A Multi-Objective VMI Model for a Two-Echelon Single Manufacturer Multiple Buyers Supply Chain

Document Type : Research Paper


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

2 Department of Industrial Engineering, Faculty of Engineering, Alzahra University, Tehran, Iran.


A model of a two-level single-producer multi-buyer supply chain (TSPMBSC) is focused on in this article with a single product made by the producer (or vendor) given to the buyers. The operational form of vendor managed inventory (VMI) is utilized by vendors and buyers. We assume the economic production quantity (EPQ) model used by the producer for inventory control with a limited production rate. Sales quantity and sales price are the parameters of each buyer as well as a certain production rate. Two objectives are considered for the model; the first objective is the maximization of channel profit while the second objective is the maximization of the production periods variances whereby the required storage space is minimized. Because of NP-hardness, the weighted sum multi-objective genetic algorithm (WSMOGA), the multi-objective particle swarm optimization algorithm (MOPSO) and the Non-dominated sorting genetic algorithm II (NSGA-II) are the three distinct heuristics embedded for tackling the problem. The instances of the considered problems with small, medium and large sizes are used to compare these heuristics. Considering the metrics of comparison, The MOPSO-based heuristic outperformed the other heuristics


       [1]        Costa, L., Oliveira, P. (2001). Evolutionary algorithms approach to the solution of mixed integer nonlinear programming problems. Computers and Chemical Engineering, 25, 257–266.
       [2]        Waller, M., Johnson, M.E., Davis, T. (2001). Vendor managed inventory in the retail supply chain. Journal of Business Logistics 20 (1), 183–203.
       [3]        Lau, A.H.L., Lau, H.S. (2003). Effects of a demand curve’s shape on the optimal solutions of a multi echelon inventory/pricing model. European Journal of Operations Research, 147, 530-548.
       [4]        Grieger, M. (2003). Electronic marketplaces: A literature review and a call for supply chain management research. European Journal of Operational Research, 144, 280–294.
       [5]        Masoudi, S., Mirzazadeh, A. (2018). A Model inventory/production of single vendor and single buyer by considering shortage and rate of deterioration, lead time uncertainty based approach the Dempster-Shafer theory. Advances in Industrial Engineering, 51 (4), 435-448.
       [6]        Aghsami, A., Samimim, Y., Aghaei, A. (2021). An integrated Markovian queueing-inventory model in a single retailer- single supplier problem with imperfect quality and destructive testing acceptance sampling. Advances in Industrial Engineering, 55 (4), 367-401.
       [7]        Gholami, M., Honarvar, M. (2015). Developing a mathematical model for vendor managed inventory considering deterioration and amelioration items in a three-level supply chain. Advances in Industrial Engineering, 49 (2), 237-256.
       [8]        Nachiappan, S.P, Jawahar, N. (2006). A genetic algorithm for optimal operating parameters of VMI system in a two-echelon supply chain. European journal of operation research, 182 (3), 1433-1452.
       [9]        Zhang, T., Liang, L., Yu, Y., Yu, Y., (2007). An integrated vendor-managed inventory model for a two-echelon system with order cost reduction, International Journal of Production Economics, 109, 241-253.
     [10]      Yao, Y., Evers, P.T., Dresner, M.E. (2007). Supply chain integration in vendor-managed inventory, Decision Support Systems 43, 663–674.
     [11]      Abdul-Jalbar, B., Segerstedt, A., Sicilia, J., Nilsson, A. (2010). A new heuristic to solve the one-warehouse N-retailer problem. Computers & Operations Research, 37(2), 265-272.
