Multi-Objective Optimization for Multi-Product Multi-Period Four Echelon Supply Chain Problems Under Uncertainty
Subject Areas : Executive ManagementMd Mashum Billal 1 , Md. Mosharraf Hossain 2
1 - Department of Industrial & Production Engineering Rajshahi University of Engineering & Technology, Rajshahi, Bangladesh.
2 - Department of Industrial & Production Engineering Rajshahi University of Engineering & Technology, Rajshahi, Bangladesh.
Keywords: Multi-Objective Optimization, Uncertainty, NSGA-II, supply chain management, MOGA,
Abstract :
The multi-objective optimization for a multi-product multi-period four-echelon supply chain network consisting of manufacturing plants, distribution centers (DCs) and retailers each with uncertain services and uncertain customer nodes are aimed in this paper. The two objectives are minimization of the total supply chain cost and maximization of the average number of products dispatched to customers. The decision variables are the number and the locations of reliable DCs and retailers, the optimum number of items produced by plants, the optimum quantity of transported products, the optimum inventory of products at DCs, retailers and plants, and the optimum shortage quantity of the customer nodes. The problem is first formulated into the framework of a constrained multi-objective mixed integer linear programming model. After that, the problem is solved by using meta-heuristic algorithms that are Multi-objective Genetic Algorithm (MOGA), Fast Non-dominated Sorting Genetic Algorithms (NSGA-II) and Epsilon Constraint Methods via the MATLAB software to select the best in terms of the total supply chain cost and the total expected number of products dispatched to customers simultaneously. At the end, the performance of the proposed multi-objective optimization model of multi-product multi-period four-echelon supply chain network design is validated through three realizations and an innumerable of various analyses in a real world case study of Bangladesh. The obtained outcomes and their analyses recognize the efficiency and applicability of the proposed model under uncertainty.
Altiparmak. F., Gen. M., Lin. L., Paksoy. T., (2006) . A genetic algorithm approach for multi-objective optimization of supply chain networks, Comput. Ind. Eng. 51, 196–215.
Amiri. A., (2006). designing a distribution network in a supply chain system: formulation and efficient solution procedure, Eur. J. Oper. Res. 171, 567–576.
Amin S.H., Zhang. G., (2013), A multi-objective facility location model for closed-loop supply chain network under uncertain demand and return, Appl. Math. Model. 37, 4165–4176.
Angelo.J.S., Eduardo Krempser. E., Barbosa. H. J.C., (2013). Differential Evolution for Bilevel Programming, IEEE Congress on Evolutionary Computation June 20-23, Cancún, México.
Bandyopadhyay. S., Bhattacharya. R., (2014). Solving a tri-objective supply chain problem with modified NSGA-II algorithm, J. Manuf. Syst. 33, 41–50.
Cardona-Valdés.Y., Alvarez. A., Ozdemir.D., (2011). A bi-objective supply Alvarez chain design problem with uncertainty, Transp. Res. Part C 19, 821–832.
Camacho-Vallejo, J. F., Munoz-Sanchez,R., & LuisGonzalez-Velarde,J., (2015). A heuristic algorithm for a supply chain’s production-distribution planning. Comput. & Operations Research, 6,110–121.
Coello CAC. (1999). A comprehensive survey of evolutionary-based multi-objective optimization techniques. Knowl Inform Syst; 1 (3), 269–308.
Chen.C.L, Wen.W.C., (2004). Multi-objective optimization of multi-echelon supply chain networks with uncertain product demands and prices, Computers and Chemical Engineering 28, 1131–1144.
Chopra. S., Meindl. P., Supply Chain Management Strategy, Planning, and Operation. Pearson Education LTD. ISBN: 0-13-208608-5.
Deb. K., Pratap. A., Agarwal. A., T. Meyarivan , (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Trans. Evol. Comput. 6 (2),182–197.
Deb K. (2001). Multi-objective optimization using evolutionary algorithms. New York: Wiley. 6,118-129.
Easwaran. G., Üster. H., (2010), A closed-loop supply chain network design problem with integrated forward and reverse channel decisions, IIE Trans. 42, 779–792.
El-Sayed.M., Afia. N., El-Kharbotly.A., (2010). A stochastic model for forward–reverse logistics network design under risk, Computer & Industrial Engineering 58, 423–431.
