Optimal Promotion and Replenishment Policies for Profit Maximization Model under Lost Units

Ever since its introduction in the second decade of the past century, the economic order quantity (EOQ) model has been the subject of extensive investigations and extensions by academicians. The physical characteristics of stocked items dictate the nature of inventory policies implemented to manage and control. The question is how reliable are the EOQ models when items stocked deteriorate one time. This paper introduces a modified EOQ model in which it assumes that a percentage of the on-hand inventory is wasted due to deterioration. There is hidden cost not account for when modeling inventory cost. We study the problem of promotion for a deteriorating item subject to loss of these deteriorated units. The objective of this paper is to determine the optimal time length, optimal units lost due to deterioration, the promotional effort and the replenishment quantity so that the net profit is maximized and the numerical analysis show that an appropriate promotion policy can benefit the retailer and that promotion policy is important, especially for deteriorating items. Furthermore crisp decision making is shown to be superior to crisp decision making without promotional effort cost in terms of profit maximization.