A Mathematical Model of Hub Location for War Equipment under Uncertainty Using Meta-Heuristic Algorithms

Document Type : Original Article

Authors

Department of Science and Technology Studies, AJA Command and Staff University, Tehran, Iran

Abstract
By providing timely transportation and dispatch of raw materials and finished goods, freight transport plays an essential role in industries, commercial activities, and trade war industries. It also has a significant impact on the overall performance of associated organizations and the ultimate costs of their products. Therefore, freight transport providers are under pressure to decrease costs and increase their service levels and should overcome these pressures by redesigning and improving their logistics processes on strategic, tactical, and operational levels. In this research, a multi-objective model is proposed for hub location in the field of war equipment under uncertainty. The first objective is to minimize costs, the second objective is to maximize the fulfillment of demands, and the third objective is to minimize congestion on the routes. Taking into account the parameters in the state of uncertainty, the mathematical model is modeled in a robust state and a robust counterpart model of the problem is proposed. In order to solve the problem on a small scale, the exact epsilon constraint method is used in GAMS software. Also, meta-heuristic approaches of grey wolf optimizer (GWO) and non-dominated sorting genetic algorithm (NSGA-II) are used to solve the model in medium and large dimensions. Next, the solution time of two algorithms was compared. 10 numerical experiments with different dimensions were designed and implemented through GWO and NSGAII algorithms. The results showed that the time to solve the GWO problem is less than the other algorithm. Finally, proper performance indicators are used to compare the performance of the used algorithms, and as a result of solving several numerical examples and calculating their performance indicator, it is concluded that the GWO algorithm has a better performance in solving the model.

