A robust fuzzy stochastic multi-objective model for stone paper closed-loop supply chain design considering the flexibility of soft constraints based on Me measure

Abstract

The Closed-Loop Supply Chain Network Design (CLSCND) encourages attention to the economic and environmental issues concerning returned products. CLSCND is a significant decision issue and it is accompanied by uncertainty. Hybrid uncertainties and the flexibility of soft constraints are some of the key issues in CLSCND. There is a research gap surrounding the utilization of the uncertainties of randomness, epistemic, and soft constraints simultaneously with a robust procedure. This study focuses on the Me measure and proposes a novel flexible, probabilistic, and stochastic programming based on robust optimization. In this approach, a convex mixture of the pessimistic–optimistic views based on the Me measure is implemented. The least level of satisfaction with soft constraints is determined Optimally that the need for repetitive reviews by Decision-Maker (DM) is obviated in the proposed model. Additionally, the model controls violations of soft constraints as well as stochastic deviations, probabilistic deviations, unfulfilled demand, and capacity. A case study is conducted on the development of a stone paper considering economic, environmental, and responsive objectives by minimizing total cost and carbon emissions as well as transportation and processing time. In addition, to estimate the weight of the objectives and handle the multi-objective model, the Best–Worst method (BWM) and the interactive fuzzy programming approach are employed, respectively. Robustness analysis and sensitivity analysis for the case study are then performed and the results are simulated and evaluated using the realization model. The findings revealed that the suggested model performed well.