Providing an Integrated Multi-Objective Model for Closed-Loop Supply Chain under Fuzzy Conditions with Upgral Approach

Abstract

This study was conducted aimed at providing a sustainable multi-objective model of supply chain location, inventory, routing under uncertainty with a passive defense approach, in which Upgral model was first introduced to world. The Upgral Paradigm is an integrated model for location-inventory-routing problem in a four-level supply chain where parameters such as demand, facility cost and inventory costs are taken into account uncertain as triangular fuzzy numbers (TFNs). In this study, characteristics and capabilities of passive defense in supply chain, such as logistical flow rate, backup path security, the possibility of resource and equipment deployment, and dispersion principle were considered for location to increase resilience of supply chain. The model was solved using Whale Optimization Algorithm (WOA) and NSGA-II meta-heuristic algorithm. First, a four-objective mathematical model was proposed for problem objectives of which were: 1) minimizing supply chain costs; 2) maximizing social responsibility or social benefits; 3) minimizing environmental impacts; and 4) minimizing risk. Moreover, experimental sample problems were solved in three small, medium, and large groups using WOA Algorithm. The results of solving this algorithm were compared with results of NSGA-II one according to indices including quality, dispersion, uniformity and solution time indices to prove efficiency of algorithm. Based on results, WOA algorithm had a higher ability to achieve higher quality and near-optimal solutions than NSGA-II algorithm in all cases. The dispersion index values indicated that WOA Algorithm performed better in exploring and extracting feasible region. In addition, with respect to results of uniformity and solution time indices, it was found that NSGA-II Algorithm had a lower solution time than WOA Algorithm and answer space more uniformly.