This study proposes a mixed-integer multi-objective integrated mathematical model solving facility location and order allocation optimisation problems simultaneously in a two-echelon supply chain network. The proposed problem is motivated by a factoryless concept and by providing a dynamic decision-making solution under a multi-period time horizon. Within the model, we also determine the optimal replenishment number of production facilities by the multi-objective functions. The multi-objective functions include minimisation of the total cost, rejected and late delivery units and, maximisation of the assessment score of the selected suppliers. The studied dynamic decision model is significant for the cost-efficient management of companies’ supply chain networks. The mixed-integer mathematical model is developed by the LP-metric method and it is solved by the GAMS optimisation software. Due to the NP-hard structure of the problem, for large-scale instances, we utilise the Multi-Objective Particle Swarm Optimisation (MOPSO) and Multi-Objective Vibration Damping Optimisation (MOVDO) heuristic solution approaches. Numerical results show that, for large-scale problems, the MOPSO method performs better in Pareto solutions and decreases run times. However, the MOVDO method performs better regarding the Mean Ideal Distance and the Number of Solutions Cover surface criterion. The developed solution approach by this paper is a generic model which can be applied for any two-level network for simultaneous optimisation of supplier selection, location determination of facilities and their replenishment amounts.
This is a preview of subscription content,to check access.
Access this article
Amin-Tahmasbi, H., & Alfi, S. (2018). A fuzzy multi-criteria decision model for integrated suppliers selection and optimal order allocation in the green supply chain. Decision Science Letters, 7, 549–566.
Arabzad, S. M., Ghorbani, M., & Ranjbar, M. J. (2017). Fuzzy goal programming for linear facility location-allocation in a supply chain; the case of steel industry. International Journal of Research in Industrial Engineering, 6, 90–105.
Arabzad, S. M., Ghorbani, M., & Zolfani, S. H. (2015). A multi-objective robust optimization model for a facility location-allocation problem in a supply chain under uncertainty. Journal of Inzinerine Ekonomika-Engineering Economics, 26, 227–238.
Atabaki, M. S., Mohammadi, M., & Naderi, B. (2017). Hybrid genetic algorithm and invasive weed optimization via priority based encoding for location-allocation decisions in a three-stage supply chain. Asia-Pacific Journal of Operational Research, 34, 44.
Behnamian, J., Fatemi Ghomi, S. M. T., & Zandieh, M. (2009). A multi-phase covering Pareto-optimal front method to multi-objective scheduling in a realistic hybrid flowshop using a hybrid metaheuristic. Expert Systems with Applications, 36, 11057–11069.
Biajoli, F. L., Chaves, A. A., & Lorena, L. A. N. (2019). A biased random-key genetic algorithm for the two-stage capacitated facility location problem. Computers & Industrial Engineering, 115, 418–426.
Brahami, M.A., Dahane, M., Souier, M., Sahnoun, M., 2020. Sustainable capacitated facility location/network design problem: a Non-dominated Sorting Genetic Algorithm based multiobjective approach. Annals of Operations Research, 1–32.
Cheraghalipour, A., & Farsad, S. (2018). A bi-objective sustainable supplier selection and order allocation considering quantity discounts under disruption risks: a case study in plastic industry. Computers & Industrial Engineering, 118, 237–250.
Coello Coello, C.A., Lechuga, M.S., 2002. MOPSO: A proposal for multiple objective particle swarm optimization. In Proceedings of the 2002 Congress on Evolutionary Computation (CEC'2002), 02, 1051–1056.
Coello Coello, C. A., Van Veldhuizen, D. A., & Lamont, G. B. (2007). Evolutionary Algorithms for Solving Multi-Objective Problems. New York: Kluwer Academic Publishers.
Correia, I., & Melo, T. (2017). A multi-period facility location problem with modular capacity adjustments and flexible demand fulfillment. Computers & Industrial Engineering, 110, 307–321.
Cortinhal, M. J., Lopes, M. J., & Melo, M. T. (2019). A multi-stage supply chain network design problem with in-house production and partial product outsourcing. Applied Mathematical Modelling, 70, 572–594.
Dai, Z., Aqlan, F., Zheng, X., & Gao, K. (2018). A location-inventory supply chain network model using two heuristic algorithms for perishable products with fuzzy constraints. Computers & Industrial Engineering, 119, 338–352.
Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm:NSGA-II. IEEE Transactions on Evolutionary Computation, 6, 182–197.
Emirhüseyinoğlu, G., & Ekici, A. (2019). Dynamic facility location with supplier selection under quantity discount. Computers & Industrial Engineering, 134, 64–74.
Feng, B., Fan, Z. P., & Li, Y. (2011). A decision method for supplier selection in multi-service outsourcing. International Journal of Production Economics, 132, 240–250.
Hajipour, V., Mehdizadeh, E., & Tavakkoli-Moghaddam, R. (2014). A novel pareto-based multi-objective vibration damping optimization algorithm to solve multi-objective optimization problems. Scientia Iranica, Transaction e: Industrial Engineering, 21, 2368–2378.
Hajipour, V., ZanjiraniFarahani, R., & Fattahi, P. (2016). Bi-objective vibration damping optimization for congested location–pricing problem. Computers & Operations Research, 70, 87–100.
