Multi-objective planning for a multi-echelon supply chain using parameter-tuned meta-heuristics

https://doi.org/10.35912/amor.v7i1.2542
Published: Aug 21, 2025

Abstract:

Purpose: This study presents a tri-objective model for the integrated planning of production and distribution within a multi-level supply chain network that encompasses multiple product types and time periods.

Research methodology: The supply chain network includes manufacturer plants (MPs), distribution centers (DCs), retailers, and final customers. The proposed model aims to minimize total supply chain costs, ensure timely delivery of products to customers, and reduce the lost demand rate. Classified as a linear integer programming problem, which is NP-Hard, the model’s complexity is addressed using two multi-objective meta-heuristic approaches based on the Pareto method: the Non-Dominated Sorting Genetic Algorithm (NSGA-II) and the Non-Dominated Ranking Genetic Algorithm (NRGA). The Taguchi method is employed to optimize the input parameters of these algorithms.

Results: The performance of the proposed solution methods is evaluated through various test problems of different dimensions. Statistical analyses confirm the effectiveness and reliability of both algorithms in achieving the defined objectives.

Conclusions: The findings highlight that multi-objective meta-heuristic approaches, when parameter-tuned appropriately, provide efficient and practical solutions for integrated supply chain planning, offering a balance among cost, service level, and demand fulfillment.

Limitations: The study acknowledges the inherent complexity of the problem and the dependency of meta-heuristic outputs on parameter settings, which may influence solution robustness.

Contribution: This research contributes to the literature by providing a robust framework for optimizing production and distribution in complex supply chain networks, delivering insights into the application of advanced algorithmic strategies in operational planning.

Keywords:
1. Multi Objective Procurement-production and Distribution Planning
2. Non-dominated Sorting Genetic Algorithm (NSGA-II)
3. Non-dominated Ranking Genetic Algorithm (NRGA)
4. Taguchi Method
Authors:
1 . Afshar Bazyar
Malek Ashtar University of Technology, Tehran, Iran
2 . Morteza Abbasi
Malek Ashtar University of Technology, Tehran, Iran
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How to Cite
Bazyar, A., & Abbasi, M. (2025). Multi-objective planning for a multi-echelon supply chain using parameter-tuned meta-heuristics. Annals of Management and Organization Research, 7(1), 45–65. https://doi.org/10.35912/amor.v7i1.2542
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Vol. 7 No. 1 (2025): August
Articles
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References

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    Bate, S., & Jones, B. (2008). A review of uniform cross-over designs. Journal of statistical planning and inference, 138(2), 336-351. doi:https://doi.org/10.1016/j.jspi.2007.06.008

    Bhattacharya, S., Govindan, K., Dastidar, S. G., & Sharma, P. (2024). Applications of artificial intelligence in closed-loop supply chains: Systematic literature review and future research agenda. Transportation Research Part E: Logistics and Transportation Review, 184, 103455. doi:https://doi.org/10.1016/j.tre.2024.103455

    Billal, M. M., & Hossain, M. M. (2020). Multi-Objective Optimization for Multi-Product Multi-Period Four Echelon Supply Chain Problems Under Uncertainty. Journal of Optimization in Industrial Engineering, 13(1), 1-17. doi:https://doi.org/10.22094/JOIE.2018.555578.1529

    Biza, A., Montastruc, L., Negny, S., & Admassu, S. (2024). Strategic and tactical planning model for the design of perishable product supply chain network in Ethiopia. Computers & Chemical Engineering, 190, 108814. doi:https://doi.org/10.1016/j.compchemeng.2024.108814

    Bo, V., Bortolini, M., Malaguti, E., Monaci, M., Mora, C., & Paronuzzi, P. (2021). Models and algorithms for integrated production and distribution problems. Computers & Industrial Engineering, 154, 107003. doi:https://doi.org/10.1016/j.cie.2020.107003

    Bouali, H., Abi, S., Benhala, B., & Guerbaoui, M. (2025). Multi-Objective Design Optimization of Planar Spiral Inductors Using Enhanced Metaheuristic Techniques. doi:https://doi.org/10.19139/soic-2310-5070-1873

    Farahani, M. S., Babaei, S., & Esfahani, A. (2024). " Black-Scholes-Artificial Neural Network": A novel option pricing model. International Journal of Financial, Accounting, and Management, 5(4), 475-509. doi:https://doi.org/10.35912/ijfam.v5i4.1684

