Myopic Policies for Inventory Control

Abstract

<p>In this thesis we study a typical retailer's problem characterized by a slngle item, periodic review of inventory levels in a multi-period setting: and stochastic demands. We consider the case of full backlogging where backorders are penalized via fixed and proportional backorder costs simultaneously. This treatment of backorder costs is a nonstandard aspect of our study. The discussion begins with an introduction in Chapter 1. Next, a review of the relevant literature is provided in Chapter 2. In Chapter 3 we study the infinite horizon case which is of both theoretical and practical interest. From a theoretical point of view tile infinite horizon solution represents the limiting behavior of the finite horizon case. Solving the infinite horizon problem has also its own practical benefits since its solution is easier to compute. Our motivation to study the infinite horizon case in the first place is pragmatic. We prove that a myopic base-stock policy is optimal for the infinite horizon case, and this result provides a basis for our study. We show that the optimal myopic policy can be computed easily for the Erlang demand in Chapter 4; solve a disposal problem which arises under the myopic policy in Chapter 5, and also study in Chapters 6 and 7 the finite horizon problem for which a myopic policy is not optimal. For the finite horizon problem computation of the exact policy may require a substantial effort. From a computational point of view, there is a need for developing a method that overcomes this burden. In Chapter 6 we develop a model for such a method by restricting our attention to the class of myopic base-stock policies, and call the resulting policy the 'best myopic' policy. We discuss analytical and numerical results for the computation of the best myopic policy in Chapter 7. Finally we present a summary of our main findings in Chapter 8.</p>