Presenting a multi-objective linear programming mathematical model of a resilient and sustainable supply chain with an emphasis on environmental factors with a robust optimization approach

Nowadays, the lack of natural resources and reserves of raw materials, besides the increased production costs and the problems with burying and destroying industrial waste, have attracted attention to product recovery and waste recycling in the framework of a closed-loop and sustainable supply chain, also able to create a competitive advantage. On the other hand, researches indicate that taking resilience approaches into account in supply chain design may protect buyers against disruptions such as natural, human, or technological disasters. The present paper presents a multi-objective mathematical model of a single-period, multi-product, and multi-level closed-loop supply chain, considering the dimensions of resilience and sustainability under conditions of uncertainty. Hence, a deterministic mixed integer linear programming model is initially presented; subsequently, to eliminate the uncertainty of the demand parameters and costs, its stochastic counterpart was presented based on Pishvaee's robust possibilistic programming (RPP) model. In order to solve the model, the Augmented Epsilon Constraint method was employed in the GAMS software environment. Ultimately, the model was solved and evaluated by a numerical example.