Quantity flexibility contracts under Bayesian updating

In this paper, we consider a decentralized supply chain consisting of two independent players – a manufacturer and a retailer. Under a quantity flexibility contract, the retailer first proposes an initial forecast as the production reference to the manufacturer. Then she uses Bayesian procedure to update demand information, and makes ultimate purchase commitment, which is constrained by the negotiated flexibility and the manufacturer's production. We model the incentives of both parties and investigate the effect of flexibility ω, transfer price c and number of Bayesian updates n on the performance of two parties. Our theoretical analysis and numerical results show that given other parameters fixed, more flexibility always benefits the retailer, while the manufacturer can only benefit from very small quantity flexibility. In addition, this contract allows them to share the benefits from information updating.