An Optimal Quantity Discount Pricing Policy for Deteriorating Items

We discuss a quantity discount problem between a seller (wholesaler) and a buyer (retailer). The seller purchases products from an upper-leveled supplier (manufacturer) and then sells them to the buyer who faces her/his customers’ demand. The seller attempts to increase her/his profit by controlling the buyer’s order quantity through a quantity discount strategy and the buyer tries to maximize her/his profit considering the seller’s proposal. In this study, we focus on the case where both the seller’s and the buyer’s inventory levels of the product are continuously depleting due to the combined effects of its demand and deterioration. The deterioration rate is assumed to be a constant fraction of the on-hand inventory. We formulate the above problem as a Stackelberg game between the seller and buyer to analyze the existence of the seller’s optimal quantity discount pricing policy which maximizes her/his total profit per unit of time. Numerical examples are presented to illustrate the theoretical underpinnings of the proposed model.