flexible programming

Attention to environmental issues in supply chain activities has been taken into consideration due to the increase in public awareness and strict laws related to environmental protection. Initially, only the economic aspects of the supply chain were considered in the network configuration, but with increasing concerns about environmental issues, reverse logistics and closed-loop supply chains were developed. Designing a closed-loop supply chain network plays an important role in reducing costs, improving service levels, and responding to environmental issues. Therefore, the purpose of this study is to design a closed-loop supply chain network taking into account hybrid uncertainties and flexibility in constraints.

In most of the conducted studies about supply chain network design, the types of cognitive and random uncertainties, as well as the flexibility of soft constraints, have not been investigated simultaneously, while the conducted modeling is not able to consider hybrid uncertainty in supply chain parameters in the real world. In this study, to simultaneously consider the hybrid uncertainties and flexibility in constraints, a novel model of robust stochastic, possibilistic, and flexible programming based on Me measurement was developed. In this model, the convex combination of optimistic and pessimistic attitudes of decision-makers was considered in the form of the Me measure, and the modeling was more flexible and realistic.

In the proposed approach, a convex combination of optimistic and pessimistic spectra was considered in the model. The need for subjective and repetitive reviews by decision-makers was eliminated in the model and the level of satisfaction was calculated optimally after solving the problem. On the other hand, due to the robustness of the model, possible deviations, scenario deviations, non-fulfillment of demand and capacity, and deviations of soft constraints were minimized. In the proposed approach based on the Me measure, the problem-solving approach was reduced and there was no need for a two-step solution to find solutions.

A case study was conducted in the supply chain of stone paper production to evaluate the efficiency of the proposed model. The results of sensitivity analysis, robustness analysis, and simulation with the realization model showed that the proposed model was able to provide robust and realistic solutions. The proposal of a realistic and flexible solution for designing problems of the supply chain network by creating a trade-off between the objective function and the risk-taking level of decision-makers and managers through changing the justified space in the Me criterion in the proposed approach was one of the achievements of the present study. As its other achievement, the present study could provide a combination of different viewpoints of decision-makers’ risk-taking through changing the justified space based on different values of the parameter λ in measuring Me and propose flexible and realistic solutions according to the results of numerical simulation in the proposed approach.

Considering the cognitive, random, uncertain, and flexible constraints, a robust, stochastic, possibilistic, and flexible chance-constrained model was developed based on credibility measurement. The ultimate aim was closed-loop supply chain network design. Different attitudes of decision-makers were answered by more flexible measurements of optimistic and pessimistic parameters in the form of credibility measurement. The model has been able to reduce the possible deviation, stochastic deviations, non-fulfillment of demand and capacity constraints, and violation of flexible constraints, which simultaneously include cognitive and random uncertainties and flexibility of constraints in the model. To apply the model, a case study was conducted to design the closed-loop supply chain network of multi-product and multi-period stone paper. The results of implementing the model showed that in different situations and according to the importance of decision makers' opinions, using the range of optimism and pessimism, the number, location of facilities, optimal flow of products and materials between centers in the stone paper supply chain network can be determined. The proposed model was evaluated using robustness and sensitivity analysis, and its performance was evaluated using nominal data in the realization model, which results showed the appropriate performance of the model.