    Forozandeh, M. (2021). The effect of supply chain management challenges on research and development projects using Fuzzy DEMATEL and TOPSIS approach. Annals of Management and Organization Research, 2(3), 175-190. doi:https://doi.org/10.35912/amor.v2i3.801

    Goodarzian, F., & Hosseini-Nasab, H. (2021). Applying a fuzzy multi-objective model for a production–distribution network design problem by using a novel self-adoptive evolutionary algorithm. International Journal of Systems Science: Operations & Logistics, 8(1), 1-22. doi:https://doi.org/10.1080/23302674.2019.1607621

    Hassanat, A., Almohammadi, K., Alkafaween, E. a., Abunawas, E., Hammouri, A., & Prasath, V. S. (2019). Choosing Mutation and Crossover Ratios for Genetic Algorithms—A Review With a New Dynamic Approach. Information, 10(12), 390. doi:https://doi.org/10.3390/info10120390

    Hong, J., Diabat, A., Panicker, V. V., & Rajagopalan, S. (2018). A Two-Stage Supply Chain Problem With Fixed Costs: An Ant Colony Optimization Approach. International Journal of Production Economics, 204, 214-226. doi:https://doi.org/10.1016/j.ijpe.2018.07.019

    Joel, O. S., Oyewole, A. T., Odunaiya, O. G., & Soyombo, O. T. (2024). Leveraging artificial intelligence for enhanced supply chain optimization: a comprehensive review of current practices and future potentials. International Journal of Management & Entrepreneurship Research, 6(3), 707-721. doi:https://doi.org/10.51594/ijmer.v6i3.882

    Jung, K.-H., & Lee, J.-H. (2024). Determination of an Optimal Parameter Combination for Single PEMFC Using the Taguchi Method and Orthogonal Array. Energies, 17(7), 1690. doi:https://doi.org/10.3390/en17071690

    Kazemi, A., Fazel Zarandi, M., & Moattar Husseini, S. (2009). A multi-agent system to solve the production–distribution planning problem for a supply chain: a genetic algorithm approach. The International Journal of Advanced Manufacturing Technology, 44, 180-193. doi:https://doi.org/10.1007/s00170-008-1826-5

    Khedr, A. M. (2024). Enhancing Supply Chain Management With Deep Learning and Machine Learning Techniques: A Review. Journal of Open Innovation: Technology, Market, and Complexity, 10(4), 100379. doi:https://doi.org/10.1016/j.joitmc.2024.100379

    Koutsokosta, A., & Katsavounis, S. (2024). Stochastic transitions of a mixed-integer linear programming model for the construction supply chain: chance-constrained programming and two-stage programming. Operational Research, 24(3), 46. doi:https://doi.org/10.1007/s12351-024-00856-3

    Lee, Y. H., & Kim, S. H. (2002). Production–distribution planning in supply chain considering capacity constraints. Computers & Industrial Engineering, 43(1-2), 169-190. doi:https://doi.org/10.1016/S0360-8352(02)00063-3

    Liang, T.-F. (2012). Integrated manufacturing/distribution planning decisions with multiple imprecise goals in an uncertain environment. Quality & Quantity, 46(1), 137-153. doi:https://doi.org/10.1007/s11135-010-9333-9

    Liu, J., Sarker, R., Elsayed, S., Essam, D., & Siswanto, N. (2024). Large-scale evolutionary optimization: A review and comparative study. Swarm and Evolutionary Computation, 101466. doi:https://doi.org/10.1016/j.swevo.2023.101466

    Liu, S., & Papageorgiou, L. G. (2013). Multiobjective optimisation of production, distribution and capacity planning of global supply chains in the process industry. Omega, 41(2), 369-382. doi:https://doi.org/10.1016/j.omega.2012.03.007

    Mbamalu, E. I., Chike, N. K., Oguanobi, C. A., & Egbunike, C. F. (2023). Sustainable supply chain management and organisational performance: Perception of academics and practitioners. Annals of Management and Organization Research, 5(1), 13-30. doi:https://doi.org/10.35912/amor.v5i1.1758

    Pasha, H., Kamalabadi, I. N., & Eydi, A. (2021). Integrated Quality?Based Production?Distribution Planning in Two?Echelon Supply Chains. Mathematical Problems in Engineering, 2021(1), 6615634. doi:https://doi.org/10.1155/2021/6615634

    Querin, F., & Göbl, M. (2017). An Analysis on the Impact of Logistics on Customer Service. Journal of Applied Leadership and Management, 5, 90-103.

