Coordinating the discount policies for retailer, wholesaler, and less-than-truckload carrier under price-sensitive demand: A tri-level optimization approach

Abstract

Quantity discounts have been broadly examined in decisions on the sale or purchase of goods. The analysis of coordinating the discount decisions for the retailer (buyer), the wholesaler (supplier), and the public transportation service provider (Less-Than-Truckload carrier), however, is still in its infancy. In this paper, we develop a tri-level programming approach to coordinate the three supply chain members' decisions on discount policies, when the demand is sensitive to the change in price. Both decentralized and centralized scenarios are examined, and a heuristic algorithm is presented to assist the three parties in establishing their discount schemes in a decentralized environment. Through a series of comprehensive numerical experiments based on the linear demand, we show that the price-sensitivity is a key motivation, for all parties, especially the carrier, to offer discounts. Specifically for the wholesale quantity discount, the data analyses also illustrate the different purposes and corresponding structures for the decentralized and centralized cases. For the former case, the discount is quantity-based, which encourages the buyer to increase the size of each order; while for the latter case, the discount is volume-based, which is used to boost the annual demand. The significant improvements to each party and to the entire supply chain resulting from the discount coordination are also demonstrated under various situations.