Optimal Pricing and Inventory Control Policy with Quantity-Based Price Differentiation

A firm facing price dependent stochastic demand aims to maximize its total expected profit over a planning horizon. In addition to the regular unit selling price, the firm can utilize quantity discounts to increase sales. We refer to this dual-pricing strategy as quantity-based price differentiation. At the beginning of each period, the firm needs to make three decisions: replenish the inventory, set the unit selling price if the unit sales mode is deployed, and set the quantity-discount price if the quantity-sales mode is deployed (or the combination of the two modes of sales). We identify conditions under which the optimal inventory control policy and selling/pricing strategy is well structured. Remarkably, under a utility-based demand framework, these conditions can be unified by a simple regularity assumption that has long been used in the auction and mechanism design literature. Moreover, sharper structural results are yielded for the optimal selling strategy. We also examine the comparative advantage of quantity-based price differentiation with respect to model parameters. Our numerical study shows that substantial profit improvement can be gained as a result of shifting from uniform pricing to quantity-based pricing, especially when the product has a low unit ordering cost and high utility.