Modeling Lateral Transshipments and Perishable Items in Inventory Systems

University dissertation from Department of Industrial Management and Logistics

Abstract: This thesis deals with two main areas in the field of stochastic inventory theory; ateral transshipments and perishable items. In the first part of this thesis we give an introduction to the field of inventory theory, and discuss some previous literature connected to the research presented in this thesis. In the second part, the original research which defines this thesis is presented in the form of five scientific papers. All five papers consider inventory distribution systems with continuous review. In Paper I we consider a single-echelon inventory system with two identical locations. Demands are generated by stationary and independent Poisson processes. In this paper, we allow lateral transshipments as an emergency supply in case of stock out. The rule for lateral transshipments is given, while the ordering policies for normal replenishments are optimized. First, we derive the optimal replenishment policy under the assumption that each location applies an (R,Q) policy. Next, we relax the assumption of (R,Q) policies and derive the true optimal replenishment policies by using stochastic dynamic programming. We show that the optimal policies are not necessarily symmetric even though the locations are identical. Paper II considers a two-echelon distribution inventory system with a central warehouse and a number of retailers. We apply (R,Q) policies, and the customer demands follow stationary compound Poisson processes. In this paper we assume that the demand at the warehouse is not only the replenishments from the retailers but also direct customer demand. At the warehouse there are now two types of demand that may have very different service requirements. The purpose of this paper is to discuss and evaluate techniques for overcoming this problem. Four techniques to handle this situation are studied and evaluated by simulation. In Paper III, we consider a perishable inventory system consisting of a single stock location with Poisson demand. Both the leadtime and the product lifetime are assumed to be fixed. The replenishment policy is assumed to be an (S-1,S) policy. In this specific case it means that whenever a unit perishes or a customer arrives, a unit is immediately ordered from the supplier. Demand that cannot be met immediately is backordered. We express the service requirements in three different ways; 1) backorder costs per unit, 2) a service level constraint, 3) backorder costs per unit and time unit. Problems 1 and 2 are solved exactly, while an approximation is developed for Problem 3. In Paper IV, we extend Paper III by considering a two-echelon serial inventory system with perishable items. As in Paper III, the transportation times and the lifetimes of items are assumed to be constant, and all locations apply (S-1,S) policies. Customers arrive at the most downstream location according to a stationary Poisson process. Demand that cannot be met immediately is backordered. Using fixed point techniques and a variant of the famous METRIC model, approximations are developed for calculating inventory level probabilities and expected outdating rates. Finally, in Paper V, we investigate an inventory system where lateral transshipments are allowed between parallel locations. However, transshipments are only allowed in one direction. All locations apply either (S-1,S) policies or (R,Q) policies. The regular replenishment leadtimes are constant, and we assume that transshipment leadtimes are negligible compared to regular leadtimes. In this paper we consider both the case of backorders and the case of lost sales. Assuming Poisson demand, we develop approximations for inventory level probabilities and fill rates.

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