Multi-location Inventory System 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).

Inventory Sharing and Demand-Side Underweighting

Problem definition : Transshipment/inventory sharing has been used in practice because of its risk-pooling potential. However, human decision makers play a critical role in making inventory decisions in an inventory sharing system, which may affect its benefits. We investigate whether the opportunity to transship inventory influences decision makers’ inventory decisions and whether, as a result, the intended risk-pooling benefits materialize. Academic/practical relevance : Previous research in transshipment, which is focused on finding optimal stocking and sharing decisions, assumes rational decision making without any systematic bias. As one of the first to study inventory sharing from a behavioral perspective, we demonstrate a persistent stocking-decision bias relevant for inventory sharing systems. Methodology : We develop a behavioral model of a multilocation inventory system with transshipments. Using four behavioral studies, we identify, test, estimate, and mitigate a demand-side underweighting bias: although inventory sharing brings both a supply-side benefit and a demand-side benefit, players underestimate the latter. We show analytically that such bias leads to underordering. We also explore whether reframing the inventory sharing decision reduces this bias. Results : Our results show that subjects persistently reduce their order quantities when transshipments are allowed. This underordering, which persists even when a decision-support system suggests optimal quantities, causes insufficient inventory in the system, in turn reducing the risk-pooling benefits of inventory sharing. Underordering is evidently caused by an underweighting bias; although players correctly estimate the supply-side potential from transshipment, they only estimate 20% of the demand-side potential. Managerial implications : Although inventory sharing can profitably reduce inventory, too much underordering undermines its intended risk-pooling benefits. The demand-side benefits of transshipment need to be emphasized when implementing inventory sharing systems.

Preventive transshipment decisions in a multi-location inventory system with dynamic approach

This paper addresses the preventive transshipment problem in a multi-location inventory system. Decisions are made before demands are observed to prevent future stock out. Both lateral transshipments (LT) and emergency orders (EO) are available in this system. The objective is to figure out the timing and quantity of preventive transshipment decisions. A Markov decision process is formulated to describe the problem. First a decomposition method is used to divide the multi-location problem into different pairs of two-location problems. Then a sorting heuristics combined with backward dynamic programming (BDP) approach and approximate dynamic programming (ADP) approach is developed to solve this problem. Extensive numerical examples are used to demonstrate the effectiveness of this method. Results show that demand distribution at the retailer affects the way transshipment performs. In addition, product’s perishability has obvious effects on transshipment decisions.

Optimal allocation policy for a multi-location inventory system with a quick response warehouse

We study a multi-location inventory problem with a so-called quick response warehouse and base stock inventory control. In case of a stock-out at a local warehouse, a demand can be satisfied by a stock transfer from the quick response warehouse. We derive the optimal policy for when to apply such a stock transfer, as well as conditions under which that is always optimal. In a numerical experiment we compare the optimal allocation policy to simpler policies.

Modeling of Spare Parts in Multi-Location Inventory System with Unidirectional Lateral Transshipments

Management of multi-echelon with unidirectional transshipments is an effective approach to improve support effectiveness. Focus on the problem, a system where transshipments are allowed only in one direction is provided. The technique is solved in a simple and efficient heuristic algorithm, and the simulation shows that the model produces accurate estimation. Numerical studies show unidirectional transshipments improves various system performance measures such as the fill rate, the average inventory on hand, and the average backorder level. The suggest method gives a good picture of how considered unidirectional lateral transshipments affect the inventory system, which has large significance for completing inventory theory and supplying decision assistance for a reasonable optimization project.

The trans-shipment problem in a two-echelon, multi-location inventory system with lost sales

In this paper, we address a two-echelon, multi-location pooling inventory system that consists of an outside supplier, a warehouse and two retailers. To control their inventories, both warehouse and retailers use (R, s, S) policy. The retailers face stochastic customer demands for a single product and the warehouse receives only the replenishment orders of retailers. In case of stock-out at retailers, emergency trans-shipments are used to satisfy the unmet demand at one retailer with the surplus from the other retailer. When the stock is insufficient at the warehouse, we propose two rationing policies to allocate on-hand stock between retailers. The demand that cannot be satisfied neither by stock on-hand nor by trans-shipment from retailers is considered lost. Our work has two objectives. First, we propose an inventory model based on three components: the optimisation inventory model, the trans-shipment policy and the rationing policies for determining the best values of (s, S) at each location that minimise total system cost. Second, we validate this model via an empirical simulation study that allows us to identify the influential parameters on trans-shipment benefits.

