A cooperation model based on CVaR measure for a two-stage supply chain

In this paper, we introduce a cooperation model (CM) for the two-stage supply chain consisting of a manufacturer and a retailer. In this model, it is supposed that the objective of the manufacturer is to maximise his/her profit while the objective of the retailer is to minimise his/her CVaR while controlling the risk originating from fluctuation in market demand. In reality, the manufacturer and the retailer would like to choose their own decisions as to wholesale price and order quantity to optimise their own objectives, resulting the fact that the expected decision of the manufacturer and that of the retailer may conflict with each other. Then, to achieve cooperation, the manufacturer and the retailer both need to give some concessions. The proposed model aims to coordinate the decisions of the manufacturer and the retailer, and balance the concessions of the two in their cooperation. We introduce an s* - optimal equilibrium solution in this model, which can decide the minimum concession that the manufacturer and the retailer need to give for their cooperation, and prove that the s* - optimal equilibrium solution can be obtained by solving a goal programming problem. Further, the case of different concessions made by the manufacturer and the retailer is also discussed. Numerical results show that the CM is efficient in dealing with the cooperations between the supplier and the retailer.