Optimization of a Multi-product Three-echelon Supply Chain

Document Type : Research Paper

Authors

Department of Industrial Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran

Abstract

This paper aims at single-objective optimization of multi-product for three-echelon supply chain architecture consisting of production plants, distribution centers (DCs) and customer zones (CZs). The key design decisions considered are: the quantity of products to be shipped from plants to DCs, from DCs to CZs , cycle length, and production quantity so as to minimize the total cost .To optimize the objective, three-echelon network model is mathematically represented considering the associated constraints, production, capacityand shipment costs and solved using genetic algorithm (GA) and Simulated Annealing (SA).Some numerical illustrations are provided at the end to not only show the applicability of the proposed methodology, butalso to select the best method using a t-test along with the simple additive weighting (SAW) method.

Keywords

Main Subjects


Alimardani, M., Jolai, F., and Rafiei, H. (2013). Bi-product inventory planning in a three-echelon supply chain with backordering, Poisson demand, and limited warehouse space. Journal of Industrial Engineering International, Vol. 9 (22), pp. 9-22.
Amiri A. (2006). Designing a distribution network in a supply chain system: Formulation and efficient solution procedure.European Journal of Operational Research,Vol.171, pp. 567-576. 
Azaron, A., Brown, K.N., Tarim, S.A., and Modarres, M. (2008). A multi-objective stochastic programming approach for supply chain design considering risk. International Journal of Production Economics, Vol. 116, pp.129-138.
Bandyopadhyay, S., and Bhattacharya, R. (2014). Solving a tri-objective supply chain problem withmodified NSGA-II algorithm. Journal of Manufacturing Systems, Vol. 33, pp. 41-50.
Baykasoglu, A., and Gocken, T. (2010). Multi-objective aggregate production planning with fuzzy parameters. Advances in Engineering Software, Vol. 41 , pp.1124-1131.
Belgin, O., Karaoglan, I., and Altiparmak, F. (2018) Two-echelon vehicle routing problem with simultaneous pickup and delivery: Mathematical model and heuristic approach. Computers & Industrial Engineering, Vol.115, pp.1-16
Bidhandi, H.M., and Yusuff R.M. (2011). Integrated supply chain planning under uncertainty using an improved stochastic approach. Applied Mathematical Modeling, Vol. 35, pp. 2618-2630.
Cardona-Valdés, Y., Alvarez, A., and Ozdemir, D. (2011). A bi-objective supply Alvarez chain design problem with uncertainty. Transportation Research, Vol.19, pp. 821-832.
Cerny V. (1985). A thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm. Journal of Optimization Theory and Applications, Vol.45, pp. 41-51.
Chandra, C, and Kumar, S. (2001). Enterprise architectural framework for supply chain integration. Industrial Management and Data Systems  Vol.101, pp. 290-303.
Chen, C.L., and Lee, W.C. (2004). Multi-objective optimization of multi-echelon supply chainnetworks with uncertain product demands and prices. Computers and Chemical Engineering  ,Vol.28, pp.1131-1144.
Chen, X., Wan, W., and Xu, X. (1998). Modeling rolling batch planning as vehicle routing problem with time windows. Computers and Operations Research, Vol. 25, pp. 1127-1136.
Costa, A., Celano, G., Fichera, S., and Trovato, E. (2010). A new efficient encoding/decoding procedure for the design of a supply chain network with genetic algorithms. Computers and Industrial Engineering, Vol.59, pp. 986-999.
Dai, Z., Aqlan, F., and Gao, K. (2017) Optimizing multi-echelon inventory with three types of demand in supply chain Transportation Research Part E. Logistics and Transportation Review, Vol.107, pp. 141-177.
El-Sayed, M., Afia, N., and El-Kharbotly, A. (2010). A stochastic model for forward–revers logistics network design under risk. Computers and Industrial Engineering, Vol.58, pp. 423-431.
Gebennini, E., Gamberini, R., and Manzini, R. (2009). An integrated production–distribution model for the dynamic location and allocation problem with safety stock optimization. International Journal of Production Economics ,Vol. 122, pp. 286-304.
Gen, M., and Cheng, R. (2000). Genetic algorithms and engineering optimization. New York: John Wiley and Sons.
Gen, M. (1997). Genetic algorithm and engineering design. New York: John Wiley & Sons
Georgiadis, M.C., Tsiakis, P., Longinidis, P., and Sofioglou, M.K. (2011). Optimal design of supply chain networks under uncertain transient demand variations. Omega,Vol. 39, pp. 254-272.
