TY - JOUR ID - 82271 TI - Mathematical Formulation and Solving of Green Closed-loop Supply Chain Planning Problem with Production, Distribution and Transportation Reliability JO - International Journal of Engineering JA - IJE LA - en SN - 1025-2495 AU - Fakhrzad, M. B. AU - Talebzadeh, P. AU - Goodarzian, F. AD - Faculty of Industrial Engineering, Yazd University, Yazd, Iran Y1 - 2018 PY - 2018 VL - 31 IS - 12 SP - 2059 EP - 2067 KW - Green Closed-loop Supply Chain KW - Uncertainty KW - Reliability KW - NSGA-II algorithm DO - N2 - In this paper, developed a new multi-product, multi-period, and multi-level closed-loop green supply chain planning model under uncertain conditions. The formulated model consists of five objective functions, which minimize the cost of the supply chain, minimize the CO2 emission of transportation vehicles, maximize the reliability of manufacturing and distribution centers, maximize the reliability of the transportation system, and maximize the level of service provided. Therefore, the problem of model formulated as a multi-objective mixed integer nonlinear programming. Also, since the proposed model is complex and NP-hard in large size, therefore, for the investigation of the results, we have used a Non-Dominated Sorting Genetic II Algorithm (NSGA-II). In addition, the small of size results of the problem achieved by GAMS software. Therefore, we try to solve these problems by analyzing and comparing them with the help of these algorithm. For this purpose, various size has been considered. UR - https://www.ije.ir/article_82271.html L1 - https://www.ije.ir/article_82271_2134fc1ca2c35c7d002a19c69922ae52.pdf ER -