A Multi-Objective Robust Optimization Model for a Facility Location-Allocation Problem in a Supply Chain under Uncertainty

The final purpose of this study is presentation a mathematical model for a facility location-allocation problem so as to design an integrated supply chain. A supply chain with multiple suppliers, multiple products, multiple plants, multiple transportation alternatives and multiple customers is taken into account for this purpose. The problem is to specify a number and capacity level of plants, allocation of customers demand, and selection and order allocation of suppliers. A scenario approach is considered to deal effectively with the uncertainty of demand and cost parameters. The formulation is a robust multi-objective mixed-integer linear programming (MOMILP), in the context of which two conflicting objectives is taken into account simultaneously: (1) minimizing the total costs of a supply chain including raw material costs, transportation costs and establishment costs of plants, and (2) minimizing the total deterioration rate occurred by transportation alternatives. Then, the problem can be reduced to a linear one. Finally, by applying the LP-metric method, the model is solved as a single objective mixed-integer programming model. An experiment study corroborates that this procedure can be proposed to design an effective supply chain.