an item is not available from any of the bases, the item is backordered until a spare becomes available. We propose a model to describe the behavior of the system and develop an algorithm to find the spare inventory level at each base, which minimizes the total expected cost of the system. The algorithm is illustrated using examples of various sizes.
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paper_title: Stocking decisions for repairable spare parts pooling in a multi-hub system

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Abstract This paper presents an analytical model for determining spare parts stocking levels in a single-item, multi-hub, multi-company, repairable inventory system in which complete pooling of stock is permitted among the hubs and companies. The objective is to minimize the total system cost which consists of inventory holding cost, downtime cost and transshipment cost. We develop an approximation method to compute the logistical system performance measures needed for calculating the cost function. To find the optimal stocking levels, a two-stage solution is proposed. In the first stage, the demands at all hubs are aggregated and treated as if occurring at a single location. The optimal number of total spare parts is determined by minimizing the sum of inventory holding cost and downtime cost. In the second stage, a heuristic procedure is developed to find the optimal allocation of the total spare parts to minimize the total transshipment cost.
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paper_title: Insights into inventory sharing in service parts logistics systems with time-based service levels

paper_content:

Service parts logistics systems are usually characterized by very low random demand, high part cost, and target time-based service levels, all of which lead inventory planners to utilize inventory sharing or ''emergency lateral transshipments'' across multiple stocking locations. Using a stylized model with one central warehouse and multiple local stocking locations, we seek insights into the behavior of an inventory sharing system with time-based service level considerations. The goal of inventory sharing is to satisfy a demand in case a local facility is out of stock, by meeting the demand with a direct delivery from another location that can provide the service within the time window necessary for the target service level. We adapt an existing model from the literature for such a system and study its performance in terms of cost and service level. In addition, we evaluate two-location and three-location scenarios to study the effect of having additional stocking locations.
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paper_title: The effects of resupply flexibility on the design of service parts supply systems

paper_content:

We apply simulation optimization to determine the optimal design and stock distribution for a single item supply system with a one-for-one replenishment policy. We investigate both the effect of the number of echelons and the degree of resupply flexibility, considering single-echelon and two-echelon systems with either no resupply flexibility, lateral transhipments only or both lateral transhipments and emergency deliveries. We show that the implementation of an emergency delivery option allows an augmentation of the fraction of customers served by lateral transhipments and that increased resupply flexibility enables increasingly important cost savings.
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paper_title: Optimal Policies for Inventory Systems with Lateral Transshipments

paper_content:

Using lateral transshipments can be beneficial in order to improve service levels and to reduce system costs. This paper deals with a single-echelon inventory system with two identical locations. Demands are generated by stationary and independent Poisson processes. In general, if a demand occurs at a location and there is no stock on hand, the demand is assumed to be backordered or lost. However, in this paper, lateral transshipments serve as an emergency supply in case of stock out. In this paper, the rule for lateral transshipments is given, while the ordering policies for normal replenishments are optimized. The transshipment rule is to always transship when there is a shortage at one location and stock on hand at the other. First, we assume that the locations apply (R,Q) policies for normal replenishments, and show that the optimal policies are not necessarily symmetric even though the locations are identical. This means that one cannot in general assume that the optimal policy is symmetric under symmetric assumptions. Second, we relax the assumption of (R,Q) policies and derive the optimal replenishment policy using stochastic dynamic programming.
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paper_title: A model for lumpy demand parts in a multi-location inventory system with transshipments

paper_content:

The inventory system considered in this work is single echelon, N-location and continuous review in which complete pooling of stock is permitted among the locations. A model is developed for slow moving, expensive items that are common to two or more locations. The model developed focuses on parts that have a lumpy demand pattern; that is, the number of units demanded at each demand occasion is a random variable. The motivating case for this research has been a real-life situation presented by a large utility company having 29 power generating plants in five southeastern states. Data analysis from the company reveals that there are a substantial number of parts that have low usage, are expensive, and have a lumpy demand pattern. At present, each location operates independently and maintains enough stock to meet its own requirements. Transshipments take place between locations whenever there is an emergency requirement for a part, but no explicit consideration is given to this effect while deciding on the inventory control policies at different locations. A model, using analytical and simulation techniques, is developed for this situation. Limited experimentation, performed on a set of problems, shows an average savings of about 31% as a result of pooling.
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paper_title: A multi-echelon inventory model for repairable items with emergency lateral transshipments

paper_content:

In multi-echelon inventory systems that cover extensive geographical regions, emergency lateral transshipment between bases is commonly practiced to provide improved service support for products. In these systems, since neighboring bases are at shorter distances than to the depot, the base may seek stock from them to satisfy its demands when it is out of stock. In this paper we develop a continuous-review multi-echelon model for repairable items when emergency lateral transshipments between identical bases are allowed. Approximations are derived and tested for the expected level of backorders and the quantity of emergency lateral transshipments in cases where fairly high service levels are required. These approximations are used to determine the optimal stocking levels in such a system. A procedure to find these stocking levels is given. Numerical examples illustrate the application of the procedure and the tradeoffs involved in emergency lateral transshipment.
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paper_title: Evaluation of two simple extreme transshipment strategies

paper_content:

Abstract We consider an organization that has more than one outlet (retailer or regional warehouse) where stock is held to meet customer demands. In such a situation, transshipments can be used to improve customer service and/or reduce the aggregate stock required. Unfortunately, the determination of an optimal transshipment policy (i.e. when to transship and how much) is a complex mathematical problem. However, in earlier research the authors observed that choosing the better of two extreme policies leads to performance that is nearly as good as a more complex analysis that takes account of the future impact of a transshipment on the cost at the location sending the shipment. These extreme policies are (i) never transship and (ii) always transship when there is a shortage at one location and stock available at another. In this paper, for the case of two stocking points, we develop an analytical approach for approximately estimating the total expected costs (carrying, replenishment, transshipments and lost sales) of these two policies. This provides a mechanism for choosing between the two policies for any given set of problem characteristics. The results of a numerical experiment are shown.
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paper_title: Stocking Decisions for Low-Usage Items in a Multilocation Inventory System

paper_content:

This research shows that organizations with a number of "sister" plants, warehouses, or other stocking points can profit from the concept of proactive use of transshipments as an element of their inventory control policy. For certain types of parts, employing transshipments can significantly reduce the total inventory needed throughout the entire collection of stocking points. The study is motivated by a real-life situation involving a large utility company having 29 power-generating plants in five Southeastern states where there are thousands of parts that are commonly used at multiple plants. ::: ::: At present, each plant operates independently and maintains enough stock to meet its own requirements. Transshipments take place between plants whenever there is an emergency requirement for a part, but no explicit consideration is given to this effect while deciding on stocking levels at different plants. In the case we examined, by setting stocking levels to explicitly take account of transshipments, total system cost could be reduced by about 70% over the company's decentralized policy. ::: ::: In general, this work considers a single-echelon, N-location, continuous-review inventory system in which complete pooling of stock is permitted among the locations. A model is developed for slow-moving, expensive, and consumable parts that are common to two or more locations. A one-for-one ordering policy and queueing theory allow development and solution of a system of equations for the probability distribution of net inventory at each location. A heuristic procedure is also developed to determine cost-effective stocking levels. Actual data from the utility company are used to demonstrate the applicability of the model. Savings achieved as a result of pooling are reported.
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paper_title: An improved heuristic for deciding on emergency transshipments

paper_content:

Abstract Utilising emergency lateral transshipments between retailers to meet customer demand can be an effective means for companies to improve service levels and/or reduce costs. This paper provides a decision rule for how much (if any) to source and from which retailer(s), taking into account the financial impact of the transshipment decision on future service levels and the timing of subsequent orders from suppliers. While the model explicitly recognises fixed and variable transshipment costs, as well as information on orders en route to retailers, it is simple enough to facilitate real-time execution and/or implementation on a spreadsheet. Simulation results indicate significant improvement on recently published results. We illustrate the method using several examples and discussing sensitivity to key parameters.
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paper_title: Sharing and Lateral Transshipment of Inventory in a Supply Chain with Expensive Low-Demand Items

paper_content:

