Optimizing Supply Chain Design for Sustainability and Reliability‎: ‎A Comparative Study of Augmented Epsilon‎‎‎ and Normalized Normal Constraint Methods

Integrating sustainability and reliability represents a synergistic approach that can be explored through the problem of a closed-loop supply chain network design (SCND)‎. ‎This study is conducted in three stages‎: ‎mathematical modeling‎, ‎model solution using exact methods‎, ‎and evaluation of the solution methods‎. ‎In the first stage‎, ‎a mixed-integer linear programming (MILP) model is developed in a multi-objective‎, ‎multi-product‎, ‎and multi-period framework‎. ‎The objectives of the proposed model aim to maximize profitability‎, ‎social responsibility‎, ‎and reliability‎. ‎In the second stage‎, ‎two methods‎, ‎namely Augmented ‎$\varepsilon‎‎$‎-Constraint (AEC) and Normalized Normal Constraint (NNC)‎, ‎are implemented in the GAMS software to solve the model and identify the optimal Pareto solutions‎. ‎In the third stage‎, ‎the Shannon Entropy technique is employed to determine the criteria weights‎, ‎and the VIKOR technique is utilized to select the superior solution method‎. ‎The overall performance accuracy of the proposed model is measured using four samples from a numerical example with randomly generated data based on the objective function coefficients‎. ‎The results indicate the presence of a conflict among the three objective functions‎. ‎Consequently‎, ‎decision-makers should consider sacrificing some profitability to enhance environmental protection and improve reliability‎. ‎In terms of three criteria‎, ‎run time‎, ‎diversification metric‎, ‎and general distance‎, ‎the NNC method is given priority over the AEC method‎. ‎Even when the criteria are given equal weight‎, ‎the superiority of the NNC method remains unchanged‎. ‎The application of the proposed model across different industries represents a significant research direction for future research‎.