Ghasemy Yaghin, R. (2018). Integrated multi-site aggregate production-pricing planning in a two-echelon supply chain with multiple demand classes Applied Mathematical Modelling,Vol.53, pp.276-295.
Goldberg, D. (1989). Genetic algorithms in search, Optimization, and machine learning. MA, USA: Addison-Wesley, Reading.
Habibi-Kouchaksaraei, M., Paydar, M.M., and Asadi-Gangraj, E. (2018) Designing a bi-objective multi-echelon robust blood supply chain in a disaster. Applied Mathematical Modelling ,Vol. 55, pp. 583-599.
Holland, J.H. (1975). Adaption in natural and artificial systems. Ann Arbor, Michigan: University of Michigan Press.
Hwang, C.L., and Yoon, K.L.(1981). Multiple attribute decision making: Methods and applications. Springer-Verlag, New York. 
Jamshidi, R., Fatemi-Ghomi S.M.T., and Karimi E. (2012). Multi-objective green supply chain optimization with a new hybrid memetic algorithm using the Taguchi method. Scientia Iranica,Vol. 19, pp.1876-1886.
Johansson, L., and Olsson, F. (2018) Age-based inventory control in a multi-echelon system with emergency replenishments. European Journal of Operational Research ,Vol.265, pp.951-961
Kayvanfar, V., Moattar Husseini, S.M., Sajadieh, M.S., and Karimi, B. (2018). A multi-echelon multi-product stochastic model to supply chain of small-and-medium enterprises in industrial clusters. Computers&IndustrialEngineering,Vol.115, pp.69-79.
Kirkpatrick, S., GelattJr, C.D., and Vecchi, M.P. (1983). Optimization by Simulated Annealing. Science ,Vol. 220, pp. 671-680.
Liu, T., Luo, Z., Qin, H., and Lim, A. (2018) A branch-and-cut algorithm for the two-echelon capacitated vehicle routing problem with grouping constraints. European Journal of Operational Research ,Vol. 266, pp.487-497.
Maghsoudlou, H., Kahag, M.R., Niaki, S.T.A., and Pourvaziri, H. (2016) Bi-objective optimization of a three-echelon multi-server supply-chain problem in congested systems: Modeling and solution Computers & Industrial Engineering ,Vol. 99, pp.41-62
Mele, F.D., Guill´en, G., Espuna, A., and Puigjaner, L. (2007). An agent-based approach for supply chain retrofitting under uncertainty.Computers and Chemical Engineering,Vol. 31, pp. 722-735.
Michalewicz, Z. (1996). Genetic algorithms + data structures = evolution programs (3rd Ed.). Berlin, Germany: Springer.
Miranbeigi, M., Moshiri, B., Rahimi-Kian, A., and Razmi, J. (2015). Demand satisfaction in supply chain management system using a full online optimal control method. The International Journal of Advanced Manufacturing Technology,Vol. 77, pp.1401-1417.
Mirzapour, Al-e-hashem, Malekly, H., Aryanezhad, M.B.(2010).A multi-objective robust optimization model for multi-product multi-site aggregate production planning in a supply chain under uncertainty. International Journal of Production Economics ,Vol. 134, pp. 28-42.
Modak, N.M., Panda, S., and Sana, S.S. (2016). Three-echelon supply chain coordination considering duopolistic retailers with perfect quality products. International Journal of Production Economics ,Vol. 182, pp. 564-578.
Mohammadi, A., Abbasi, A., Alimohammadlou, M., Eghtesadifard, M., and Khalifeh, M. (2017). Optimal design of a multi-echelon supply chain in a system thinking framework: An integrated financial-operational approach. Computers & Industrial Engineering,Vol. 114, pp. 297-315.
Murthy, D.N.P., Solem, B.O., and Roren, T. (2004). Product warranty logistics: Issues and challenges. European Journal of Operational Research ,Vol. 156, pp. 110-126.
 Naimi Sadigh, A.,  Mozafari, M., and Karimi, B. (2012). Manufacturer–retailer supply chain coordination: A bi-level programming approach. Advances in Engineering Software,Vol. 45, pp.144-152.
Olivares-Benitez, E., González-Velarde, J.L., and Ríos-Mercado, R.Z. (2012). A supply chain design problem with facility location and bi-objective transportation choices. Sociedad de Estadística e Investigación Operativa ,Vol. 20, pp. 729-753.
Owen, S.H., and Daskin, M.S. (1998). Strategic facility location: A review. European Journal of Operational Research ,Vol. 111, pp. 423-47.
Park Y. A. (2001). hybrid genetic algorithm for the vehicle scheduling problem with due times and time deadlines. International Journal of Production Economics, Vol. 73, pp.175-188.
Panda, S., Modak, N.M., and Cárdenas-Barrón, L.E. (2017). Coordination and benefit sharing in a three-echelon distribution channel with deteriorating product. Computers & Industrial Engineering ,Vol. 113, pp. 630-645.