Fonseca CM, Fleming PJ. Multi-objective genetic algorithms. (1993), In: IEE colloquium on ‘Genetic Algorithms for Control Systems Engineering’ (Digest No. 1993/130). London, UK: IEE.
Fung,J., Singh,G., & Zinder,Y. (2015). Capacity planning in supply chains of mineral resources. Information Sciences, 316 397–418.
Georgiadis.M.C, Tsiakis.P., Longinidis. P., M.K. Sofioglou, (2011). Optimal design of supply chain networks under uncertain transient demand variations, Omega. 39, 254–272.
Gebennini. E., Gamberini. R., Manzini. R., (2009). An integrated production–distribution model for the dynamic location and allocation problem with safety stock optimization, Int. J. Prod. Econ. 122,286–304.
Goldberg DE. (1989). Genetic algorithms in search, optimization, and machine learning. Reading, MA: Addison-Wesley,6,145-164.
Guoquan Zhang.G., Shang.J., Li.L., (2011). Collaborative production planning of supply chain under price and demand uncertainty, Eur. J. of Oper. Res. 215, 590–603.
Haimes, Y. Y., Lasdon, L. S., & Wismer, D. A. (1971). On a bicriterion formulation of the problems of integrated system identification and system optimization. IEEE Transactions on Systems, Man, and Cybernetics – TSMC, 1(3) 296–297.
Hnaiena. F., Delormeb. X., Dolgui. A., (2010). Multi-objective optimization for inventory control in two-level assembly systems under uncertainty of lead times, Comput. Oper. Res. 37, 1835–1843.
Hwang. C.L., Masud. A.S.M.,(1979) Multiple-Objective Decision Making, Methods and Applications: Astate-of-the-art Survey, Springer-Verlag, Berlin.
Jones D. F., Mirrazavi S. K, Tamiz M., (2002) Multiobjective meta-heuristics: An overview of the current state-of-the-art. Eur J Oper Res; 137 (1),1–9.
Kannan. D., Khodaverdi. R., Olfat. L., Jafarian. A., Diabat. A.I., (2013). Integrated fuzzy multi criteria decision making method and multi-objective programming approach for supplier selection and order allocation in a green supply chain, J. Clean. Prod. 47, 355–367.
Konak.A., Coit.D.W., Smith.A.E., (2006). Multi-objective optimization using genetic algorithms: A tutorial, Reliability Engineering and System Safety 91, 992–1007.
K. Shimizu and E. Aiyoshi, (2013). “A new computational method for stackelberg and min-max problems by use of a penalty method,” IEEE Trans. on Automatic Control, vol. 26,(2)460–466.
Lu. Z., Bostel.N., (2007). A facility location model for logistics systems including reverse flows: the case of remanufacturing activities, Comput. Oper. Res. 34, 299–323.
Marufuzzaman. M., Eksioglu. S.D., Huang. Y., (2014). Two-stage stochastic programming supply chain model for biodiesel production via wastewater treatment, Comput. Oper. Res. 49, 1–17.
Maghsoudlou.H., Kahag M.R., Niaki.S.T.A., Pourvaziri .H., (2016). Bi-objective optimization of a three-echelon multi-server supply-chain problem in congested systems: Modeling and solution, Computers & Industrial Engineering. 99, 41–62.
Mehrbod. M., Tu.N., Miao.L., Dai. W., (2012). Interactive fuzzy goal programming for a multi-objective closed-loop logistics network, Annals Oper. Res. 201, 367–381.
Olivares-Benitez.E., González-Velarde. J.L., Ríos-Mercado. R.Z., (2012), A supply chain design problem with facility location and bi-objective transportation choices, Sociedad de Estadísticae Investigación Operativa 20, 729–753.
Pasandideh.S.H.R., Niaki. S. T A., Asadi.K., (2015). Optimizing a bi-objective multi-product multi-period three echelon supply chain network with warehouse reliability, Expert Systems with Applications 42, 2615–2623.
Pasandideh, S. H. R., Niaki, S. T. A., & Asadi, (2015). K. Bi-objective optimization of a multi-product multi-period three-echelon supply chain problem under uncertain environments: NSGA-II and NRGA. Information Sciences, 292, 57–74.
