On coordinating an assembly system under random yield and random demand

We consider a decentralized assembly system in which the customer demand and the yield of the suppliers are random. We establish the concavity of expected supply chain profit for arbitrary number of suppliers. We propose two contracts and show that they coordinate the chain under forced compliance. The contracts are mixed type of contracts that include payments from different contract schemes. Particularly, a payment or a penalty to the worst performing supplier seems inevitable. Apart from providing a coordinating contract, we also provide qualitative insights based on a numerical illustration of centralized and decentralized solutions.