    Rajabi-Kafshgar, A., Gholian-Jouybari, F., Seyedi, I., & Hajiaghaei-Keshteli, M. (2023). Utilizing hybrid metaheuristic approach to design an agricultural closed-loop supply chain network. Expert Systems with applications, 217, 119504. doi:https://doi.org/10.1016/j.eswa.2023.119504

    Razmi, J., Songhori, M. J., & Khakbaz, M. H. (2009). An integrated fuzzy group decision making/fuzzy linear programming (FGDMLP) framework for supplier evaluation and order allocation. The International Journal of Advanced Manufacturing Technology, 43, 590-607. doi:https://doi.org/10.1007/s00170-008-1719-7

    Schott, J. R. (1995). Fault tolerant design using single and multicriteria genetic algorithm optimization. Massachusetts Institute of Technology.

    Stadler, W. (1988). Multicriteria Optimization in Engineering and in the Sciences (Vol. 37): Springer Science & Business Media.

    Tapia-Ubeda, F. J., Miranda-Gonzalez, P. A., & Gutiérrez-Jarpa, G. (2024). Integrating supplier selection decisions into an inventory location problem for designing the supply chain network. Journal of Combinatorial Optimization, 47(2), 2. doi:https://doi.org/10.1007/s10878-023-01100-y

    Thomas, D. J., & Griffin, P. M. (1996). Coordinated supply chain management. European journal of operational research, 94(1), 1-15. doi:https://doi.org/10.1016/0377-2217(96)00098-7

    Tsai, J.-F., Tan, P.-N., Truong, N.-T., Tran, D.-H., & Lin, M.-H. (2024). Optimizing Supply Chain Design under Demand Uncertainty with Quantity Discount Policy. Mathematics, 12(20), 3228. doi:https://doi.org/10.3390/math12203228

    Vishnu, C., Das, S. P., Sridharan, R., Ram Kumar, P., & Narahari, N. (2021). Development of a reliable and flexible supply chain network design model: a genetic algorithm based approach. International Journal of Production Research, 59(20), 6185-6209. doi:https://doi.org/10.1080/00207543.2020.1808256

    Yeniay, Ö. (2005). Penalty function methods for constrained optimization with genetic algorithms. Mathematical and computational Applications, 10(1), 45-56. doi:https://doi.org/10.3390/mca10010045

    Zahedi, M., Abbasi, M., & Khanachah, S. N. (2020). Providing a lean and agile supply chain model in project-based organizations. Annals of Management and Organization Research, 1(3), 213-233. doi:https://doi.org/10.35912/amor.v1i3.440

    Zhang, Y., & Gu, X. (2024). A biogeography-based optimization algorithm with local search for large-scale heterogeneous distributed scheduling with multiple process plans. Neurocomputing, 595, 127897. doi:https://doi.org/10.1016/j.neucom.2024.127897

    Zhu, W., Liang, T.-C., Yeh, W.-C., Yang, G., Tan, S.-Y., Liu, Z., & Huang, C.-L. (2024). Non-dominated sorting simplified swarm optimization for multi-objective omni-channel of pollution-routing problem. Journal of Computational Design and Engineering, 11(4), 203-233. doi:https://doi.org/10.1093/jcde/qwae062

