Multi-location Inventory Systems Research Articles

Nonparametric data-driven learning algorithms for multilocation inventory systems

We study a multilocation inventory system with unknown demand distribution using a nonparametric approach. The system consists of multiple distribution centers and customer locations, where products are shipped from the distribution centers to fulfill customer demands. We propose a novel algorithm, DMLI, for adaptive inventory management. Under specific conditions, we establish that the average expected T-period regret of DMLI converges to the optimal rate of O(1/T).

Approximate dynamic programming for lateral transshipment problems in multi-location inventory systems

Companies commonly allocate their inventories across multiple locations based on their historical sales rates. However, random fluctuations in customer purchases, such as those caused by weather conditions and other external factors, might cause significant deviations from expected demand, leading to excess stock in some locations and stockouts in others. To fix this mismatch, companies often turn to lateral transshipments, e.g., the movement of stock between locations of the same echelon.In this paper, we examine multi-location inventory systems under periodic review with multiple opportunities for proactive transshipments within one order cycle. If stockouts occur, demand is lost with no opportunity to backorder. The objective of our model is to find an optimal policy that indicates the sources and the destinations of transshipments as well as the number of units, to maximise the profit of the network. We create a dynamic program that can, in principal, be solved to optimality using Bellman’s equation. However, the size of the state and decision spaces makes it impossible to find the optimal policy for real-world sized problem instances. Thereby, we use forward approximate dynamic programming to find a near-optimal transshipment policy.Finally, we conduct an extensive numerical study to gauge the performance of our transshipment policy. For small size instances, we compare our policy to the optimal one. For larger scale instances, we consider other practically oriented heuristics. Our numerical experiments show that our proposed algorithm performs very well compared to state-of-the-art methods in the literature.

How to order and transship in multi-location inventory systems: The simulation optimization approach

Abstract The efficient control of multi-location inventory systems with lateral transshipments has become increasingly important. However, existing models are analytically solvable only under simplifying assumptions. There is a variety of heuristics to find approximate solutions, but interdependencies between ordering and transshipment decisions for continuous time are not addressed. Thus, we suggest using simulation optimization. In our paper, we describe a widely adaptable simulation model for mapping highly complex multi-location inventory systems with lateral transshipments. By applying this model to a special case from the literature and to some examples, we show its validity and generality.

Reference Dependence in Multilocation Newsvendor Models: A Structural Analysis

We propose a behavioral theory to predict actual ordering behavior in multilocation inventory systems. The theory rests on a well-known stylized fact of human behavior: people's preferences are reference dependent. We incorporate reference dependence into the newsvendor framework by assuming that there are psychological costs of leftovers and stockouts. We also hypothesize that the psychological aversion to leftovers is greater than the disutility for stockouts. We then experimentally test the proposed theory in both the centralized and decentralized inventory structures using subjects motivated by substantial financial incentives. Consistent with the proposed theory, actual orders exhibit the so-called “pull-to-center” bias and the degree of bias is greater in the high-profit margin than in the low-profit margin condition. These systematic biases are shown to eliminate the risk-pooling benefit when the demands across store locations are strongly correlated. Because the proposed model nests the standard inventory and ex post inventory error minimization theories as special cases, one can systematically evaluate the predictive power of each alternative using the generalized likelihood principle. We structurally estimate all three theories using the experimental data, and the estimation results strongly suggest that the proposed behavioral theory captures actual orders and profits better. We also conduct two experiments to validate the behavioral model by manipulating the relative salience of the psychological costs of leftovers versus that of stockouts to alleviate the pull-to-center bias.

