Two-Stage Multiobjective Optimization for Emergency Supplies Allocation Problem under Integrated Uncertainty

This paper proposes a new two-stage optimization method for emergency supplies allocation problem with multisupplier, multiaffected area, multirelief, and multivehicle. The triplet of supply, demand, and the availability of path is unknown prior to the extraordinary event and is descriptive with fuzzy random variable. Considering the fairness, timeliness, and economical efficiency, a multiobjective expected value model is built for facility location, vehicle routing, and supply allocation decisions. The goals of proposed model aim to minimize the proportion of demand nonsatisfied and response time of emergency reliefs and the total cost of the whole process. When the demand and the availability of path are discrete, the expected values in the objective functions are converted into their equivalent forms. When the supply amount is continuous, the equilibrium chance in the constraint is transformed to its equivalent one. To overcome the computational difficulty caused by multiple objectives, a goal programming model is formulated to obtain a compromise solution. Finally, an example is presented to illustrate the validity of the proposed model and the effectiveness of the solution method.