On the EOQ model with inventory-level-dependent demand rate and random yield

This paper deals with an EOQ-type inventory problem where the demand rate is a function of the inventory level. It has been noted by marketing researchers and practitioners that an increase in a product's shelf space usually has a positive impact on the sales of the product. In such a case, the demand rate is no longer a constant, but it depends on the amount of on-hand inventory. Our objective is to develop a model that can accommodate the dependency of demand on the inventory level. We also assume that the yield is random, i.e., when Q units are ordered, the amount received is YQ where the yield rate Y is a non-negative random variable. With these assumptions of inventory-dependent demand rate and random yield, we develop an extension of the EOQ model. Expected long-run average cost function for the resulting continuous review stochastic inventory model is obtained using the renewal reward theorem. We choose order quantity as the decision variable of the model. Since the computation of the objective function requires the expected stationary inventory level, we develop the stationary distribution of thos stochastic process by using level crossing theory. We discuss three special cases of the objective function which correspond to the following special models: The standard EOQ model; the EOQ model modified to consider random yield; and the EOQ model modified to consider inventory level dependent demand rate. We then discuss the general case where demand rate is a power function of the inventory level and yield rate Y is distributed as a beta random variable. Numerical examples for all four models are presented.