New mathematical modeling for a location–routing–inventory problem in a multi-period closed-loop supply chain in a car industry

Journal of Industrial Engineering International

دوره 14، شماره 3، آذر 2018   

نویسندگان

F. Forouzanfar¹؛ R. Tavakkoli-Moghaddam^{* 2، 3}؛ M. Bashiri⁴؛ A. Baboli⁵؛ S. M . Hadji Molana¹

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

²School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran

³LCFC, Arts et Métier Paris Tech, Metz, France

⁴Department of Industrial Engineering, Faculty of Engineering, Shahed University, Tehran, Iran

⁵DISP Laboratory, INSA-Lyon, University of Lyon, Villeurbanne, France

چکیده

This paper studies a location–routing–inventory problem in a multi-period closed-loop supply chain with multiple suppliers, producers, distribution centers, customers, collection centers, recovery, and recycling centers. In this supply chain, centers are multiple levels, a price increase factor is considered for operational costs at centers, inventory and shortage (including lost sales and backlog) are allowed at production centers, arrival time of vehicles of each plant to its dedicated distribution centers and also departure from them are considered, in such a way that the sum of system costs and the sum of maximum time at each level should be minimized. The aforementioned problem is formulated in the form of a bi-objective nonlinear integer programming model. Due to the NP-hard nature of the problem, two meta-heuristics, namely, non-dominated sorting genetic algorithm (NSGA-II) and multi-objective particle swarm optimization (MOPSO), are used in large sizes. In addition, a Taguchi method is used to set the parameters of these algorithms to enhance their performance. To evaluate the efficiency of the proposed algorithms, the results for small-sized problems are compared with the results of the ε-constraint method. Finally, four measuring metrics, namely, the number of Pareto solutions, mean ideal distance, spacing metric, and quality metric, are used to compare NSGA-II and MOPSO.

کلیدواژه‌ها

Location؛ routing؛ inventory . Multi-period . Closed-loop supply chain . Lost sales . Backlog