Enhanced lateral transshipments in a multi-location inventory system

In managing an inventory network, two approaches to the pooling of stock have been proposed. Reactive transshipments respond to shortages at a location by moving inventory from elsewhere within the network, while proactive stock redistribution seeks to minimize the chance of future stockouts. This paper is the first to propose an enhanced reactive approach in which individual transshipments are viewed as an opportunity for proactive stock redistribution. We adopt a quasi-myopic approach to the development of a strongly performing enhanced reactive transshipment policy. In comparison to a purely reactive approach to transshipment, service levels are improved while a reduction in safety stock levels is achieved. The aggregate costs incurred in managing the system are significantly reduced, especially so for large networks. Moreover, an optimal policy is determined for small networks and it is shown that the enhanced reactive policy substantially closes the gap to optimality.

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.

Evolutionary multiobjective optimization of the multi-location transshipment problem

We consider a multi-location inventory system where inventory choices at each location are centrally coordinated. Lateral transshipments are allowed as recourse actions within the same echelon in the inventory system to reduce costs and improve service level. However, this transshipment process usually causes undesirable lead times. In this paper, we propose a multiobjective model of the multi-location transshipment problem which addresses optimizing three conflicting objectives: (1) minimizing the aggregate expected cost, (2) maximizing the expected fill rate, and (3) minimizing the expected transshipment lead times. We apply an evolutionary multiobjective optimization approach using the strength Pareto evolutionary algorithm (SPEA2), to approximate the optimal Pareto front. Simulation with a wide choice of model parameters shows the different trades-off between the conflicting objectives.

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.

Optimal Solutions in the Multi-location Inventory System with Transshipments

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.

Lateral transshipment for managing excesses and shortages in a multilocation inventory system: a case study of Timex Watches Ltd.

This paper describes a large watch manufacturer in India and a proposed system to reduce its cost and simultaneously improve its service level by planning lateral transshipments. Many authors have studied the multilocation inventory situations, under different demand and cost characteristics, and almost all of them have developed push systems developing optimum or good replenishment/transshipment policies. Yet pull systems may offer simpler and more practical joint replenishment/transshipment policies, particularly when practical considerations as faced by real companies are studied. The process map including the inputs and the outputs for the replenishment system is described, as well as the feedback mechanism to revise the system parameters.

Simple, efficient heuristics for multi-item multi-location spare parts systems with lateral transshipments and waiting time constraints

This paper deals with the analysis of a multi-item, continuous review model of a multi-location inventory system of repairable spare parts, in which lateral and emergency shipments occur in response of stock-outs. The objective is to determine close-to-optimal stocking policies minimizing the total cost for inventory holding, lateral transshipments, and emergency shipments subject to a target level for the average waiting times at all locations. We structure the optimization problem as a combinatorial problem and four different heuristics are developed and evaluated in terms of their total costs and computation times. It is shown that the greedy-type heuristic has the best performance. A numerical study is carried out to look at the relative cost savings obtained from the use of multi-item approach and lateral transshipments.

A model for lumpy demand parts in a multi-location inventory system with transshipments

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.

A comparison of different inventory policies of the one-period multi-location inventory system

In this paper we compare different policies that must meet some demand requirement in a multi-center one-period inventory system. More specifically, this paper concerns a multi-location, one-period inventory problem with linear holding costs and a probability of out-of-stock constraint at each location. Such systems are common in the public sector. Three different policies are considered: (a) A decentralized policy, (b) a centralized policy without priorities, and (c) a centralized priority policy. The superiority of policy (c) over policies (a) and (b) is discussed and demonstrated for some specific examples. It is shown that this superiority is very sensitive to the size of the system.

Priority centralization of the one period multi-location inventory system

In this paper, we will examine a multi-center one-period inventory system. The usual penalty cost for being out of stock will be replaced by an assurance of service constraint at each location. That is, we will constrain our inventory size to meet a specific maximum probability of being out of stock at each location. The centralized system we shall propose will define a priority rule which will cause us to satisfy the entire demand of high priority locations before we begin satisfying the demands of lower priority locations. This will allow us to find a minimum initial inventory level for the centralized system that will meet all of the assurance of service constraints. We will look at the special case where the variance of the total demand of several locations is non-decreasing in locations included in the total. In this case, we will show the computations required for finding the optimal centralized priority system are minimal. Finally, we will show that such a system is superior to a decentralized system.