A mathematical multi-objective model for treatment network design (physical-biological-thermal) using modified NSGA II

Document Type : Research Paper

Authors

1 Faculty of Engineering, University of Ilam, Ilam, Iran

2 University of Tehran, Tehran, Iran

3 Department of Industrial Engineering, Ilam Branch, Islamic Azad University, Ilam, Iran

Abstract

Today, sustainable development is one of the important issues in regard to the economy of a country. This issue magnifies the necessity for increased scrutiny towards issues such as environmental considerations and product recovery in closed-loop supply chains (CLSCs). The most important motivational factors influencing research on these topics can be considered in two general groups: environment-friendly legal requirements and cost efficiencies. The most important elements in the closed-loop supply chain include collection centers and treatment centers. This paper intended to design a network according to the mentioned principles. In this regard, three types of product treatment centers were taken into account: physical, biological, and thermal. The network design was made via a new mixed multi-objective nonlinear mathematical model of integers. In this model, three objective functions were considered that included profit maximization, pollution minimization, and the minimization of the number of facilities under construction. The model was obtained after determining the number of collection and treatment centers, the number of containers for storage of different waste materials, the amount of waste sent from collection centers to the treatment centers, and the areas covered by collection centers. Due to the conflicting objective functions, a corrected NSGAII algorithm was used to solve this model. The change applied in the mentioned algorithm was made to determine the appropriate amount of the crossover percentage. The improvement in the performance of the proposed solution algorithm is shown using a numerical example. To prove the improved performance, a T-test was used to compare the means between the two populations. To select the optimum answer from the Pareto solution set, indices of D, S, and solution time were used and solved with TOPSIS.

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[1] Ramezani, M., Bashiri, M., Tavakkoli-Moghaddam, R. (2013). A new multi-objective stochastic model for a forward/reverse logistic network design with responsiveness and quality level. Applied mathematical modelling, 37(1), 328-344.
[2] Govindan, K., Soleimani, H., Kannan, D. (2015). Reverse logistics and closed-loop supply chain: A comprehensive review to explore the future. European journal of operational research, 240(3), 603-626.
[3] Zeballos, L. J., Méndez, C. A., Barbosa-Povoa, A. P., Novais, A. Q. (2014). Multi-period design and planning of closed-loop supply chains with uncertain supply and demand. Computers and chemical engineering, 66, 151-164.
[4] Hatefi, S. M., Jolai, F. (2014). Robust and reliable forward–reverse logistics network design under demand uncertainty and facility disruptions. Applied mathematical modelling, 38(9), 2630-2647.
[5] Validi, S., Bhattacharya, A., Byrne, P.J. (2012). Greening the Irish food market supply chain through minimal carbon emission: an integrated multi-objective location-routing approach. In: Proceedings of the 10th international conference on manufacturing research, Aston University, UK, pp. 805-810.
[6] Subramanian, P., Ramkumar, N., Narendran, T. T., Ganesh, K. (2013). PRISM: Priority based Simulated annealing for a closed loop supply chain network design problem. Applied soft computing, 13(2), 1121-1135.
[7] Soleimani, H., Seyyed-Esfahani, M., & Shirazi, M. A. (2013). Designing and planning a multi-echelon multi-period multi-product closed-loop supply chain utilizing genetic algorithm. The international journal of advanced manufacturing technology, 68(1-4), 917-931.
[8] Pazhani, S., Ramkumar, N., Narendran, T. T., Ganesh, K. (2013). A bi-objective network design model for multi-period, multi-product closed-loop supply chain. Journal of industrial and production engineering, 30(4), 264-280.
[9] Fallah-Tafti, A. L., Sahraeian, R., Tavakkoli-Moghaddam, R., Moeinipour, M. (2014). An interactive possibilistic programming approach for a multi-objective closed-loop supply chain network under uncertainty. International journal of systems science, 45(3), 283-299.
[10] Validi, S., Bhattacharya, A., Byrne, P. J. (2014). Integrated low-carbon distribution system for the demand side of a product distribution supply chain: a DoE-guided MOPSO optimizer-based solution approach. International journal of production research, 52(10), 3074-3096.
[11] Validi, S., Bhattacharya, A., Byrne, P. J. (2014). A case analysis of a sustainable food supply chain distribution system—A multi-objective approach. International journal of production economics, 152, 71-87.
[12] Garg, K., Jain, A., Jha, P. C. (2014). Designing a closed-Loop Logistic Network in Supply Chain by Reducing its unfriendly consequences on environment. In Proceedings of the second international conference on soft computing for problem solving (SocProS 2012), December 28-30, 2012 (pp. 1483-1498). Springer India.
[13] Validi, S., Bhattacharya, A., Byrne, P. J. (2015). A solution method for a two-layer sustainable supply chain distribution model. Computers and operations research, 54, 204-217.
[14] Keshtzari, M., Naderi, B., Mehdizadeh, E. (2016). An improved mathematical model and a hybrid metaheuristic for truck scheduling in cross-dock problems. Computers and industrial engineering, 91, 197-204.
[15] Lin, C., Choy, K. L., Ho, G. T., Chung, S. H., Lam, H. Y. (2014). Survey of green vehicle routing problem: past and future trends. Expert Systems with applications, 41(4), 1118-1138.
[16] Luque-Almagro, V. M., Moreno-Vivián, C., Roldán, M. D. (2016). Biodegradation of cyanide wastes from mining and jewellery industries. Current opinion in biotechnology, 38, 9-13.
[17] Panicker, V. V., Vanga, R., Sridharan, R. (2013). Ant colony optimisation algorithm for distribution-allocation problem in a two-stage supply chain with a fixed transportation charge. International journal of production research, 51(3), 698-717.
[18] Hasani, A., Zegordi, S. H., Nikbakhsh, E. (2015). Robust closed-loop global supply chain network design under uncertainty: the case of the medical device industry. International journal of production research, 53(5), 1596-1624.