     [12]      Wang, C.X. (2009). Random yield and uncertain demand in decentralized supply chains under the traditional and VMI arrangements. International Journal of Production Research, 47 (7), 1955-1968.
     [13]      Yu, Y., Chu, F., Chen, H. (2009).A Stackelberg game and its improvement in a VMI system with a manufacturing vendor. European Journal of Operational Research, 192 (3), 929-948.
     [15]      Zavanella, L., Zanoni, S. (2009). A one-vendor multi-buyer integrated production-inventory model: The ‘Consignment Stock’ case. International Journal of Production Economics, 118 (1), 225-232.
     [16]      Bichescu, B.C., Fry, M.J. (2009).Vendor-managed inventory and the effect of channel power. OR Spectrum, 31 (1), 195-228.
     [17]      Almehdawe, E. Mantin, B. (2010).Vendor managed inventory with a capacitated manufacturer and multiple retailers: Retailer versus manufacturer leadership. International Journal of Production Economics, 128 (1), 292-302.
     [18]      Darwish, M.A. Odah, O.M. (2010).Vendor managed inventory model for single-vendor multi-retailer supply chains. European Journal of Operational Research, 204 (3), 473-484.
     [19]      Wang, W-T., Wee, H-M., Jacob Tsao H-S. (2010). Revisiting the note on supply chain integration in vendor-managed inventory.Decision Support Systems, 48 (2), 419-420.
     [20]      Guan, R., Zhao, X. (2010). On contracts for VMI program with continuous review (r, Q) policy. European Journal of Operational Research, 207 (2), 656-667.
     [22]      Goh S-A., Ponnambalam, S. G. (2010). A Particle Swarm Optimization Algorithm for Optimal Operating Parameters of VMI Systems in a Two-Echelon Supply Chain. Swarm, Evolutionary, and Memetic Computing, 6466, 440-447.
     [23]      Pasandideh, S.H.R, Akhavan Niaki, S.T., Roozbeh Nia, A. (2010). An investigation of vendor-managed inventory application in supply chain: the EOQ model with shortage. The International Journal of Advanced Manufacturing Technology, 49 (1-4), 329-339.
     [24]      Pasandideh, S.H.R., Akhavan Niaki, S.T., Roozbeh Nia, A. (2011).A genetic algorithm for vendor managed inventory control system of multi-product multi-constraint economic order quantity model. Expert Systems with Applications, 38 (3), 2708-2716.
     [25]      Goh, S-A., Ponnambalam, S.G., Jawahar, N. (2012).Evolutionary algorithms for optimal operating parameters of vendor managed inventory systems in a two-echelon supply chain. Advances in Engineering Software, 52, 47-54.
     [26]      Sadeghi, J., Mousavi, S.M., Akhavan Niaki, S.T., Sadeghi, S. (2013). Optimizing a multi-vendor multi-retailer vendor managed inventory problem: Two tuned meta-heuristic algorithms. Knowledge-Based Systems, 50, 159-170. 
     [27]      Roozbeh Nia, A., Hemmati Far, M., Akhavan Niaki, S.T. (2014).A fuzzy vendor managed inventory of multi-item economic order quantity model under shortage: An ant colony optimization algorithm. International Journal of Production Economics, 155, 259-271.
     [28]      Diabat A. (2014). Hybrid algorithm for a vendor managed inventory system in a two-echelon supply chain. European Journal of Operational Research, 238 (1), 114-121. 
     [29]      Taleizadeh, A.A., Noori-daryan, M. (2016). Pricing, manufacturing and inventory policies for raw material in a three-level supply chain. International Journal of Systems Science, 47(4), 919-931.
     [30]      Pasandideh, S.H.R., Akhavan Niaki, S.T., Hemmati Far, M. (2014).Optimization of vendor managed inventory of multiproduct EPQ model with multiple constraints using genetic algorithm. The International Journal of Advanced Manufacturing Technology, 71(1-4), 365-376
     [31]      Pasandideh, S.H.R., AkhavanNiaki, S.T., Niknamfar, A.M. (2014). Lexicographic max–min approach for an integrated vendor-managed inventory problem.  Knowledge-Based Systems, 59, 58-65.
