Determination of production level in a make-to-stock system with stochastic demands and returns

Abstract

We consider the problem to find Economic Production Quantity (EPQ) of a single commodity exposed to stochastic demands and product returns. We assume that production times of each product are generally distributed, and times between successive demands are random and the amounts of products in each demand are also random. We also consider cancellations of orders and returns of the products which affect the level of inventory. However, in contrast to the traditional EPQ model, we assume that once the amount of inventory reaches to a predetermined level then the production is not halted but its speed decreases until the inventory level drops to zero. We establish two probabilistic models representing the behaviors at the high-production period and low-production period, respectively, and derive the relationship between the level of inventory and costs of production, cancellation, and holding, from which the quantity of economic production is obtained. © 2012 International Information Institute.