A decision model for an inventory system with two compound poisson demands

Abstract

A real inventory system for single item with specific demand characteristics motivates this works. The demand can be seen as two types of independent demand, where compound Poisson process describes the characteristics of each demand. The first type of demand is rarely occurred with relatively large size, while the second type of demand is often happened with relatively small size. In order to maintain inventory level, every time the first type of demand occurs a replenishment of stock is conducted which follows order-up-to-level inventory policy. In order to find the optimal inventory decision for that system, a mathematical model of the system is developed with the objective to minimize expected total inventory cost. Some of model assumptions are infinite replenishment, deterministic lead time, and completely backlogged shortages. To solve the model, it is then divided into two sub-problems and classical optimization technique is employed to help find the solution of each sub problem.