Reference-Dependence in Multi-Location Newsvendor Models: A Structural Analysis

We propose a behavioral theory to predict actual ordering behavior in multi-location inventory systems. The theory rests on a well-known stylized fact of human behavior: People's preferences are reference-dependent. We incorporate reference-dependence into the newsvendor framework by assuming that there are psychological costs of left-overs and stock outs. We also hypothesize that the psychological aversion to leftovers is greater than the disutility for stock outs. We then experimentally test the proposed theory in both the centralized and decentralized inventory structures using subjects motivated by substantial nancial incentives. Consistent with the proposed theory, actual orders exhibit the so-called pull-to-center bias and the degree of bias is greater in the high-pro t margin than in the low-pro t margin condition. These systematic biases are shown to eliminate the risk pooling bene t when the demands across store locations are strongly correlated. Since the proposed model nests the standard inventory and ex-post inventory error minimization theories as special cases, one can systematically evaluate the predictive power of each alternative using the generalized likelihood principle. We structurally estimate all three theories using the experimental data and the estimation results strongly suggest that the proposed behavioral theory captures actual orders and pro ts better. We also conduct two experiments to validate the behavioral model by manipulating the relative salience of the psychological costs of leftovers versus that of stock outs to alleviate the pull-to-center bias.

An index heuristic for transshipment decisions in multi-location inventory systems based on a pairwise decomposition

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.

USING SIMULATION TO EVALUATE THE PERFORMANCE OF TRANSSHIPMENT POLICIES WITHIN TWO ECHELONS

ABSTRACT Transshipments refer to a variety of actions that can result in the sharing of inventory among locations, possibly at different levels of the supply chain. The implementation of transshipment can minimize the cost while maintaining a certain service. It is common for a distributor to use several retailers of different locations to transship its products throughout a region. Therefore, the selection of effective transshipment rules in multi-location inventory systems is important for a successful retail sector. Our research is motivated by observations from various industries such as apparel, fashion goods, and toys, particularly by those retailers with brick and click outlets. The objective of this study is to evaluate a variety of transshipment policies via simulation. A simulation model is used to evaluate the performance of various transshipment policies in corporation with two inventory control policies. According to the numerical experiment results, some managerial implications are suggested. The main findings of this study is that using lateral transshipment in corporation with (Q,R) and (R,s,S) policies inventory policies can result in lower cost and high service level. Furthermore, the (R,s,S)policy is more effective than (Q,R) policy when transshipment policy is applied for the set of circumstances under investigation. The same methodology and modeling approach used in this study could be applied to various supply chains of products with the similar characteristics.

Modelling replenishment and transshipment decisions in periodic review multilocation inventory systems

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.

Approximate solutions for multi-location inventory systems with transshipments

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.

Transshipments: An emerging inventory recourse to achieve supply chain leagility

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.

Allocation policies and cost approximations for multilocation inventory systems

AbstractConsider a central depot that supplies several locations experiencing random demands. Periodically, the depot may place an order for exogenous supply. Orders arrive after a fixed leadtime, and are then allocated among the several locations. Each allocation reaches its destination after a further delay. We consider the special case where the penalty‐cost/holding‐cost ratio is constant over the locations. Several approaches are given to approximate the dynamic program describing the problem. Each approach provides both a near‐optimal order policy and an approximation of the optimal cost of the original problem. In addition, simple but effective allocation policies are discussed.

Coordinated Replenishments in a Multi-Item Inventory System with Compound Poisson Demands

In many practical applications or multi-item inventory systems significant economies of scale can be exploited when coordinating replenishment orders for groups of items. This paper considers a continuous review multi-item inventory system with compound Poisson demand processes; excess demands are backlogged and each replenishment requires a lead time. There is a major setup cost associated with any replenishment of the family of items, and a minor (item dependent) setup cost when including a particular item in this replenishment. Moreover there are holding and penalty costs. We present an algorithm which searches for a simple coordinated control rule minimizing the long-run average cost per unit time subject to a service level constraint per item on the fraction of demand satisfied directly from on-hand inventory. This algorithm is based on a heuristic decomposition procedure and a specialized policy-iteration method to solve the single-item subproblems generated by the decomposition procedure. The model applies to multi-location inventory systems with similar cost structures for coordinated deliveries.