Value Iteration for Perishable Inventory Control

Abstract

This thesis focuses on finding optimal order policies for perishable inventory in supermarkets. By means of value iteration (VI) and simulation, several inventory dynamics are compared. First, several cases were designed: three cases without taking perishability into account, and one case based on perishability. Case 1-3 have the following characteristics, respectively: 1) backlogging is possible, and costs should be minimized; 2) backlogging is not permitted, and profit should be maximized; 3) the customer service level (CSL) should be met, and costs should be minimized. The fourth case, 4) contains products which perish after one day, and the profit should be maximized. The calculation of an optimal order policy is performed by implementing a VI method. The optimal order quantity per inventory level calculated in VI, is used in the simulation. The four cases gave different optimal order-policies. The first three cases showed a lot of similarities, and had the characteristics of an (s; S)-policy. Case 4, containing perishable products, was highly influenced by the fixed order cost k. If the fixed order costs were low, an optimal order policy could be determined. This was not possible for high fixed order costs, the order moments and order quantities turned out to be periodic. For fixed costs which were too high, no orders were placed. The order policy for the low fixed costs did not match the policies in the inventory control chapter. In case 4, we had to deal with the curse of dimensionality. The limited shelf-life causes an increase in state space. To deal with this problem, we had to keep the elements per set of states low.