Hybridization of an interactive fuzzy methodology with a lexicographic min-max approach for optimizing a multi-period multi-product multi-echelon sustainable closed-loop supply chain network

Abstract

Here, a fuzzy multi-period multi-echelon multi-objective mixed-integer non-linear programming (MOMINLP) model is considered for a sustainable multi-product multi-site multi-distribution multi-customer supply chain in forward flow having multi-centers for collecting, checking, repairing and decomposing and multi-disposal centers in the reverse flow. Minimizing the total cost of the closed-loop supply chain (CLSC), elevating the customer satisfaction degrees, minimizing the total waiting time, minimizing the manufacturing site greenhouse gases and minimizing the CO2 emissions from vehicles are considered as the objective functions. Furthermore, integration of strategic decisions of flow allocations and vehicle routing with tactical and operational decisions such as production and workforce planning and improving upon customer satisfaction are considered. Also, we are concerned with the stability of the model and the accuracy of the obtained solution. We consider uncertainty and propose an appropriate method to develop a fair optimization of the distribution of raw materials and products to the supply chain participants. The presented solution method initially considers an adaptation of the lexicographic min–max fairness approach to finding a short delay for the delivery time of all the existing flows between every two consecutive echelons of the CLSC network. Then, a service quality measure is introduced to evaluate the uncertain delivery time considering the delay unpleasantness measure (DUM) index and measure the delay unpleasantness of all the existing delivery time delays. The model is converted to an auxiliary crisp MOMINLP problem by taking appropriate strategies, and a novel interactive fuzzy approach is proposed to find a compromised solution. The effectiveness of the algorithm is illustrated through a generated case study. The validity of the proposed method is confirmed by comparing the obtained results with the ones obtained by some other valid approaches, making use of distance and dispersion measure functions. Computational results show the proposed fuzzy method to be more efficient than other approaches. The encouraging results provide motivations for the use of our proposed fuzzy approach to solving other kinds of multi-objective mixed-integer models.