Supply Chain Coordination through a Revenue-Sharing Contract with Two Kinds of Fuzzy Demand

Revenue-sharing contract is used in many industries. However, it is hard to guarantee that the retailer report the sales truly to the supplier. In fact, the retailer has both incentive and opportunity to underreport the sales to reduce the sharing revenue to the supplier. What the supplier should do when meeting with the opportunistic retailer(s)? This paper studies a kind of opportunistic phenomenon in a supply chain in which a supplier sells to a retailer under a revenue-sharing contract. Two settings are discussed. The first one is that the retailer does not, or cannot underreport the sales to the supplier to share when the supplier design a strict auditing mechanism under which no lies allowed. The second one is that the retailer can underreport the sales to the supplier to share under another soft auditing mechanism. Due to the uncertainty of market demand, it is characterized by a fuzzy variable. Interestingly, we find that the supplier's profit is higher in the second setting than the one in the first setting. We hope that the conclusion drawn in the paper can provide a new viewpoint to help the supplier to solve the problem when meeting with an opportunistic retailer in a supply chain under a revenue-sharing contract in uncertain environments.