Shape of power yield distribution: impact on EOQ model with nonlinear holding cost and random quality

Abstract

The Economic Order Quantity (EOQ) model is based on a series of highly restrictive assumptions among which are deterministic demand, constant holding costs across time and perfect quality of replenishment items. Many variants of the EOQ model have been developed as a result of relaxing one or more of these assumptions. These variants include models that treat holding cost as a nonlinear function of the amount of time that an item is held in inventory. Such models are known as perishable inventory models. A second class of EOQ models that have received significant attention in the literature over the past few decades relax the perfect quality assumption by treating the proportion of acceptable (non-defective) units in each lot, referred to as yield, as a random variable. In this paper we combine these two classes of inventory paradigms by integrating the nonlinear holding cost aspect and the random yield factor. In addition to the general relationships provided, explicit expressions are also given for the special case of power yield distribution. Finally, we present analytical results for the evaluation of monetary trade-offs associated with efforts aimed at alteration of the shape parameter of the power yield distribution for a special case of the investment function.

Keywords:

• Inventory
• random yield
• quality improvement
• prescriptive analytics