A composite contract for coordinating a supply chain with sales effort-dependent fuzzy demand

In this paper, we study the coordination problem for a supply chain composed of one supplier and one retailer when the demand is a fuzzy variable that is dependent on sales effort. We find that neither a buyback contract nor a promotion cost-sharing contract can coordinate the supply chain in this setting. Furthermore, we design a composite contract by combining a buyback contract with a promotion cost-sharing contract to coordinate the supply chain and analyze the coordination conditions. We also draw a performance comparison of the designed composite contract and the price-only contract for the profit maximization of the supply chain and present some extensions. Finally, the main theoretical results and the effectiveness of the designed composite contract are illustrated with numerical examples. We show that the production cost and sensitivity parameter of effort cost have negative impacts on the expected profits of the supplier, the retailer and the entire supply chain, whereas basic demand and the sensitivity parameter of demand stimulation have positive impacts on their profits.

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