     [32]      Seifbarghy, M., Kalani, M.M., Hemmati, M. (2016). A discrete particle swarm optimization algorithm with local search for a production-based two-echelon single-vendor multiple-buyer supply chain. Journal of Industrial Engineering International, 15(2), 221-248.
     [33]      Park, Y.-B., Yoo, J.-S., Park, H.-S. (2016). A genetic algorithm for the vendor-managed inventory routing problem with lost sales. Expert Systems with Applications, 53, 149–159.
     [34]      Han, J., Lu, J., Zhang, G., (2017). Tri-level decision-making for decentralized vendor- managed inventory. Inf. Sci. 421, 85–103.
     [35]      Filho, J.Z., Dias, F., Moura, A. (2018). Application of a vendor managed inventory (VMI) system model in an animal nutrition industry. 11th CIRP Conference on Intelligent Computation in Manufacturing Engineering - CIRP ICME '17. Procedia CIRP 67, 528-533.
     [36]      Sainathan, A., Groenevelt, H. (2019). Vendor managed inventory contracts–coordinating the supply chain while looking from the vendor’s perspective. European. Journal of Operational Research, 272 (1), 249–260.
     [37]      Weraikat, D., Zanjani, M.K., Lehoux, N. (2019). Improving sustainability in a two-level pharmaceutical supply chain through the Vendor-Managed Inventory system. Operations Research for Health Care, 21, 44-55.
     [38]      Golpîra, H. (2020). Optimal integration of the facility location problem into the multi- project multi-supplier multi-resource Construction Supply Chain network design under the vendor managed inventory strategy. Expert Systems with Applications, 139, 112841.
     [39]      Chankong,V., Haimes, Y. (1983). Multi-objective decision making theory and methodology. New York: North-Holland.
     [40]      Hans, A.E. (1988). Multicriteria optimization for highly accurate systems. Multicriteria Optimization in Engineering and Sciences. W. Stadler (Ed.), Mathematical Concepts and Methods in Science and Engineering, 19, 309-352.
     [41]      Disney, S.M., Towill, D.R. (2002). A procedure for optimization of the dynamic response of a vendor managed inventory system. Computers and Industrial Engineering 43, 27–58.
     [42]      Dong, Y., Xu, K. (2002). A supply chain model of vendor managed inventory. Transportation Research Part E: Logistics and Transportation Review 38 (2), 75–95.
     [43]      Silver A.E., Pyke, D.F., Peterson, R. (1998). Inventory Management and Production Planning and Scheduling, John Wiley & Sons.
     [44]      Kennedy, J., Eberhart R.C. (1995). Particle Swarm Optimization in Proceedings of IEEE International Conference on Neural Networks, IV, 1942-1948.
     [45]      Hyun, C. J., Kim, Y. K., Kim, Y. (1998). A genetic algorithm for multiple objective sequencing problems in mixed model assembly lines. Computers and Operations Research, 25, 675-690.
     [46]      Behnamian, J., Zandieh, M., FatemiGhomi, S.M.T. (2009). A multi-phase covering Pareto-optimal front method to multi-objective parallel machine scheduling. International Journal of Production Research, 48(17), 2010.
     [47]      Andersson, J. (2000). A survey of multi-objective optimization in engineering design. In Technical Report LiTH-IKP-R-1097, Department of Mechanical Engineering, Linköping University, Linköping, Sweden.
     [48]      Coello Coello, C.A. (2006). Evolutionary multi-objective optimization: an historical view of the field, Computational Intelligence Magazine, 1, 28–36.
     [49]      Coello Coello, C.A., Van Veldhuizen, D.A., Lamont, G.B. (2002). Evolutionary algorithms for solving multi objective problems, Kluwer Academic Publishers.
     [50]      Srinivas, N., Deb, K. (1994). Multiobjective optimization using non-dominated sorting in genetic algorithms. Evolutionary Computation 2(3): 221-248. MIT Press Journals.