Modeling a two-stage supply contract problem in a hybrid uncertain environment

This study examines the supply contract problem in supply chain management, in which the uncertain demand is affected by a variety of factors. Since the available historical data cannot adequately determine the exact probability distribution of future demand, the prediction of experienced experts about uncertain demand is usually required in the practical modeling process of supply contract problem. The main contributions of this study are to model the uncertain demand by both probability distribution and possibility distribution, and develop a new two-stage expected value optimization model for our supply contract problem, in which an options futures contract is employed to reduce the risk of uncertain demand. In the first decision-making stage, the distributor signs an options-futures contract with the supplier to determine the futures and options ordering quantities. After knowing the realization of uncertain demand, the distributor takes the signed options as the recourse decision in the second stage. When the actual demand follows some common probability and possibility distributions, the proposed two-stage optimization model can be turned into its deterministic equivalent programming model so that it can be solved efficiently via commercial optimization software. To illustrate the effectiveness of the proposed optimization method, a practical natural gas supply contract problem is provided in our numerical experiments. The computational results demonstrate that the possibility distribution of uncertain demand does affect the ordering decisions, and modeling uncertain demand by both probability distribution and possibility distribution is more realistic in our natural gas supply contract problem. As a result, the proposed two stage optimization method can guide distributors to make their informed decisions in practical supply contract problem when the probability distribution of uncertain demand is partially known.