Contracting under uncertain capacity: a generalisation

In this paper, we develop a two-stage supply chain model consisting of a supplier with uncertain capacity and a retailer facing an uncertain demand. We consider that the payment of the retailer to the supplier has two steps: a prepayment based on the quantity ordered by the retailer and a final payment based on the quantity actually delivered by the supplier. We first consider the centralised version of this model and determine the optimal policy analytically. We investigate the effects of the prepayment and capacity restriction. We then consider a decentralised version and characterise optimal decisions of both the supplier and the retailer in the framework of Stackelberg equilibrium. We analyse the efficiency loss of the described decentralised system compared to the centralised system. We discuss different contracting alternatives and propose a generalised contract structure that enables coordination of the decentralised system to achieve the performance of the centralised one.