Quantity Discounts for Channel Coordination: Transaction and Channel Efficiency

Coordinating activities among members of a distribution channel has been a subject of great attention in the past two decades. Among various methods to coordinate independent channel members, a number of studies in the literature suggest quantity discount as a mechanism to achieve incentive-compatible coordination between a manufacturer and his retailer. The rationale behind this coordination mechanism is that a quantity discount schedule can be designed to align the players' interests with the maximum channel gain. Two separate streams of quantity discount models have been developed in the literature. The operations management literature views quantity discount as a way to minimize the system-wide cost of operation. The manufacturer can offer quantity discount such that the retailer finds it optimal to order a larger quantity that minimizes the total channel's operating cost. The marketing literature employs quantity discount to induce the retailer to lower the retail price than the level she would choose otherwise. The increased market demand more than compensates the reduced margin so that the total channel profit is maximized. In both models, the channel members' profit goals are aligned with the total channel profit, and the resulting channel coordination creates efficiency gains that can be shared between the members. In this paper, we present a model of quantity discount that combines these two sources of efficiency gains. We briefly review the existing approaches, and then develop a combined model of quantity discount that provides an incentive-compatible mechanism to coordinate the retailer's behavior. The objective for the manufacturer is to find a discount schedule that induces the retailer to choose the channel-optimal retail price and order quantity. A three-step approach is developed to solve the complex problem, and a graphical interpretation is provided. A numerical illustration demonstrates its practicality.