Mathematical Formulation and Solving of Green Closed-loop Supply Chain Planning Problem with Production, Distribution and Transportation Reliability

Authors

Faculty of Industrial Engineering, Yazd University, Yazd, Iran

Abstract

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.

Keywords


1.     Hatefi, S. and Jolai, F., "Robust and reliable forward–reverse logistics network design under demand uncertainty and facility disruptions", Applied Mathematical Modelling,  Vol. 38, No. 9-10, (2014), 2630-2647.
2.     Ramazankhani, M.-E., Mostafaeipour, A., Hosseininasab, H. and Fakhrzad, M.-B., "Feasibility of geothermal power assisted hydrogen production in iran", International Journal of Hydrogen Energy,  Vol. 41, No. 41, (2016), 18351-18369.
3.     Pasandideh, S.H.R., Niaki, S.T.A. and Asadi, K., "Bi-objective optimization of a multi-product multi-period three-echelon supply chain problem under uncertain environments: Nsga-ii and nrga", Information Sciences,  Vol. 292, (2015), 57-74.
4.     Khatami, M., Mahootchi, M. and Farahani, R.Z., "Benders’ decomposition for concurrent redesign of forward and closed-loop supply chain network with demand and return uncertainties", Transportation Research Part E: Logistics and Transportation Review,  Vol. 79, (2015), 1-21.
5.     Zeballos, L.J., Méndez, C.A., Barbosa-Povoa, A.P. and Novais, A.Q., "Multi-period design and planning of closed-loop supply chains with uncertain supply and demand", Computers & Chemical Engineering,  Vol. 66, (2014), 151-164.
6.     Dai, Z. and Zheng, X., "Design of close-loop supply chain network under uncertainty using hybrid genetic algorithm: A fuzzy and chance-constrained programming model", Computers & Industrial Engineering,  Vol. 88, (2015), 444-457.
7.     Soleimani, H., Govindan, K., Saghafi, H. and Jafari, H., "Fuzzy multi-objective sustainable and green closed-loop supply chain network design", Computers & Industrial Engineering,  Vol. 109, (2017), 191-203.
8.     Garg, K., Kannan, D., Diabat, A. and Jha, P., "A multi-criteria optimization approach to manage environmental issues in closed loop supply chain network design", Journal of Cleaner Production,  Vol. 100, (2015), 297-314.
9.     Pasandideh, S.H.R., Niaki, S.T.A. and Asadi, K., "Optimizing a bi-objective multi-product multi-period three echelon supply chain network with warehouse reliability", Expert Systems with Applications,  Vol. 42, No. 5, (2015), 2615-2623.
10.   Kalaitzidou, M.A., Longinidis, P. and Georgiadis, M.C., "Optimal design of closed-loop supply chain networks with multifunctional nodes", Computers & Chemical Engineering,  Vol. 80, (2015), 73-91.
11.   Cardoso, S.R., Barbosa-Póvoa, A.P. and Relvas, S., "Integrating financial risk measures into the design and planning of closed-loop supply chains", Computers & Chemical Engineering,  Vol. 85, (2016), 105-123.
12.   Ning Ma, M. S., Ashayeri, P. d. i. J., and Sotirov, A. P. R., "Robust optimization of supply chain downsizing problem under bankruptcy", Tilburg University,  (2010),
13.   Ramezani, M., Kimiagari, A.M., Karimi, B. and Hejazi, T.H., "Closed-loop supply chain network design under a fuzzy environment", Knowledge-Based Systems,  Vol. 59, (2014), 108-120.
14.   Jabbarzadeh, A., Haughton, M. and Khosrojerdi, A., "Closed-loop supply chain network design under disruption risks: A robust approach with real world application", Computers & Industrial Engineering,  Vol. 116, (2018), 178-191.
15.   Jerbia, R., Boujelben, M.K., Sehli, M.A. and Jemai, Z., "A stochastic closed-loop supply chain network design problem with multiple recovery options", Computers & Industrial Engineering,  Vol. 118, (2018), 23-32.
16.   Kim, J., Do Chung, B., Kang, Y. and Jeong, B., "Robust optimization model for closed-loop supply chain planning under reverse logistics flow and demand uncertainty", Journal of Cleaner Production, Vol. 196, (2018), 1314-1328, doi: org/10.1016/j.jclepro.2018.06.157.
17.   Ghahremani-Nahr, J., Kian, R. and Sabet, E., "A robust fuzzy mathematical programming model for the closed-loop supply chain network design and a whale optimization solution algorithm", Expert Systems with Applications,  Vol. 116, (2019), 454-471.
18.   Ben-Tal, A., El Ghaoui, L. and Nemirovski, A., "Robust optimization, Princeton University Press,  Vol. 28,  (2009).
19.   Srinivas, N. and Deb, K., "Muiltiobjective optimization using nondominated sorting in genetic algorithms", Evolutionary Computation,  Vol. 2, No. 3, (1994), 221-248.
20.   Naderi, B., Zandieh, M., Balagh, A.K.G. and Roshanaei, V., "An improved simulated annealing for hybrid flowshops with sequence-dependent setup and transportation times to minimize total completion time and total tardiness", Expert Systems with Applications,  Vol. 36, No. 6, (2009), 9625-9633.
21.   Fakhrzad, M., Sadeghieh, A. and Emami, L., "A new multi-objective job shop scheduling with setup times using a hybrid genetic algorithm",International Journal of Engineering-Transactions B: Applications, Vol. 26, No. 2, 207-218
22.   Fakhrzad, M. and Heydari, M., "A heuristic algorithm for hybrid flow-shop production scheduling to minimize the sum of the earliness andf tardiness costs", Journal of the Chinese Institute of Industrial Engineers,  Vol. 25, No. 2, (2008), 105-115.
23.   Hosseini-Nasab, H., Fereidouni, S., Ghomi, S.M.T.F. and Fakhrzad, M.B., "Classification of facility layout problems: A review study", The International Journal of Advanced Manufacturing Technology,  Vol. 94, No. 1-4, (2018), 957-977.