On improving incentive in a supply chain: Wholesale price contract vs quantity dependent contract

In this paper, we first study the performance of a supply chain consisting of one retailer and one supplier. The supplier sets the price scheme of some goods and the retailer then decides the order level and sells the goods in the market. Specifically, a quadratic cost function is assumed here to approximate the U-shape cost curve commonly observed in industries. Two kinds of contracts offered by the supplier are investigated, namely wholesale price contract and quantity dependent contract. Wholesale price is fixed under the first contract but varies depending on order level under the second one. We show that certain wholesale price contract successfully induces the retailer to order at a level such that supply chain profit is maximized, but extra cost in implementation may occur due to supplier´s disagreement on this price. Given this, we propose an efficiency measure to show to what extent the wholesale price contract helps to increase supply chain profit. For quantity dependent contract, we show that it can coordinate the supply chain and leads to a proportional division of supply chain profit. We then generalize the analysis to cover the case of multiple retailers and single supplier where similar results are also obtained.