Price Discount and Stochastic Initial Inventory in the Newsboy Problem

Many extension of the newsboy problem have been solved in the literature. One of those extensions solves a newsboy problem with stochastic initial inventory, earlier extensions have focused on quantity discounts offered by suppliers. An important practical extension would address a combination of the two pervious extensions. In this paper we consider a newsboy problem in which the suppliers offer quantity discount and the initial inventory at the beginning of the period is a random variable. We obtain the optimal value of the order quantity which maximizes the total profit and then present the results for some practical distributions of both random variables, demand and initial inventory.