Coordinating supply chains with uncertain production cost by incomplete contracts

Production cost affects heavily supply chain coordination, but it is uncertain in many cases. We consider a supply chain consisting of a manufacturer and a retailer, where the unit production cost is uncertain when the firms sign a procurement contract. We derive the optimal decisions and profits for the centralised and decentralised cases. We show that production cost uncertainty exaggerates the supply chain’s incentive conflict, but may increase the expected profit in the centralised decision case. Then we design an incomplete contract, which sets a wholesale price and an order quantity in the first stage, which the firms can re-negotiate after the production cost is realised in the second stage. We prove that such an incomplete contract can lead to the first best outcome. We further consider the case with asymmetric cost information and show that the incomplete contract can also coordinate the supply chain. Furthermore, we discuss how the degree of contract incompleteness, re-negotiation freedom, and residual control rights affect the supply chain performance. The results reveal that the hold-up problem is prone to occur with improper contract incompleteness, re-negotiation freedom, and residual control rights, while the incomplete contract we propose can effectively avoid the problem.