Heuristic and Exact Evaluation of Two-Echelon

Abstract: The main theme of this project is inventory control with stochastic demand. In this thesis, we consider a two-echelon inventory system that consists of one central warehouse and N retail stores. Customer demands at the retailers follow independent Poisson demand processes and each customer only demands one unit. Customer demands which are not satisfied directly from stock on hand are assumed to backordered, i.e., no lost sales exist. All transportation times are assumed to be constant. Replenishment, at the warehouse and at each retailer, is made according to so-called order-up-to-S policies (also denoted as (S − 1, S)-policies). The first main goal is to derive an expected system cost function which consists of inventory holding costs and backorder costs. Secondly, we will optimize this cost function with respect to the base-stock levels Si, i = 0, . . . , N , where Si represents the base-stock-level at retailer i (index 0 is for the warehouse). We will first consider an exact method to optimize the expected system cost function. In this exact method, the lead-times for the retail stores are stochastic due to possible delays when replenishing from the central warehouse. However, in practice, it is common to use an approximate method where the stochastic lead-times for the retailers are replaced by the corresponding mean values. Here, we will investigate the robustness of this approximate method in terms of changes in system parameters.