Designing a Fuzzy Mathematical Model for a Two-Echelon Allocation-Routing Problem by Applying Route Conditions: A New Interactive Fuzzy Approach
DOI:
https://doi.org/10.31181/dmame7220241029Keywords:
Two-echelon allocation-routing model, Reliability, Multi-objective optimization, Interactive fuzzy approachAbstract
In vehicle routing problems (VRP), the optimal allocation of transportation by considering factors such as route hardness, driver experience and vehicle worn-out has a significant effect on costs reduction and approaching real-world conditions. In this paper, a novel fuzzy mixed integer non-linear mathematical model to address the two-echelon allocation-routing problem under uncertainty is proposed by applying route and fleet conditions. The cost of allocating drivers to diverse vehicles is computed at the first echelon of the problem, considering factors such as vehicle type, vehicle wear-out, and driver experience. Additionally, different routes are defused with varying levels of hardness. The goal of the second echelon of the model is to improve reliability by defining the reliability of routes within each section. To solve the model, the Torabi and Hessini (TH), the Selimi and Ozkarahan (SO) methods, and a newly proposed approach (PIA) were utilized to transform the multi-objective model into a single-objective one. Numerical tests and performance indicators were used to validate the effectiveness of both the multi-objective mathematical model and the proposed solution method. The validation computation results indicate that the proposed solution approach outperforms both the TH and SO approaches.
Downloads
References
Farahbakhsh, A., & Kheirkhah, A. S. (2023). A new efficient genetic Algorithm-Taguchi-based approach for multi- period inventory routing problem. International journal of research in industrial engineering, 12(4), 397-413. https://doi.org/10.22105/riej.2023.403685.1387
do C. Martins, L., Hirsch, P., & Juan, A. A. (2021). Agile optimization of a two‐echelon vehicle routing problem with pickup and delivery. International Transactions in Operational Research, 28(1), 201-221. https://doi.org/10.1111/itor.12796
Movafaghpour, M. A. (2023). Developing an efficient algorithm for robust school bus routing with heterogeneous fleet. Journal of Decisions and Operations Research, 8(3), 566-577. http://dorl.net/dor/20.1001.1.25385097.1402.8.3.1.7
Yu, X., Zhou, Y., & Liu, X. F. (2020). The two-echelon multi-objective location routing problem inspired by realistic waste collection applications: The composable model and a metaheuristic algorithm. Applied Soft Computing, 94, 106477. https://doi.org/10.1016/j.asoc.2020.106477
Cheng, C., Zhu, R., Costa, A. M., Thompson, R. G., & Huang, X. (2022). Multi-period two-echelon location routing problem for disaster waste clean-up. Transportmetrica A: Transport Science, 18(3), 1053-1083. https://doi.org/10.1080/23249935.2021.1916644
Chaube, S., Singh, S. B., Pant, S., & Kumar, A. (2018). Time-dependent conflicting bifuzzy set and its applications in reliability evaluation. Advanced Mathematical Techniques in Engineering Sciences, 4, 111-28. https://doi.org/10.1201/b22440-6
Lagzaie, L., & Hamzehee, A. (2022). Providing a Multiproduct and Multiperiodic Model for Closed-Loop Green Supply Chain under Conditions of Uncertainty Based on a Fuzzy Approach for Solving Problem of Business Market. Complexity, 2022. https://doi.org/10.1155/2022/2780073
Wang, Y., Sun, Y., Guan, X., Fan, J., Xu, M., & Wang, H. (2021). Two-echelon multi-period location routing problem with shared transportation resource. Knowledge-Based Systems, 226, 107168. https://doi.org/10.1016/j.knosys.2021.107168
