Supply chain coordination based on a buyback contract under fuzzy random variable demand

The demand of production is random in the supply chain. Furthermore, it is difficult to measure the demand in the real world. Hence, the interval is more likely to be used to present the demand. The interval can be viewed as a random variable. This paper introduces this random variable as the demand of production into the model of supply chain. We represent uncertain and fuzzy demand by a fuzzy random variable in a supply chain system based on a two-level buyback contract for a newsvendor model with a single cycle. For the sake of computational convenience, the crisp possibilistic mean which has been widely used in supply chain is employed to defuzzify the fuzzy random demand. In this paper, the expected profit is defuzzified using a crisp possibilistic mean value. The optimal order quantities in decentralized and centralized systems are analyzed and the conditions for supply chain coordination are obtained. A realistic example is presented to illustrate the effectiveness of supply chain coordination and the impact of mixed imprecise and uncertain demand on the retailer order quantities and the expected profits for all sides.