Modern Research in Decision Making

Multi-objective honey-badger metaheuristic and genetic algorithms for solving a robust mathematical model of a sustainable supply chain

Document Type : Original Article

Authors

Massoumeh Nazari 1
Mahmoud Dehghan Nayeri 2

1 Phd. Candidate, Department of Industrial Management, faculty of Management, Islamic Azad University, South Tehran branch, Iran.

2 Assocciate professor, Department of Industrial Management, faculty of Management and Economics, Tarbiat Modares University, Tehran, Iran.

Abstract
With increasing market uncertainty and the growing complexity of competitive environments, supply chains have become more vulnerable to disruptions. Even minor fluctuations in demand or reductions in capacity can generate widespread negative impacts on overall supply chain performance. As a result, developing mathematical models that capture this complexity has become more challenging and requires appropriate solution methodologies. This study proposes an effective solution approach for the robust, scenario-based multi-objective mathematical model developed by Nazari et al. (2024), which seeks to reduce total system costs and environmental emissions. A key innovation of the model is the simultaneous consideration of demand uncertainty—driven by inflation rates—and capacity reductions caused by disruptions. Because exact solution methods become impractical for large-scale, multi-objective problems, two powerful metaheuristic algorithms were employed: a multi-objective extension of the emerging Honey Badger Algorithm (HBA) and the well-known Non-dominated Sorting Genetic Algorithm II (NSGA-II). To evaluate the performance of the proposed model and algorithms, a numerical case study was designed and executed. The results indicate that the proposed model is highly effective in handling uncertainty and supports more optimal decision-making aligned with economic, social, and environmental sustainability. Furthermore, the computational results demonstrate that the HBA algorithm achieves higher efficiency and accuracy in solving hard (NP-hard) problems with large, complex search spaces.

