Supply chain coordination with target profit

Much of the literature pertaining to supply chain coordination have mentioned about the inefficiency of decentralised supply chain compared to the centralised one. In this paper, using quantity discount as coordination mechanism, a single vendor and a single buyer supply chain a coordination model is proposed where both the parties have a certain amount of target profit from the business. The problem is formulated as a non-linear optimisation problem and the proposed model is used to show analytically that efficiency of a centralised supply chain is higher than that of a decentralised supply chain. A procedure is also developed for an equitable distribution of profit when both the parties have a profit target. A numerical example is carried out to illustrate the proposed model and the procedure for the division of the surplus.