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Mathematical Problems in Engineering
Volume 2015, Article ID 179102, 18 pages
Research Article

A Hybrid Approach to Solve a Model of Closed-Loop Supply Chain

1Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
2Department of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran

Received 18 October 2014; Revised 11 January 2015; Accepted 2 February 2015

Academic Editor: Lionel Amodeo

Copyright © 2015 Nafiseh Tokhmehchi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper investigates a closed-loop supply chain network, including plants, demand centers, as well as collection centers, and disposal centers. In forward flow, the products are directly sent to demand centers, after being produced by plants, but in the reverse flow, reused products are returned to collection centers and, after investigating, are partly sent to disposal centers and the other part is resent to plants for remanufacturing. The proposed mathematical model is based on mixed-integer programming and helps minimizing the total cost. Total costs include the expenditure of establishing new centers, producing new products, cargo transport in the network, and disposal. The model aims to answer these two questions. (1) What number and in which places the plants, collection centers, and disposal centers will be constructed. (2) What amount of products will be flowing in each segment of the chain, in order to minimize the total cost. Four types of tuned metaheuristic algorithms were used, which are hybrid forms of genetic and firefly algorithms. Finally an adequate number of instances are generated to analyse the behavior of proposed algorithms. Computational results reveal that iterative sequentialization hybrid provides better solution compared with the other approaches in large size.