Coordinating a three level supply chain under generalized parametric interval-valued distribution of uncertain demand

Abstract

In uncertain supply chain management problem, the optimal order quantity often depends heavily on the distribution of uncertain demand. When the exact possibility distribution is unavailable, it is required to develop a novel method to characterize the uncertain demand and deal with the corresponding supply chain coordination problem. This paper addresses the coordination problem for a three level supply chain in a single period model, where the uncertain demand is characterized by generalized parametric interval-valued possibility distribution. We define the lambda selection of uncertain demand, and discuss its parametric possibility distribution and mean value. In addition, we construct L–S measure by parametric possibility distribution of the lambda selection, and use it to define the L–S integral of uncertain profits under different scenarios. Under the risk-neutral criterion, we demonstrate that the mean supply chain profit in centralized decision is greater than the total mean supply chain profit in decentralized decision. Then a three level supply chain with revenue-sharing contract and return policy is studied and the analytical expressions of the optimal order quantity for different members are derived. Under the variable parametric possibility distribution of demand, we provide the sufficient conditions to ensure the three level supply chain can be fully coordinated and show the total mean profit of the channel can be allocated with any specified ratios among the members. Finally, we provide some managerial implications in a practical supply chain coordination problem. The computational results demonstrate the efficiency of the proposed parametric credibilistic optimization method.