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

Document Type : Research Paper


1 Industrial Management Department of South Tehran Branch, Islamic Azad University, Tehran, Iran

2 Department of Management, Faculty of Management, Malek Ashtar University of Technology, Tehran, Iran

3 Department of Industrial Management, Faculty of Management and Accounting, Shahid Beheshti University, Tehran, Iran


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 the Upgral model was first introduced to the world. The Upgral Paradigm is an integrated model for the 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, the characteristics and capabilities of passive defense in the supply chain, such as "logistical flow rate", "backup path security", "the possibility of resource and equipment deployment", and the dispersion principle were considered for location to increase the 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 the problem the 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, the experimental sample problems were solved in three small, medium, and large groups using the WOA Algorithm. The results of solving this algorithm were compared with the results of NSGA-II one according to the indices including quality, dispersion, uniformity and solution time indices to prove the efficiency of the algorithm. Based on the results, the 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 the WOA Algorithm performed better in exploring and extracting the feasible region. In addition, with respect to the results of the uniformity and the solution time indices, it was found that the NSGA-II Algorithm had a lower solution time than the WOA Algorithm and the answer space more uniformly.


Volume 11, Issue 1
April 2020
Pages 107-136
  • Receive Date: 05 June 2019
  • Revise Date: 19 October 2019
  • Accept Date: 24 December 2019