Keywords


Alumur, S., & Kara, B. Y. (2008). Network hub location problems: The state of the art. European Journal of Operational Research, 190, 1-21.
Alumur, S. A., & Yaman, H., & Kara, B. Y. (2012). Hierarchical multimodal hub location problem with time-definite deliveries. Transportation Research Part E: Logistics and Transportation Review, 48(6), 1107-1120.
Bashiri, M., Rezanezhad, M., Tavakkoli-Moghaddam, T., & Hasanzadeh, H. (2018). Mathematical modeling for a p-mobile hub location problem in a dynamic environment by a genetic algorithm. Applied Mathematical Modelling, 54, 151-169.
Campbell, J. F. (1994a). A survey of network hub locations. Studies in Locational Analysis, 6, 31-49.
Campbell, J. F. (1994b). Integer programming formulation for discrete hub location problems. European Journal of Operational Research, 72, 387-405.
Campbell, J. F., Stiehr, G., Ernst, A. T., & Krishnamoorthy, M. (2003). Solving hub arc location problems on a cluster of workstations. Parallel Computing, 29(5), 555-574.
Chobar, A. P., Adibi, M. A., & Kazemi, A. (2022). Multi-objective hub-spoke network design of perishable tourism products using combination machine learning and meta-heuristic algorithms. Environment, Development and Sustainability, 1-28.
Demir, İ., Kiraz, B., & Ergin, F. C. (2022). Experimental evaluation of meta-heuristics for multi-objective capacitated multiple allocation hub location problem. Engineering Science and Technology, an International Journal, 29, 101032.
Derakhshan, H., Mehrmanesh, H., & Fadavi Asghari, A. (2023). Presenting a multi-objective model to develop depot location through particle swarm optimization algorithm in Artawheel Tire Company. International Journal of Nonlinear Analysis and Applications.
Ghaderi, A., & Rahmaniani, R. (2016). Meta-heuristic solution approaches for robust single allocation p-hub median problem with stochastic demands and travel times. The International Journal of Advanced Manufacturing Technology, 82, 1627-1647.
Golabi, M., Shavarani, S. M., & Izbirak, G. (2017). An edge-based stochastic facility location problem in UAV-supported humanitarian relief logistics: A case study of Tehran earthquake. Natural Hazards, 87(3), 1545-1565.
Hajipour, V., Fattahi, P., Bagheri, H., & Babaei Morad, S. (2022). Dynamic maximal covering location problem for fire stations under uncertainty: Soft-computing approaches. International Journal of System Assurance Engineering and Management, 13(1), 90-112.
Hoseininezhad, F., Makui, A., & Tavakkoli-Moghaddam, R. (2021). Pre-positioning of a relief chain in humanitarian logistics under uncertainty in road accidents: A real-case study. South African Journal of Industrial Engineering, 32(1), 86-104.
Li, C., Han, P., Zhou, M., & Gu, M. (2023). Design of multimodal hub-and-spoke transportation network for emergency relief under COVID-19 pandemic: A meta-heuristic approach. Applied Soft Computing, 133, 109925.
Li, S., Fang, C., & Wu, Y. (2020). Robust hub location problem with flow-based set-up cost. IEEE Access, 8, 66178-66188.
Lindsey, C., Mahmassani, H. S., Mullarkey, M., Nash, T., & Rothberg, S. (2014). Regional logistics hubs, freight activity and industrial space demand: Econometric analysis. Research in Transportation Business & Management, 11, 98-104.
Lopes, M. C., de-Andrade, C. E., de-Queiroz, T. A., Mauricio, G., Resende, C., & Miyazawa, F. K. (2016). Heuristics for a Hub Location-Routing Problem. Special Issue: 2nd Special Issue on Metaheuristics in Network Optimization, 68(1), 54-90.
Mulvey, J. M., Vanderbei, R. J., & Zenios, S. A. (1995). Robust optimization of large-scale systems. Operations Research, 43, 264-281.
Musavi, M. M., & Bozorgi-Amiri, A. (2017). A multi-objective sustainable hub location-scheduling problem for perishable food supply chain. Computers & Industrial Engineering, 113, 766-778.
O'Kelly, M. E. (1987). A quadratic integer program for the location of interacting hub facilities. European Journal of Operational Research, 32, 393-404.
O’Kelly, M. E., & Miller, H. J. (1994). The hub network design problem – a review and synthesis. Journal of Transport Geography, 2, 31-40.
Pourmohammadi, P., Tavakkoli-Moghaddam, R., Rahimi, Y., & Triki, C. (2021). Solving a hub location-routing problem with a queue system under social responsibility by a fuzzy meta-heuristic algorithm. Annals of Operations Research, 1-30.
Rahmati, R., & Bashiri, M. (2018). Robust hub location problem with uncertain inter hub flow discount factor. In Proceedings of the International Conference on Industrial Engineering and Operations Management (pp. 264-281), Paris, France, July 26-27.
Shavarani, S. M., Golabi, M., & Izbirak, G. (2021). A capacitated biobjective location problem with uniformly distributed demands in the UAV‐supported delivery operation. International Transactions in Operational Research, 28(6), 3220-3243.
Soleimani, M., Khalilzadeh, M., Bahari, A., & Heidary, A. (2021). NSGA-II algorithm for hub location-allocation problem considering hub disruption and backup hub allocation. World Journal of Engineering.
Soltanpour, A., Baroughi, F., & Alizadeh, B. (2020). Classical and Inverse Median Location Problems under Uncertain Environment. Acta Mathematicae Applicatae Sinica, English Series, 36(2), 419-438.
Sun, J. Y. (2016). A Hierarchical Bio-inspired Computing for the Hub Location-Routing Problem in Parcel Service. International Journal of Applied Engineering Research, 11, 5357-5362.
Taghipourian, F., Mahdavi, I., Mahdavi-Amiri, N., & Makui, A. (2011). A fuzzy programming approach for dynamic virtual hub location problem. Applied Mathematical Modelling, 36, 3257-3270.
Taguchi, G. (1995). Quality engineering (Taguchi methods) for the development of electronic circuit technology. IEEE Transactions on Reliability, 44(2), 225-229.
Yu, B., Zhu, H., Cai, W., Ma, N., Kuang, Q., & Yao, B. (2013). Two-phase optimization approach to transit hub location – the case of Dalian. Journal of Transport Geography, 33, 62-71.
Yılmaz, O., Yakıcı, E., & Karatas, M. (2019). A UAV location and routing problem with spatio-temporal synchronization constraints solved by ant colony optimization. Journal of Heuristics, 25(4), 673-701.
Zheng, J., Qi, J., Sun, Z., & Li, F. (2018). Community structure based global hub location problem in liner shipping. Transportation Research Part E: Logistics and Transportation Review, 118, 1-19.
Zahiri, B., & Suresh, N. C. (2021). Hub network design for hazardous-materials transportation under uncertainty. Transportation Research Part E: Logistics and Transportation Review, 152, 102424.