An extended supply chain buy back contract with consideration of influence of order time

Supply chain contract is a key factor influencing Supply chain performances and has been valued by many numerous scholars. For a two-stage supply chain consisting of one Supplier and one retailer who faces stochastic market demand, it can be coordinated with buy back contract under some settings. On supply chain coordination, order time is not embedded in classic buy back contract. It is only an order quantity that the retailer should decide. The whole price is not related with the retailer's order time. Both the order time and the time-variant variance of the demand are neglected. The problem about supply chain coordinating decision, and, Optimum based on time has significant value in theory and practice to recognize the nature Of Supply chain. Both the order time and tile order quantity are simultaneously considered as the decision variables of the extended buy back contract in this paper. The model in this paper could be used in making decisions for the retailer to decide how many and when to order the commodities.