Presenting a Bi-objective Integrated Model for Production-Distribution Problem in a Multi-level Supply Chain Network

Document Type: Research Paper


1 Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran

2 Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA 02115, USA,


In this study, a bi-objective model for integrated planning of production-distribution in a multi-level supply chain network with multiple product types and multi time periods is presented. The supply chain network including manufacturers, distribution centers, retailers and final customers is proposed. The proposed model minimizes the total supply chain costs and transforming time of products for customers in the chain. The proposed model is in the class of linear integer programming problems. The complexity of the problem is large and in the literatur, this problem has been shown to be NP-hard. Therefore, for solving this problem, two multi objective meta-heuristic approaches based on Pareto method including non-dominated Sorting Genetic Algorithm-II (NSGA-II) and non-dominated Ranking Genetic Algorithm (NRGA) have been suggested. Since the output of meta- heuristic algorithms are highly dependent on the input parameters of the algorithm, Taguchi method (Taguchi) is used to tune the parameters. Finally, in order to evaluate the performance of the proposed solution methods, different test problems with different dimensions have been produced and the performances of the proposed algorithms on the test problems have been analyzed.


Main Subjects

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