A fuzzy supply chain contract problem with pricing and warranty

This paper analyzes a supply chain contract problem combining pricing with warranty under incomplete information, in which the supplier's product quality is usually unobservable and has a vagueness boundary to the buyer, it is reasonable to be characterized as a fuzzy variable. There are two important decisions of the buyer: the pricing decision and the warranty decision. Thus, a pricing and warranty contract model is developed with the purpose of maximizing the buyer's expected payoff under incentive feasible scheme. The analysis method is mainly decomposing the buyer's problem into an implementation problem and an optimization problem. The results demonstrate that, if purchasing quantity and product quality are complementary, the buyer's second-best purchasing quantity will be less than the first-best one; if substitutable, the opposite is true. Moreover, in order to demonstrate the superiority/novelty of the proposed model, two degenerated contracts, i.e., the pricing contract and the warranty contract are discussed, respectively, and the advantage of the combined pricing and warranty contract is also given. Finally, one numerical example is given to illustrate the applicability of the proposed model.