Robust fuzzy programming for designing a closed-loop supply chain under uncertainty and flexible constraints

Due to enacting laws and increasing awareness of environmental issues, the design of a Closed-Loop Supply Chain network (CLSC) has received attention. The design of CLSC is a strategic issue with long-term effects and faces uncertainty in the real world, which affects its performance. In the studies on CLSC, robust optimization, cognitive uncertainty, and soft constraints are not assessed simultaneously in modeling and this area is deficient. So, in this investigation, mixed-robust-possibilistic-flexible programming is proposed. This research develops CLSC problem-solving approaches under conditions of cognitive uncertainty and soft constraints and leads to the presentation of operation engineering and optimization in CLSC. The Decision Maker’s (DM) risk level is measured flexibly using a credibility criterion. Also, deviation of possibilistic and constraint violations are controlled in the proposed approach. To evaluate the presented approach, a study is executed to design a paper supply chain with economic and environmental objectives. The results show that it is possible to determine the number, place of facilities, and optimal flow of products and materials between different centers. The proposed approach and multi-objective model solution method are capable of providing realistic and flexible solutions based on the trade-off between other objectives and DMs’ preferences. The performance of the proposed approach was analyzed and results confirmed the developed approach compared to similar approaches for the design of CLSC.