Keywords

Sustainable Supply Chain
Multi-Objective Optimization
Uncertainty
Metaheuristic Algorithm
Subjects
[1] Amini, A., Alinezhad, A., & Gharakhani, D. (2023). A New Rough BWM Approach for Evaluating and Selecting a Sustainable Supplier in Supply Chain Management.  Journal of Industrial Management Perspective, 13(3), 9-38.‏ [In Persian]
[2] Farrokh, M. (2023). Designing a Sustainable Closed-Loop Supply Chain Considering Carbon Tax and Technology Selection in the Battery Industry. Journal of Industrial Management Perspective, 13(4), 46-84.‏ [In Persian]
Seifbarghy, M. (2022). A Multi-Objective Sustainable Closed Loop Supply Chain Model Considering Suppliers Evaluation and using SWARA-WASPAS Method. Journal of Industrial Management Perspective, 12(3), 88-63. [In Persian]
[4] Azar, A., Ardakani, D. A., & Keshavarz, P. (2017). The principles of sustainable supply chain management.‏ [In Persian]. 
[5] Azar, A., & Farrokh, M. (2018). Mathematical programming under uncertainty: stochastic, fuzzy and robust approaches. Tehran: research institute for humanities research and development.‏ [In Persian].
[6] Nazari, M., Dehghan Nayeri, M., & Fathi Hafshjani, K. (2025). Prediction of Uncertain Parameters of a Sustainable Supply Chain Using an Artificial Intelligence Approach. Operations Research Forum, 6(1), 25-1.‏ DOI:10.1007/s43069-024-00408-7
[7] Wang, W., Zhang, Y., Zhang, W., Gao, G., & Zhang, H. (2021). Incentive mechanisms in a green supply chain under demand uncertainty. Journal of cleaner production, 279, 123636.‏ DOI:10.1016/j.jclepro.2020.123636
[8] Nazari, M., Dehghan Nayeri, M., Fathi Hafshejani, K. (2024). Presenting a Bi-objective mathematical model of a sustainable supply chain based on uncertainty parameters (capacity reduction due to disruption, shipping, and demand costs). Organizational Resources Management Researches, 14(2), pp. 145-176. [In Persian]
[9] Fattahi, M. (2020). A data-driven approach for supply chain network design under uncertainty with consideration of social concerns. Annals of Operations research, 288(1), 265-284.‏ DOI:10.1007/s110479-020-03532-9
[10] Li, J., & Liu, P. (2022). Modeling green supply chain games with governmental interventions and risk preferences under fuzzy uncertainties. Mathematics and Computers in Simulation, 192, 182-200.‏ DOI:10.1016/j.matcom.2021.08.020
[11] Shen, J. (2020). An environmental supply chain network under uncertainty. Physica A: Statistical Mechanics and its Applications, 542, 123478.‏ DOI:10.1016/j.physa.2019.123478
[12] Vali-Siar, M. M., & Roghanian, E. (2022). Sustainable, resilient and responsive mixed supply chain network design under hybrid uncertainty with considering COVID-19 pandemic disruption. Sustainable production and consumption, 30, 278-300.‏ DOI:10.1016/j.spc.2021.12.003
[13] Mohaghar, Ali, & Abbasi, Hamid. (2019). Designing and Explaining the Sustainability Model for Banking Supply Chain (A Case Study of Mellat Bank). Management Research in Iran (Modares Human Sciences), 23(3), 74-55. [In Persian]
[14] Izadyar, M., Toloie Eshlaghy, A., Mehri, Z. (2021). Application of system dynamics in assessing sustainability performance of LARG supply chain in the automotive industry. Management Research in Iran (Modares Human Sciences), 25(1), 24-1. [In Persian]
[15] Hashemzahi, P., Mohammadi, M. and Atabaki, M. S. (2024). Social Considerations in Designing Closed-Loop Sustainable Supply Chain: A Many-Objective Evolutionary Algorithm Approach for Deep Decarbonization. Modern Research in Decision Making, 9(2), 61-29. [In Persian]
[16] Fathiheliabadi, A., raad, A., Motameni, A. and Talebi, D. (2023). Presenting a mathematical model for supply chain network design considering trade credit under uncertainty. Modern Research in Decision Making, 8(2), 121-98. [In Persian]
[17] Sherafati, M. and Najafi Ghobadi, S. (2022). Provide a novel model for designing a sustainable supply chain network considering development and multi-level environmental decisions. Modern Research in Decision Making, 7(4), 124-104. [In Persian]
[18] Dreger, C. (2023). The impact of demand and supply shocks on inflation. Evidence for the US and the Euro area.‏
 [19] Kausar, A., Hasan, A., Maheshwari, S., Gautam, P., & Jaggi, C. K. (2024). Sustainable production model with advertisement and market price dependent demand under salvage option for defectives. Opsearch, 61(1), 333-315.‏ DOI:10.1007/s12597-023-00688-3
[20] Foroozesh, N., Karimi, B., & Mousavi, S. M. (2022). Green-resilient supply chain network design for perishable products considering route risk and horizontal collaboration under robust interval-valued type-2 fuzzy uncertainty: A case study in food industry. Journal of environmental management, 307, 114470.‏ DOI:10.1016/j.jenvman.2022.114470
[21] Jabbarzadeh, A., Fahimnia, B., Sabouhi, F. (2018). Resilient and sustainable supply chain design: sustainability analysis under disruption risks. International Journal of Production Research, 56(17), 5945-5968.‏ DOI:10.1080/00207543.2018.1461950
[22] Afshar, M., Molana, H., & Parchicolaie, B. R. (2024). A multi objective optimization model for multi-commodity closed-loop supply chain network considering disruption risk. International Journal of Engineering, 37(4), 646-661.‏ DOI:10.5829/IJE.2024.37.04A.07
 [23] Khalili-Fard, A., Parsaee, S., Bakhshi, A., Yazdani, M., Aghsami, A., & Rabbani, M. (2024). Multi-objective optimization of closed-loop supply chains to achieve sustainable development goals in uncertain environments. Engineering Applications of Artificial Intelligence, 133, 108052.‏ DOI:10.1016/j.engappai.2024.108052
[24] Arab Momeni, M., Jain, V., & Bagheri, M. (2024). A multi-objective model for designing a sustainable closed-loop supply chain logistics network. Logistics, 8(1), 29.‏ DOI:10.3390/logistics8010029
 [25] Hashim, F. A., Houssein, E. H., Hussain, K., Mabrouk, M. S., & Al-Atabany, W. (2022). Honey Badger Algorithm: New metaheuristic algorithm for solving optimization problems. Mathematics and Computers in Simulation, 192, 84-110.‏ DOI:10.1016/j.matcom.2021.08.013
Modern Research in Decision Making
Volume 11, Issue 1
Spring 2026
Pages 1-24

Home

Guide for Authors

Submit Manuscript

Reviewers

Contact Us