Pishvaee. M.S., Farahani. R.Z., Dullaert. W., (2010). A memetic algorithm for bi-objective integrated forward/reverse logistics network design, Comput. Oper. Res. 37 (6),1100–1112.
Pishvaee, M. S., Razmi, J., & Torabi, S. A. (2014). An accelerated Benders decomposition algorithm for sustainable supply chain network design under uncertainty: A case study of medical needle and syringe supply chain. Transportation Research Part E: Logist. and Transport. Review, 67, 14–38.
Prakash. A., Chan. F.T.S., Liao. H., Deshmukh. S.G., (2012). Network optimization in supply chain: a KBGA approach, Decis. Support Syst. 52, 528–538.
Rabiee. M., Zandieh . M., Ramezani. P., (2012). Bi-objective partial flexible job shop scheduling problem: NSGA-II, NRGA, MOGA and PAES approaches, Int. J. Prod. Res. 50 (24),7327–7342.
Ren,J., Tan,S., Yang,L., Goodsite, M.E., Pang,C., & Dong,L. (2015), Optimization of emergy sustainability index for bio diesel supply network design. Energy Conversion and Management, 92, 312–321.
Ripon, K. S. N., Khan, K. N., Glette, K., Hovin, M., & Torresen, J. (2011). Using Pareto optimality for solving multi-objective unequal area facility layout problem. In 13th annual genetic and evolutionary computation conference, Dublin, Ireland,12–16.
Rodriguez. M.A., Vecchietti. A.R., Harjunkoski. L., Grossmann. L.E., (2014). Optimal supply chain design and management over a multi-period horizon under demand uncertainty. Part I: MINLP and MILP models, Comput. Chem. Eng. 62, 194–210.
Ruiz-Femenia. R., Guillén-Gosálbez. G., Jiménez L., Caballero. J.A., (2013). Multi-objective optimization of environmentally conscious chemical supply chains under demand uncertainty, Chem. Eng. Sci. 96, 1–11.
Sarrafha, K., Rahmati, S, H, A., Niaki, S, T, A., Zaretalab, A., (2014). A bi-objective integrated procurement, production and distribution problem of a multi-echelon supply chain network design: A new tuned MOEA. Comput. & Oper. Research. 54, 35–51.
Shankar, B, L., Basavarajappa, S., Chen, J, C, H., Kadadevaramath, R, S., (2013). Location and allocation decisions for multi-echelon supply chain network–A multi-objective evolutionary approach. Expert Syst. with Applications. 40, 551–562.
Scavarda,L.F., Reichhart,A., Hamacher,S., Holweg,M., (2010). Managing product variety in emerging markets. Int. J. Oper. Prod. Manag. 30 (2),205–224.
Schut. P.Z., Tomasgard. A., Ahmed. S., (2009), Supply chain design under uncertainty using sample average approximation and dual decomposition, Eur. J. Oper. Res. 199, 409–419.
Shi.S., Liu.Z., Tang.L., Xiong.J., (2017). Multi-objective optimization for a closed-loop network design problem using an improved genetic algorithm, Appl. Mathe. Modeling 45, 14–30.
Srinivas N, Deb K. (1994) Multiobjective optimization using nondominated sorting in genetic algorithms. J Evol Comput, 2 (3), 221–48.
Ulungu. E.L., Teghaem. J., Fortemps. P., Tuyttens. D., (1999). MOSA method: a tool for solving multi-objective combinatorial decision problems, J. Multi-criteria Decis. Anal. 8, 221–236.
Wang. K.J., Makond. B., Liu. S.Y., (2011). Location and allocation decisions in a two-echelon supply chain with stochastic demand – a genetic-algorithm based solution, Expert Syst. Appl. 38, 6125–6131.
Wieland, A., Handfield, R.B. & Durach, C.F., (2016). Mapping the Landscape of Future Research Themes in Supply Chain Management. Journal of Business Logistics, 37 (3), 1–8.
Xiujuan L, Zhongke S. ( 2004). Overview of multi-objective optimization methods. J Syst Eng Electron;15 (2), 142–6.
Zitzler E, Deb K, Thiele L. ( 2000). Comparison of multi-objective evolutionary algorithms: empirical results. Evol Comput; 8 (2) 173–95.
Zitzler E, Thiele L., (1999). Multi-objective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans Evol Comput;3 (4) 257–71.