A composite contract based on buy back and quantity flexibility contracts

We introduce a composite (CP) contract for a two-stage supply chain by organically combining two component contracts: a buy back (BB) contract and a quantity flexibility (QF) contract. The CP contract is shown to have advantages over both component contracts in terms of supply chain coordination, profit allocation, and risk allocation. In particular, we obtain the following results: (a) as long as one of the component contracts is able to coordinate the supply chain, so is the CP contract. Moreover, when contract parameters are constrained, we find situations where the CP contract coordinates the supply chain when neither of the component contracts coordinates. (b) When contract parameters are constrained, the CP contract is more flexible in terms of profit allocation among supply chain members than the component contracts. (c) The CP contract is more flexible in terms of risk allocation than the component contracts.