The emergence of carriers that deliver items to geographically dispersed destinations quickly and at a reasonable cost, combined with the low cost of sharing information through networked databases, has opened up new opportunities to better manage inventory. We investigate these benefits in the context of a supply chain in which a manufacturer supplies expensive, low-demand items to vertically integrated or autonomous retailers via one central depot. The manufacturer's lead time is assumed to be due to the geographical distance from the market or a combination of low volumes, high variety, and inflexible production processes. We formulate and solve an appropriate mathematical model based on one-for-one inventory policies in which a replenishment order is placed as soon as the customer withdraws an item. We find that sharing and transshipment of items often, but not always, reduces the overall costs of holding, shipping, and waiting for inventory. Unexpectedly, these cost reductions are sometimes achieved throughincreasing overall inventory levels in the supply chain. Finally, while sharing of inventory typically benefits all the participants in decentralized supply chains, this is not necessarily the case--sharing can hurt the distributor or individual retailers, regardless of their relative power in the supply chain.
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paper_title: A multi-echelon integrated JIT inventory model using the time buffer and emergency borrowing policies to deal with random delivery lead times

paper_content:

This paper proposes a multi-echelon integrated just-in-time (JIT) inventory model with random delivery lead times for a serial supply chain in which members exchange information to jointly make purchase, production, and delivery decisions. The performance of the whole supply chain depends on whether or not uncertain delivery can be handled properly. In this paper, a time buffer and emergency borrowing policies are used simultaneously to deal effectively with random delivery lead times and to protect a JIT system against shortages of goods. To construct easily the proposed multi-echelon integrated JIT inventory (MEIJITI) model, a duplication methodology is created. Since optimizing the proposed model is equivalent to solving an extremely complex mixed nonlinear integer programming problem, three propositions used to reduce the solution space and simplify the solution procedure are derived. Accordingly, a proposed search method for finding the optimal solution and a simulated annealing algorithm used succes...
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paper_title: Inventory pooling of repairable spare parts with non-zero lateral transshipment time and delayed lateral transshipments

paper_content:

In this paper, we develop an analytical model to estimate several performance measures in a single-item, multi-company, repairable inventory system where complete pooling of stock is permitted among the companies. Compared to previous research, this paper is different in that both non-zero lateral transshipment time and delayed lateral transshipments are considered in the model. We model the system as a multi-dimensional Markovian problem and solve it using a two-stage solution method. The proposed method is very accurate and computationally efficient.
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paper_title: Cost allocation in spare parts inventory pooling

paper_content:

In this paper we present the use of game theoretic models to analyse the cost allocation problem in the context of repairable spare parts pooling. Two situations are studied. In the first situation, all pooling members fully cooperate without having self-interest. We use the core concept from cooperative game theory as the basis for designing a fair cost allocation. In the second situation, competition exists as each member has an interest in maximizing his own benefit. Using the concept of Nash equilibrium, we show that the cost allocation policy influences the companies in making their inventory decisions.
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paper_title: An inventory sharing and allocation method for a multi-location service parts logistics network with time-based service levels

paper_content:

We consider a model to allocate stock levels at warehouses in a service parts logistics network. The network is a two-echelon distribution system with one central warehouse with infinite capacity and a number of local warehouses, each facing Poisson demands from geographically dispersed customers. Each local warehouse uses a potentially different base stock policy. The warehouses are collectively required to satisfy time-based service targets: Certain percentages of overall demand need to be satisfied from facilities within specified time windows. These service levels not only depend on the distance between customers and the warehouses, but also depend on the part availabilities at the warehouses. Moreover, the warehouses share their inventory as a way to increase achieved service levels, i.e., when a local warehouse is out of stock, demand is satisfied with an emergency shipment from another close-by warehouse. Observing that the problem of finding minimum-cost stock levels is an integer non-linear program, we develop an implicit enumeration-based method which adapts an existing inventory sharing model from the literature, prioritizes the warehouses for emergency shipments, and makes use of a lower bound. The results show that the proposed inventory sharing strategy results in considerable cost reduction when compared to the no-sharing case and the method is quite efficient for the considered test problems.
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paper_title: Modelling Emergency Lateral Transshipments in Inventory Systems

paper_content:

In inventory systems with several bases that support different geographical regions, it is quite common to allow emergency lateral transshipments between the bases. This may be advantageous if neighbouring bases are at shorter distances than the central depot or the external supplier. This paper provides a new technique for modelling such lateral transshipments in continuous review inventory systems with one-for-one replenishments and Poisson demand. We apply this technique to a two-echelon system with repairable items.
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paper_title: VARI-METRIC: Improved Approximations for Multi-Indenture, Multi-Echelon Availability Models

paper_content:

