Pooling and emergency replenishment policies in inventory systems
Abstract: This thesis deals with two types of problems occurring in inventory theory; pooling of stock and perishable items. All three papers in this thesis 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. Finally, 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.
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