Optimal replenishment policy for non‐instantaneous deteriorating items with stochastic demand under advance sales discount and available capacity

Abstract

This paper presents a two‐warehouse inventory model for non‐instantaneous deteriorating items with a price‐dependent stochastic demand under advance sales discount and available capacity. In this model, the retailer offers a price discount to customers if they can commit their orders prior to the sales period. It encourages the retailer to order a large quantity that can be stored in an owned warehouse and then in a rented warehouse if there are excess items. Shortages are allowed and partially backlogged. The objective of this paper is to simultaneously determine the optimal price discount, the optimal order quantity, and the optimal replenishment schedule in such a way that the expected total profit is maximized. Two theorems are proved in order to verify that the expected total profit function is concave and to identify that an optimal replenishment decision exists. We further propose an algorithm to find the optimal replenishment policy by the retailer. Finally, we use numerical examples to illustrate the results presented herein. Moreover, based upon the sensitivity analysis, some important managerial implications are also discussed.