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  2. Bate, S., & Jones, B. (2008). A review of uniform cross-over designs. Journal of statistical planning and inference, 138(2), 336-351. doi:https://doi.org/10.1016/j.jspi.2007.06.008
  3. Bhattacharya, S., Govindan, K., Dastidar, S. G., & Sharma, P. (2024). Applications of artificial intelligence in closed-loop supply chains: Systematic literature review and future research agenda. Transportation Research Part E: Logistics and Transportation Review, 184, 103455. doi:https://doi.org/10.1016/j.tre.2024.103455
  4. Billal, M. M., & Hossain, M. M. (2020). Multi-Objective Optimization for Multi-Product Multi-Period Four Echelon Supply Chain Problems Under Uncertainty. Journal of Optimization in Industrial Engineering, 13(1), 1-17. doi:https://doi.org/10.22094/JOIE.2018.555578.1529
  5. Biza, A., Montastruc, L., Negny, S., & Admassu, S. (2024). Strategic and tactical planning model for the design of perishable product supply chain network in Ethiopia. Computers & Chemical Engineering, 190, 108814. doi:https://doi.org/10.1016/j.compchemeng.2024.108814
  6. Bo, V., Bortolini, M., Malaguti, E., Monaci, M., Mora, C., & Paronuzzi, P. (2021). Models and algorithms for integrated production and distribution problems. Computers & Industrial Engineering, 154, 107003. doi:https://doi.org/10.1016/j.cie.2020.107003
  7. Bouali, H., Abi, S., Benhala, B., & Guerbaoui, M. (2025). Multi-Objective Design Optimization of Planar Spiral Inductors Using Enhanced Metaheuristic Techniques. doi:https://doi.org/10.19139/soic-2310-5070-1873
  8. Farahani, M. S., Babaei, S., & Esfahani, A. (2024). " Black-Scholes-Artificial Neural Network": A novel option pricing model. International Journal of Financial, Accounting, and Management, 5(4), 475-509. doi:https://doi.org/10.35912/ijfam.v5i4.1684
  9. Forozandeh, M. (2021). The effect of supply chain management challenges on research and development projects using Fuzzy DEMATEL and TOPSIS approach. Annals of Management and Organization Research, 2(3), 175-190. doi:https://doi.org/10.35912/amor.v2i3.801
  10. Goodarzian, F., & Hosseini-Nasab, H. (2021). Applying a fuzzy multi-objective model for a production–distribution network design problem by using a novel self-adoptive evolutionary algorithm. International Journal of Systems Science: Operations & Logistics, 8(1), 1-22. doi:https://doi.org/10.1080/23302674.2019.1607621
  11. Hassanat, A., Almohammadi, K., Alkafaween, E. a., Abunawas, E., Hammouri, A., & Prasath, V. S. (2019). Choosing Mutation and Crossover Ratios for Genetic Algorithms—A Review With a New Dynamic Approach. Information, 10(12), 390. doi:https://doi.org/10.3390/info10120390
  12. Hong, J., Diabat, A., Panicker, V. V., & Rajagopalan, S. (2018). A Two-Stage Supply Chain Problem With Fixed Costs: An Ant Colony Optimization Approach. International Journal of Production Economics, 204, 214-226. doi:https://doi.org/10.1016/j.ijpe.2018.07.019
  13. Joel, O. S., Oyewole, A. T., Odunaiya, O. G., & Soyombo, O. T. (2024). Leveraging artificial intelligence for enhanced supply chain optimization: a comprehensive review of current practices and future potentials. International Journal of Management & Entrepreneurship Research, 6(3), 707-721. doi:https://doi.org/10.51594/ijmer.v6i3.882
  14. Jung, K.-H., & Lee, J.-H. (2024). Determination of an Optimal Parameter Combination for Single PEMFC Using the Taguchi Method and Orthogonal Array. Energies, 17(7), 1690. doi:https://doi.org/10.3390/en17071690
  15. Kazemi, A., Fazel Zarandi, M., & Moattar Husseini, S. (2009). A multi-agent system to solve the production–distribution planning problem for a supply chain: a genetic algorithm approach. The International Journal of Advanced Manufacturing Technology, 44, 180-193. doi:https://doi.org/10.1007/s00170-008-1826-5
  16. Khedr, A. M. (2024). Enhancing Supply Chain Management With Deep Learning and Machine Learning Techniques: A Review. Journal of Open Innovation: Technology, Market, and Complexity, 10(4), 100379. doi:https://doi.org/10.1016/j.joitmc.2024.100379
  17. Koutsokosta, A., & Katsavounis, S. (2024). Stochastic transitions of a mixed-integer linear programming model for the construction supply chain: chance-constrained programming and two-stage programming. Operational Research, 24(3), 46. doi:https://doi.org/10.1007/s12351-024-00856-3
