Quantity Discounts for Supply Chain Coordination

Abstract

Coordinating activities among members of a supply chain/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 seller/manufacturer and his buyer/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.

This chapter first reviews two separate streams of quantity discount models that 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. On the other hand, 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.

Then we review models that combine these two sources of efficiency gains. When the two models are combined, there is a synergy between the two effects. However, the resulting models tend to be difficult to solve analytically. Finally, we introduce a quantity discount model that also includes a third-party logistics partner. Due to the model complexity, we examine the model using a couple of popular demand functions and show that it is also feasible to coordinate three supply chain partners using quantity discount. We conclude the paper with a discussion of further research directions.

This research was partially funded by the Rutgers Business School Research Resources Committee Grant. The authors thank Professor Amiya Chakravarty for valuable comments and suggestions on earlier versions of this chapter, and Carter Daniel of the Rutgers Business School for his help in improving its readability.