Multi-indenture models for s-1, s inventory policies, such as mod-metric and the Logistics Management Institute LMI Aircraft Availability Model, understate the delay in the repair of a higher indenture item caused by backorders on the item's lower indenture components. These models also understate the multi-echelon delay in the resupply of a base from a depot that has backorders. Consequently, the models tend to understate expected backorders and overstate expected availability of repair items. We show that it is possible to improve the accuracy of multi-indenture models in a manner similar to the way in which the metric approximation for multi-echelon availability has been improved. We do so by showing that the multi-indenture improvement for a single echelon is valid for compound Poisson demand and arbitrary repair distributions, and that the new approximation is easy to incorporate. Simulation shows that the new approximation provides a much more accurate estimate of the expected backorders. We then present the improved approximation for the combination of multi-indenture and multi-echelon, using the vari-metric model. The vari-metric estimate of backorders is very close to the "true" value from simulation, and the allocation of investment across one item group consisting of a first indenture item and its second indenture components is better than mod-metric when there is a difference.
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paper_title: A Two-Echelon Inventory System with Priority Shipments

paper_content:

A two-echelon system for spare parts is analyzed. The system allows the use of priority inventory pooling to expedite service when a stock-out occurs. First, a tractable aggregate model is derived. This model is then disaggregated to approximate the performance of the exact system. Results of computer tests are also presented.
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paper_title: Modeling Emergency Supply Flexibility in a Two-Echelon Inventory System

paper_content:

We consider a two-echelon inventory system for service parts. To obtain high service levels at a low cost we allow not only for normal supply of parts but also for emergency supply options in terms of lateral transshipments and direct deliveries. After presenting the strategy we use for satisfying customer demand, we construct an analytical model that we use to calculate relevant performance measures. Simulation shows that our model produces accurate estimates, and that the performance of the inventory system is insensitive to the lead-time distribution. After introducing a cost structure we show that the strategy we propose can result in considerable savings when compared to using only normal supply. Comparison of the results of our model with the results of other models indicates that the combined use of lateral transshipments and direct deliveries can lead to significant cost savings.
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paper_title: The influence of individual cost factors on the use of emergency transshipments

paper_content:

Emergency transshipments represent one way in which logistics managers can reduce inventories while simultaneously maintaining customer service levels. This paper examines the cost implications of these actions and offers a straightforward approach to analyzing their suitability. Simulation results indicate that the cost of a stockout is the primary determinant in the transshipment decision, with higher stockout cost levels generally increasing the likelihood that transshipment usage will lead to lower overall cost. A metamodel is proposed as a practical means of providing insight into when emergency transshipments should be employed.
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paper_title: Batch Ordering Policy of Multi-location Spare Parts Inventory System with Emergency Lateral Transshipments

paper_content:

Abstract A batch ordering model for multi-location spare parts inventory system with emergency lateral transshipments is provided, and algorithms for calculating the probabilities of demand fulfillment by inventory point self, by transshipment, or backorder are also given. Based on these, a procedure is given to find the best ordering point for a constrained model that minimizes holding plus transshipment cost subject to a certain service level, assuming the ordering quantity is predetermined. The results were tested through simulation.
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paper_title: Estimating customer service in a two-location continuous review inventory model with emergency transshipments

paper_content:

Abstract In this paper, an approximate analytical two-location inventory transshipment model is developed that combines the popular order-quantity, reorder-point ( Q , R ) continuous review ordering policy with a third parameter, the hold-back amount, which limits the level of outgoing transshipments. The degree to which transshipments improve both Type I (no-stockout probability) and Type II (fill rate) customer service levels can be calculated using the model. Simulation studies conducted to test the validity of the approximations in the analytical model indicate that it performs very well over a wide range of inputs.
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paper_title: Heuristics for assessing emergency transshipments

paper_content:

Abstract It is not uncommon for organizations with multiple stock-keeping facilities to have some locations facing shortages while others have excess inventory. This paper examines emergency transshipments of product as an approach to solve this problem. Specifically, two heuristics are developed to assist managers in determining when stock transfers should be made. The heuristics produce critical values for on-hand inventory levels above which transshipments minimize overall expected costs. They also provide insight into the factors affecting transshipment usage.
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paper_title: The value of virtual pooling in dual sales channel supply chains

paper_content:

Recently the most significant growth in online retailing has been attributed to traditional offline retailers extending their brands online. Unfortunately, there is little research addressing the value of better information in retail/e-tail organizations. To fill this gap, this paper examines how investing in the continuous monitoring of online demands and inventory positions can provide economic benefit for companies that handle both in-store and online sales. Specifically, we develop and evaluate two dynamic assignment policies that incorporate real time information to specify which of a firm's e-fulfillment locations will handle each of its Internet sales. Computational results indicate that investing in dynamic assignment capability can reduce system cost (holding, backorder, and transportation) by as much as 8.2% over the optimal static policy. The percentage of sales occurring online plays a critical role in determining the magnitude of the benefit.
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paper_title: Inventory sharing and rationing in decentralized dealer networks

paper_content:

An increasing number of manufacturers have started to pursue a strategy that promotes inventory sharing among the dealers in their distribution network. In this paper we analyze a decentralized dealer network in which each independent dealer is given the flexibility to share his inventory. We model inventory sharing as a multiple demand classes problem in which each dealer faces his own customer demand with high priority, and inventory-sharing requests from other dealers with low priority. Assuming that each dealer uses a base-stock and threshold-rationing policy for his inventory-stocking and inventory-sharing decisions, we explicitly model the interactions between the dealers through inventory sharing and obtain aclosed-form cost function for each dealer based on the steady-state distribution of the inventory levels at the two dealers. We then provide a detailed supermodularity analysis of the inventory-sharing and inventory-rationing game in which each dealer has a two-dimensional strategy set (stocking level and rationing level). We show that the full-sharing game (in which dealers precommit to sharing all of their on-hand inventory) and the fixed-sharing-level game (in which dealers precommit to sharing a portion of their on-hand inventory) are supermodular, and thus a pure-strategy Nash equilibrium is guaranteed to exist. For the rationing game (in which dealers precommit to their stocking levels), we show that there exists a dominant strategy equilibrium on the dealers' sharing (rationing) levels. Finally, a comprehensive computational study is conducted to highlight the impact of the manufacturer's incentives, subsidies, and/or transshipment fees on the dealers' sharing behavior.
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paper_title: Evaluation of Inventory Policies with Unidirectional Substitutions

paper_content:

We propose evaluation approaches to multi-item base-stock inventory policies where unidirectional substitutions are allowed. The problems in the paper are in the context of spare parts management and we identify two substitution cases: substitution upon demand arrivals and substitution upon order deliveries. This leads us to three unidirectional substitution policies, for each of which we develop Markovian models. As the number of part types increases, computational effort required to solve the Markovian models increases rapidly. To reduce computation burden, an approximation approach based on the decomposition of multi-dimensional state transition is used for systems with two or more spare part types. Numerical studies show unidirectional substitution improves various system performance measures such as the average inventory level, the average backlogged demand, and the fill rate. The proposed decomposition approach reduces the computation required to compute the performance measures and the approximation errors seems to be quite small.
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paper_title: An improved heuristic for deciding on emergency transshipments

paper_content:

Abstract Utilising emergency lateral transshipments between retailers to meet customer demand can be an effective means for companies to improve service levels and/or reduce costs. This paper provides a decision rule for how much (if any) to source and from which retailer(s), taking into account the financial impact of the transshipment decision on future service levels and the timing of subsequent orders from suppliers. While the model explicitly recognises fixed and variable transshipment costs, as well as information on orders en route to retailers, it is simple enough to facilitate real-time execution and/or implementation on a spreadsheet. Simulation results indicate significant improvement on recently published results. We illustrate the method using several examples and discussing sensitivity to key parameters.
---
paper_title: Sharing and Lateral Transshipment of Inventory in a Supply Chain with Expensive Low-Demand Items

paper_content:

The emergence of carriers that deliver items to geographically dispersed destinations quickly and at a reasonable cost, combined with the low cost of sharing information through networked databases, has opened up new opportunities to better manage inventory. We investigate these benefits in the context of a supply chain in which a manufacturer supplies expensive, low-demand items to vertically integrated or autonomous retailers via one central depot. The manufacturer's lead time is assumed to be due to the geographical distance from the market or a combination of low volumes, high variety, and inflexible production processes. We formulate and solve an appropriate mathematical model based on one-for-one inventory policies in which a replenishment order is placed as soon as the customer withdraws an item. We find that sharing and transshipment of items often, but not always, reduces the overall costs of holding, shipping, and waiting for inventory. Unexpectedly, these cost reductions are sometimes achieved throughincreasing overall inventory levels in the supply chain. Finally, while sharing of inventory typically benefits all the participants in decentralized supply chains, this is not necessarily the case--sharing can hurt the distributor or individual retailers, regardless of their relative power in the supply chain.
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paper_title: HIDDEN BENEFITS OF EMERGENCY TRANSSHIPMENTS.

paper_content:

A cryogenic, submersible, synthetic air-breathing system which provides the diver with a proper breathing atmosphere, including provisions for a water-jet propulsion unit to propel the diver to an extended underwater range. The system utilizes liquid oxygen and liquid nitrogen, each stored in respective tanks, whereby the gases pass through a series of heat exchangers, regulators, check valves and a slider valve into which the regulated gases enter a mixing chamber wherein breathable air is generated therein, and then delivered to the diver's face mask-an unmixed portion of the gas being used as the means to power a conventional air motor which, in turn, powers an underwater jet engine.
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paper_title: Relaxing channel separation: Integrating a virtual store into the supply chain via transshipments

paper_content:

Many established companies have started to use virtual stores as a direct distribution channel in addition to their existing indirect retail channels. These companies must now decide on how to integrate these channels. The alternatives are to operate dedicated distribution channels for the virtual store and the retail stores or to tightly integrate the virtual store into the existing distribution channels. In such an integrated supply chain, retail stores would continue to serve all in-store customers, but excess stock at retail stores could be used to fill some online orders. We analyze this problem from a supply chain perspective by developing and solving mathematical models for both dedicated and integrated supply chains. We characterize the optimal inventory policy and quantify the expected cost savings that can be achieved by using an integrated supply chain over a dedicated supply chain. We show that the cost savings can be significant and that both retailers and customers benefit from an integrated supply chain. We also analyze how the optimal solutions depend on the characteristics of the supply chain and identify conditions under which it would be optimal to operate the virtual store without dedicating any inventory to the virtual store. Throughout the paper, we illustrate our analytical results with numerical examples.
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paper_title: On queueing models for some multi-location problems

paper_content:

Abstract It is known that an equivalence between queueing models and single-location inventory models exists if the demand is assumed as a continuous stochastic process. The paper points out how queueing network models and their methods of investigation can be used for modeling and solving multi-location inventory problems
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paper_title: Evaluation of unidirectional lateral transshipments and substitutions in inventory systems

paper_content:

One interpretation of the model considered in this paper is a single-echelon inventory system consisting of a number of local warehouses, which normally replenish from an outside supplier. In case of a stockout at a warehouse an emergency lateral transshipment from another warehouse may be possible. However, such transshipments are only allowed in one direction, i.e., the flow structure is unidirectional. Such policies can be of interest if the warehouses have very different shortage costs. Another interpretation is substitution in an inventory system. We then instead consider different items in a single warehouse. When a demand for a low quality item cannot be met directly, the item can be replaced by another high quality item. We provide a simple and efficient approximate technique for policy evaluation in such systems. The performance of this technique is evaluated in a simulation study. Although the errors are not always negligible, the suggested method gives a good picture of how the considered lateral transshipments or substitutions affect the inventory system.
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paper_title: Emergency transshipment in decentralized dealer networks: When to send and accept transshipment requests

paper_content:

While there has been significant previous literature on inventory transshipment, most research has focused on the dealers' demand filling decision (when to fill transshipment requests from other dealers), ignoring the requesting decision (when to send transshipment requests to other dealers). In this paper we develop optimal inventory transshipment policies that incorporate both types of decisions. We consider a decentralized system in which the dealers are independent of the manufacturer and of each other. We first study a network consisting of a very large number of dealers. We prove that the optimal inventory and transshipment decisions for an individual dealer are controlled by threshold rationing and requesting levels. Then, in order to study the impact of transshipment among independent dealers in a smaller dealer network, we consider a decentralized two‐dealer network and use a game theoretic approach to characterize the equilibrium inventory strategies of the individual dealers. An extensive numerical study highlights the impact of the requesting decision on the dealers' equilibrium behavior in a decentralized setting. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006
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paper_title: THE IMPACT OF TRANSSHIPMENTS ON SAFETY STOCK REQUIREMENTS

paper_content:

A blast-furnace tuyere having excellent thermal shock resistance and high durability consists of a tuyere substrate composed of copper or copper alloy, a self-fluxing alloy metallized layer sprayed on the substrate, a cermet coating sprayed on the alloy metallized layer, and a ceramic coating sprayed on the cermet coating. The cermet coating is made from a mixture of an alloy material consisting essentially of 5 to 60 wt% of Co, 5 to 50 wt% of Ni, 5 to 25 wt% of Cr, 5 to 40 wt% of Mo, 5 to 40 wt% of W, 3 to 40 wt% of Si and inevitable impurities, and a ceramic eutectic material consisting essentially of 95 to 65 wt% of Al2O3, 5 to 30 wt% of ZrO2, 2 to 20 wt% of TiO2, 3 to 30 wt% of SiO2 and inevitable impurities. The ceramic coating is made from the same ceramic material as used in the formation of the cermet coating.
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paper_title: A multi-echelon integrated JIT inventory model using the time buffer and emergency borrowing policies to deal with random delivery lead times

paper_content:

This paper proposes a multi-echelon integrated just-in-time (JIT) inventory model with random delivery lead times for a serial supply chain in which members exchange information to jointly make purchase, production, and delivery decisions. The performance of the whole supply chain depends on whether or not uncertain delivery can be handled properly. In this paper, a time buffer and emergency borrowing policies are used simultaneously to deal effectively with random delivery lead times and to protect a JIT system against shortages of goods. To construct easily the proposed multi-echelon integrated JIT inventory (MEIJITI) model, a duplication methodology is created. Since optimizing the proposed model is equivalent to solving an extremely complex mixed nonlinear integer programming problem, three propositions used to reduce the solution space and simplify the solution procedure are derived. Accordingly, a proposed search method for finding the optimal solution and a simulated annealing algorithm used succes...
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paper_title: An Optimal Policy for a Two Depot Inventory Problem with Stock Transfer

paper_content:

Multiple depot inventory systems with stock transfer are used by many companies especially when demand is high relative to storage capacity. The key issues in such systems are how many of each item to hold at each depot and what to do if there is a demand for an item at a depot that has none of that item in stock. This study was motivated by the inventory problem faced by a UK car part retailer that groups its depots into pairs. The company's policy for dealing with a demand at a depot that cannot be satisfied from local stock is to either transfer the item from the other depot in the group or to place an emergency order. The object of this paper is to characterise an optimal policy for this problem and to propose a method of calculating the parameters of such a policy.
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Title: Inventory Models with Lateral Transshipments: A Review

Section 1: Introduction
Description 1: Provide an overview of inventory systems, the need for lateral transshipments, and the two main types of transshipments (proactive and reactive).

Section 2: Classification
Description 2: Discuss the classification of inventory models with lateral transshipments based on characteristics such as timing, order policies, and system structure.

Section 3: Proactive Lateral Transshipments
Description 3: Review models and research focusing on proactive lateral transshipments, including standalone redistribution and redistribution combined with replenishments.

Section 4: Reactive Lateral Transshipments
Description 4: Examine the literature on reactive lateral transshipments, separating the analysis into periodic review and continuous review settings.

Section 5: Reactive Lateral Transshipments under Periodic Review
Description 5: Discuss centralized systems (both one and two echelon) and decentralized systems with reactive lateral transshipments under a periodic review setting.

Section 6: Reactive Lateral Transshipments under Continuous Review
Description 6: Explore models of continuous review reactive lateral transshipments with complete pooling and partial pooling.

Section 7: Conclusion and Some Proposals for Future Research
Description 7: Summarize the findings, outline the key conclusions, and identify future research opportunities in the field of inventory models with lateral transshipments.