A bi-objective robust optimization approach for designing a green closed-loop supply chain network under uncertainty

Imposition of strict environmental protection acts and the imperative need of best possible allocation of resources have given birth to the concept of low carbon logistics. Environmental laws force the manufacturers to extend their existing supply chains to form a closed loop supply chain (CLSC) through the setup of an efficient recovery system. In this paper a multi-objective robust optimization model is proposed for the design of CLSC network under uncertainty First, a deterministic Bi-objective Mixed-integer Linear Programming (BOMILP) model is developed for designing a CLSC network. Then, the robust counterpart of the proposed BOMILP is presented. The first objective aims to maximize the total profit generated in the CLSC network and the second objective minimizes the environmental pollution of the CLSC network. The proposed bi-objective model is solved using LP-Metric method. The model is able to determine the number and locations of facilities and the material flow between these facilities so that the profit of CLSC is maximized and the environmental pollution is minimized. Numerical results are provided to show the performance and validity of the proposed model.

Keywords:

Closed-loop supply chain , Environmental issues , Robust optimization , LP-Metric