Hamdan, S., & Cheaitou, A. (2017). Supplier selection and order allocation with green criteria: an MCDM and multi-objective optimization approach. Computers & Operations Research, 81, 282–304.
Kang, H. Y., Lee, A. H. I., & Yang, C. Y. (2012). A fuzzy ANP model for supplier selection as applied to IC packaging. Journal of Intelligent Manufacturing, 23, 1477–1488.
Keshavarz Ghorabaee, M., Amiri, M., Zavadskas, E. K., Turskis, Z., & Antucheviciene, J. (2017). A new multi-criteria model based on interval type-2 fuzzy sets and EDAS method for supplier evaluation and order allocation with environmental considerations. Computers & Industrial Engineering, 112, 156–174.
Kilic, H. S. (2013). An integrated approach for supplier selection in multi-item/ multi-supplier environment. Applied Mathematical Modelling, 37, 7752–7763.
Kim, T., Hong, Y., & Lee, J. (2005). Joint economic production allocation and ordering policies in a supply chain consisting of multiple plants and a single retailer. International Journal of Production Research, 43, 3619–3632.
Kubat, C., & Yuce, B. (2012). A hybrid intelligent approach for supply chain management system. Journal of Intelligent Manufacturing, 23, 1237–1244.
Lai, C. H. M., Chiu, C. H. C. H., Liu, W. C. H., & Yeh, W. C. H. (2019). A novel nondominated sorting simplified swarm optimization for multi-stage capacitated facility location problems with multiple quantitative and qualitative objectives. Applied Soft Computing, 84, 105684.
Li, Y., Ding, K., Wang, L., Zheng, W., Peng, Z., & Guo, S. (2018). An optimizing model for solving outsourcing supplier selecting problem based on particle swarm algorithm. Journal of Industrial and Production Engineering, 35, 526–534.
Mehdizadeh, E., Tavakkoli-Moghaddam, R., 2008. Vibration Damping Optimization. Proc. of the Int. Conf. Operations Research - OR and Global Business, Germany, 3–5 September.
Melo, M. T., Nickel, S., & Saldanha-Da-Gama, F. (2009). Facility location and supply chain management – a review. European Journal of Operational Research, 196, 401–412.
Mirzaee, H., Naderi, B., & Pasandideh, S. H. R. (2018). A preemptive fuzzy goal programming model for generalized supplier selection and order allocation with incremental discount. Computers & Industrial Engineering, 122, 292–302.
Mohammed, A. (2020). Towards a sustainable assessment of suppliers: an integrated fuzzy TOPSIS-possibilistic multi-objective approach. Annals of Operations Research, 293, 639–668.
Mohammed, A., Harris, I., & Govindan, K. (2019). A hybrid MCDM-FMOO approach for sustainable supplier selection and order allocation. International Journal of Production Economics, 217, 171–184.
Mousavi, S. M., Alikar, N., Akhavan Niaki, S. T., & Bahreininejad, A. (2015). Optimizing a location allocation-inventory problem in a two-echelon supply chain network: a modified fruit fly optimization algorithm. Computers & Industrial Engineering, 87, 543–560.
Nazemi, J. (2013). Strategies for factory less manufacturing. Journal of Industrial Management, 7, 1–17.
Ranjbar Tezenji, F., Mohammadi, M., Pasandideh, S. H. R., & Nouri Koupaei, M. (2016). An integrated model for supplier location-selection and order allocation under capacity constraints in an uncertain environment. Journal of Sharif University of Technology, 23, 3009–3025.
Rohaninejad, M., Navidi, H., Vahedi Nouri, B., & Kamranrad, R. (2017). A new approach to cooperative competition in facility location problems: mathematical formulations and an approximation algorithm. Computers & Operations Research, 83, 45–53.
Rohaninejad, M., Sahraeian, R., & Tavakkoli-Moghaddam, R. (2018). An accelerated benders decomposition algorithm for reliable facility location problems in multi-echelon networks. Computers & Industrial Engineering, 124, 523–534.
Saidi-Mehrabad, M., Aazami, A., & Goli, A. (2017). A location-allocation model in the multi –level supply chain with multi-objective evolutionary approach. Journal of Industrial and System Engineering, 10, 140–160.
Seifbarghy, M., & Esfandiari, N. (2013). Modeling and solving a multi-objective supplier quota allocation problem considering transaction costs. Journal of Intelligent Manufacturing, 24, 201–209.
Seyed Haeri, S. A., & Rezaei, J. (2019). A grey-based green supplier selection model for uncertain environments. Journal of Cleaner Production, 221, 768–784.
Weng, Z. K. (1999). The power of coordination decisions for short life cycles products in a manufacturing and distribution supply chain. IIE Transactions, 31, 1037–1049.
Yu, V. F., Normasari, N. M. E., & Luong, H. T. (2015). Integrated location-production-distribution planning in a multiproducts supply chain network design model. Mathematical Problems in Engineering, 13, 13.
Zitzler, E., 1999. Evolutionary algorithms for multi-objective optimization: method and applications. Ph.D. Thesis, dissertation ETH NO. 13398, Swaziland Federal Institute of Technology Zorik
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Amin-Tahmasbi, H., Sadafi, S., Ekren, B.Y. et al. A multi-objective integrated optimisation model for facility location and order allocation problem in a two-level supply chain network. Ann Oper Res 324, 993–1022 (2023). https://doi.org/10.1007/s10479-022-04635-1