Pasandideh, S.H.R., Niaki, S.T.A., and  Aryan Yeganeh, J. A. (2010). Parameter-tuned genetic algorithm for multi-product economic production quantity model with space constraint, discrete delivery orders and shortages. Advances in Engineering Software,Vol. 41, pp. 306-314.
Pasandideh, S.H.R., and Niaki, S.T.A. (2008). A genetic algorithm approach to optimize a multi-products EPQ model with discrete delivery orders andconstrained space.Applied Mathematics and Computation,Vol. 195, pp. 506-514.
Pishvaee, M.S., Razmi, J., and 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: Logistics and Transportation Review, ,Vol. 67, pp.14-38.
Prakash, A., Chan, F.T.S, Liao, H.,  and Deshmukh, S.G. (2012). Network optimization in supply chain: AKBGA approach. Decision Support Systems,Vol. 52, pp. 528-538.
Rodriguez, M.A., Vecchietti, A.R., Harjunkoski, L., and Grossmann, L.E. (2014). Optimal supply chain design and management over a multi-period horizon under demand uncertainty. Part I:MINLP and MILP models. Computers & Chemical Engineering,Vol.  62, pp.194-210.
Ross, A., Khajehnezhad, M., Otieno, W., and Aydas, O. (2017). Integrated location-inventory modelling under forward and reverse product flows in the used merchandise retail sector: A multi-echelon formulation. European Journal of Operational Research, Vol.259, pp.664-676
Ruiz-Femenia, R., Guillén-Gosálbez, G., Jiménez, L., and Caballero, J.A. (2013). Multi-objective optimization of environmentally conscious chemical supply chains under demand uncertainty. Chemical Engineering Science,Vol.  96, pp. 1-11.
Schüt, P.Z., Tomasgard, A., and Ahmed, S. (2009). Supply chain design under uncertainty using sample average approximation and dual decomposition. European Journal of Operational Research ,Vol. 199, pp.409-419.
Shen Z.(2007). Integrated supply chain design models: A survey and future research directions. Journal of Industrial and Management Optimization,Vol. 3, pp. 1-27.
Simchi-Levi, D., Kaminsky, P., and Simchi-Levi, E. (2000).Designing and managing the supply chain. New York: Irwin McGraw-Hill.
Snyder, L.V. (2006). Facility location under uncertainty: A review. IIE Transactions,Vol. 38, pp. 537-554.
Song, D.P., Dong, J.X, and Xu, J. (2014). Integrated inventory management and supplier base reduction in a supply chain with multiple uncertainties. European Journal of Operational Research,Vol. 232, pp. 522-536.
Stenius, O., Marklund, J., and Axsäter, S. (2017). Sustainable Multi-echelon Inventory Control with Shipment Consolidation and Volume Dependent Freight Costs. European Journal of Operational Research, in press.  
Topan, E., Bayındır, Z.P., and Tan, T. (2017) Heuristics for multi-item two-echelon spare parts inventory control subject to aggregate and individual service measures. European Journal of Operational Research ,Vol. 256, pp.126-138.
Tsai C.F., and Chao K.M. (2009). Chromosome refinement for optimizing multiple supplychains. Information Sciences ,Vol. 179, pp. 2403-2415.
Van Landeghem, H., and Vanmaele, H. (2002).Robust planning: A new paradigm for demand chain planning. Journal of Operation Management ,Vol. 20, pp. 769-783.
Wan,g H.F., and Hsu, H.W.(2010). A closed-loop logistic model with a spanning-tree based genetic algorithm. Computers & Operations Research ,Vol. 37, pp. 376-389.
Wang, K.J., Makond, B., and Liu, S.Y. (2011). Location and allocation decisions in a two echelon supply chain with stochastic demand  :? A genetic-algorithm based solution. Expert Systems with Applications,Vol. 38, pp. 6125-6131.
Weber, C.A., Current, J., and Desai. A.(2000). An optimization approach to determining the number of vendors to employ. Supply Chain Management,Vol. 5, pp. 90-98.
Wu, D., Wu, D.D., Zhang, Y., and Olson, D.L. (2013). Supply chain outsourcing risk using anintegrated stochastic-fuzzy optimization approach. Information Sciences ,Vol. 235, pp. 242-258.
You, F., Grossmann, and I.E. (2008). Design of responsive supply chains under demand uncertainty.Computers and Chemical Engineering,Vol. 32, pp. 3090-3111.
Zegordi, S.H., Abadi, L.N.K., and Beheshtinia, M.A. (2010). A novel genetic algorithm for solving production and transportation scheduling in a two-stage supply chain. Computers and Industrial Engineering ,Vol. 58, pp. 373-281.
Zhou, L., Baldacci, R., Vigo, D.,and Wang, X. (2018) A Multi-Depot Two-Echelon Vehicle Routing Problem with Delivery Options Arising in the Last Mile Distribution. European Journal of Operational Research ,Vol. 265, pp.765-778.
Zhou, W.Q., Chen, L., and Ge, H.M. (2013). A multi-product multi-echelon inventory control model with joint replenishment strategy. Applied Mathematical Modelling,Vol.37, pp. 2039-2050.