A multi item probabilistic inventory model

Abstract

In this paper, we develop a mathematical model for an inventory problem which consists of several products. Demands for these products are following Gamma distribution. Our objective is to determine the optimal ordering quantity that minimizes the total cost for each product. This is called an individual replenishment policy. The total cost consists of the purchasing cost, ordering cost, handling and shortage costs. Using the same model, we also develop a periodic review model that determines an optimal ordering time for all the products. This is called a joint replenishment policy. We then compare the total cost of the individual and the joint replenishment policy and determine a policy that gives minimum total cost. Our numerical experiments show that in general the joint replenishment policy is preferable than the individual replenishment policy. The joint replenishment policy gives higher shortage cost, but less in ordering and handling costs than the individual replenishment policy.