Multi-Period, Multi-Product Supply Chain Network Design Using an Approach Combining Multi-objective Mathematical Programming and Data Envelopment Analysis

In this paper, in order to increase the performance of the proposed supply chain network, the multi-period, multi-product model with multiple simultaneous objectives has been considered. To design the network, use has been made of the multi-objective mixed integer mathematical programming model, where the objectives of the problem include minimization of production costs, reduction of products delivery time, and increase in the reliability of the supply chain. To solve the model and present non-dominated solutions, the Epsilon Constraint Method has been used; to this end, the model’s code has been written in the LINGO software. Considering the multiplicity of Pareto solutions, to prevent the decision maker from confusion, use has been made of Data Envelopment Analysis for evaluation of non-dominated solutions. To solve the Data Envelopment Analysis model, GAMS software has been used. The outputs of this problem include the optimal number of facilities at each level of the supply chain and the optimal amount of goods delivery from each level to another.