  18. Lee, Y. H., & Kim, S. H. (2002). Production–distribution planning in supply chain considering capacity constraints. Computers & Industrial Engineering, 43(1-2), 169-190. doi:https://doi.org/10.1016/S0360-8352(02)00063-3
  19. Liang, T.-F. (2012). Integrated manufacturing/distribution planning decisions with multiple imprecise goals in an uncertain environment. Quality & Quantity, 46(1), 137-153. doi:https://doi.org/10.1007/s11135-010-9333-9
  20. Liu, J., Sarker, R., Elsayed, S., Essam, D., & Siswanto, N. (2024). Large-scale evolutionary optimization: A review and comparative study. Swarm and Evolutionary Computation, 101466. doi:https://doi.org/10.1016/j.swevo.2023.101466
  21. Liu, S., & Papageorgiou, L. G. (2013). Multiobjective optimisation of production, distribution and capacity planning of global supply chains in the process industry. Omega, 41(2), 369-382. doi:https://doi.org/10.1016/j.omega.2012.03.007
  22. Mbamalu, E. I., Chike, N. K., Oguanobi, C. A., & Egbunike, C. F. (2023). Sustainable supply chain management and organisational performance: Perception of academics and practitioners. Annals of Management and Organization Research, 5(1), 13-30. doi:https://doi.org/10.35912/amor.v5i1.1758
  23. Pasha, H., Kamalabadi, I. N., & Eydi, A. (2021). Integrated Quality?Based Production?Distribution Planning in Two?Echelon Supply Chains. Mathematical Problems in Engineering, 2021(1), 6615634. doi:https://doi.org/10.1155/2021/6615634
  24. Querin, F., & Göbl, M. (2017). An Analysis on the Impact of Logistics on Customer Service. Journal of Applied Leadership and Management, 5, 90-103.
  25. Rajabi-Kafshgar, A., Gholian-Jouybari, F., Seyedi, I., & Hajiaghaei-Keshteli, M. (2023). Utilizing hybrid metaheuristic approach to design an agricultural closed-loop supply chain network. Expert Systems with applications, 217, 119504. doi:https://doi.org/10.1016/j.eswa.2023.119504
  26. Razmi, J., Songhori, M. J., & Khakbaz, M. H. (2009). An integrated fuzzy group decision making/fuzzy linear programming (FGDMLP) framework for supplier evaluation and order allocation. The International Journal of Advanced Manufacturing Technology, 43, 590-607. doi:https://doi.org/10.1007/s00170-008-1719-7
  27. Schott, J. R. (1995). Fault tolerant design using single and multicriteria genetic algorithm optimization. Massachusetts Institute of Technology.
  28. Stadler, W. (1988). Multicriteria Optimization in Engineering and in the Sciences (Vol. 37): Springer Science & Business Media.
  29. Tapia-Ubeda, F. J., Miranda-Gonzalez, P. A., & Gutiérrez-Jarpa, G. (2024). Integrating supplier selection decisions into an inventory location problem for designing the supply chain network. Journal of Combinatorial Optimization, 47(2), 2. doi:https://doi.org/10.1007/s10878-023-01100-y
  30. Thomas, D. J., & Griffin, P. M. (1996). Coordinated supply chain management. European journal of operational research, 94(1), 1-15. doi:https://doi.org/10.1016/0377-2217(96)00098-7
  31. Tsai, J.-F., Tan, P.-N., Truong, N.-T., Tran, D.-H., & Lin, M.-H. (2024). Optimizing Supply Chain Design under Demand Uncertainty with Quantity Discount Policy. Mathematics, 12(20), 3228. doi:https://doi.org/10.3390/math12203228
  32. Vishnu, C., Das, S. P., Sridharan, R., Ram Kumar, P., & Narahari, N. (2021). Development of a reliable and flexible supply chain network design model: a genetic algorithm based approach. International Journal of Production Research, 59(20), 6185-6209. doi:https://doi.org/10.1080/00207543.2020.1808256
  33. Yeniay, Ö. (2005). Penalty function methods for constrained optimization with genetic algorithms. Mathematical and computational Applications, 10(1), 45-56. doi:https://doi.org/10.3390/mca10010045
  34. Zahedi, M., Abbasi, M., & Khanachah, S. N. (2020). Providing a lean and agile supply chain model in project-based organizations. Annals of Management and Organization Research, 1(3), 213-233. doi:https://doi.org/10.35912/amor.v1i3.440
  35. Zhang, Y., & Gu, X. (2024). A biogeography-based optimization algorithm with local search for large-scale heterogeneous distributed scheduling with multiple process plans. Neurocomputing, 595, 127897. doi:https://doi.org/10.1016/j.neucom.2024.127897
  36. Zhu, W., Liang, T.-C., Yeh, W.-C., Yang, G., Tan, S.-Y., Liu, Z., & Huang, C.-L. (2024). Non-dominated sorting simplified swarm optimization for multi-objective omni-channel of pollution-routing problem. Journal of Computational Design and Engineering, 11(4), 203-233. doi:https://doi.org/10.1093/jcde/qwae062