Designing a sustainable closed-loop supply chain using robust possibilistic-stochastic programming in pentagonal fuzzy numbers

The lack of information and hybrid uncertainties in Supply Chain (SC) parameters affect managerial decisions. It is inevitable to consider random uncertainty based on fuzzy scenarios and cognitive uncertainty to model a Sustainable Closed-Loop SC (SCLSC) problem. Using Pentagonal Fuzzy Numbers (PFNs) has higher comprehensiveness and accuracy than triangular and trapezoidal fuzzy numbers due to taking into account higher uncertainty, less lack of information, and taking into account maximum subjectivity Decision-Makers (DMs). There is a gap in the literature regarding the use of PFNs in SCLSC problems. This research presents a new model using PFNs to solve deficiencies in stochastic-possibilistic programming. Developing a Robust Stochastic-Possibilistic (RSP) based on PFNs under fuzzy scenarios, presenting measures of necessity, possibility, and credibility for making decisions founded on different levels of DMs’ risk, and proposing global solutions through providing linear programming models are the main innovations and contributions of the present research. An actual case study evaluates the presented approach to reduce the cost and carbon pollution in the stone paper SC. In the suggested method, trade-offs could be formed between the mean of objective functions and risk by modifying the robustness coefficients. According to the proposed approach, an optimal value of confidence is specified. Additionally, robustness deviations are controlled in the model, which results in more accurate and reliable results. Numerical simulations confirmed the efficacy of the robust approach proposed. First published online 7 February 2025