Bahmani, V., Adibi, M. A., & Mehdizadeh, E. (2023). Integration of Two-Stage Assembly Flow Shop Scheduling and Vehicle Routing Using Improved Whale Optimization Algorithm. Journal of applied research on industrial engineering, 10(1). https://doi.org/10.22105/jarie.2022.329251.1450
Gandra, V. M. S., Çalık, H., Wauters, T., Toffolo, T. A., Carvalho, M. A. M., & Berghe, G. V. (2021). The impact of loading restrictions on the two-echelon location routing problem. Computers & Industrial Engineering, 160, 107609. https://doi.org/10.1016/j.cie.2021.107609
Fallahtafti, A., Ardjmand, E., Young Ii, W. A., & Weckman, G. R. (2021). A multi-objective two-echelon location-routing problem for cash logistics: A metaheuristic approach. Applied Soft Computing, 111, 107685. https://doi.org/10.1016/j.asoc.2021.107685
Cao, J. X., Wang, X., & Gao, J. (2021). A two-echelon location-routing problem for biomass logistics systems. Biosystems Engineering, 202, 106-118. https://doi.org/10.1016/j.biosystemseng.2020.12.007
Hajghani, M., Forghani, M. A., Heidari, A., Khalilzadeh, M., & Kebriyaii, O. (2023). A two-echelon location routing problem considering sustainability and hybrid open and closed routes under uncertainty. Heliyon, 9(3). https://doi.org/10.1016/j.heliyon.2023.e14258
Khodashenas, M., Kazemipoor, H., Najafi, S. E., & Movahedi Sobhani, F. (2022). A two-stage uncertain model to arrange and locate vehicle routing with simultaneous pickup and delivery. International journal of research in industrial engineering, 11(3), 273-305. https://doi.org/10.22105/jarie.2023.368851.1510
Mohamed, I. B., Klibi, W., Sadykov, R., Şen, H., & Vanderbeck, F. (2023). The two-echelon stochastic multi-period capacitated location-routing problem. European Journal of Operational Research, 306(2), 645-667. https://doi.org/10.1016/j.ejor.2022.07.022
Xue, G., Wang, Y., Guan, X., & Wang, Z. (2022). A combined GA-TS algorithm for two-echelon dynamic vehicle routing with proactive satellite stations. Computers & Industrial Engineering, 164, 107899. https://doi.org/10.1016/j.cie.2021.107899
Du, J., Wang, X., Wu, X., Zhou, F., & Zhou, L. (2023). Multi-objective optimization for two-echelon joint delivery location routing problem considering carbon emission under online shopping. Transportation Letters, 15(8), 907-925. https://doi.org/10.1080/19427867.2022.2112857
Heidari, A., Imani, D. M., Khalilzadeh, M., & Sarbazvatan, M. (2023). Green two-echelon closed and open location-routing problem: application of NSGA-II and MOGWO metaheuristic approaches. Environment, Development and Sustainability, 25(9), 9163-9199. https://doi.org/10.1007/s10668-022-02429-w
Neira, D. A., Aguayo, M. M., De la Fuente, R., & Klapp, M. A. (2020). New compact integer programming formulations for the multi-trip vehicle routing problem with time windows. Computers & Industrial Engineering, 144, 106399. https://doi.org/10.1016/j.cie.2020.106399
Kumar, A., Vohra, M., Pant, S., & Singh, S. K. (2021). Optimization techniques for petroleum engineering: A brief review. International Journal of Modelling and Simulation, 41(5), 326-334. https://doi.org/10.1080/02286203.2021.1983074
Kumar, A., Pant, S., Ram, M., & Yadav, O. (Eds.). (2022). Meta-heuristic optimization techniques: applications in engineering (Vol. 10). Walter de Gruyter GmbH & Co KG. https://doi.org/10.1515/9783110716214
Uniyal, N., Pant, S., Kumar, A., & Pant, P. (2022). Nature-inspired metaheuristic algorithms for optimization. Meta-heuristic Optimization Techniques, 1-10. https://doi.org/10.1515/9783110716214-001
Kumar, A., Negi, G., Pant, S., Ram, M., & Dimri, S. C. (2021). Availability-cost optimization of butter oil processing system by using nature inspired optimization algorithms. Reliability: Theory & Applications, 16(SI 2 (64)), 188-200. https://doi.org/10.24412/1932-2321-2021-264-188-200
Kumar, A., Pant, S., Singh, M. K., Chaube, S., Ram, M., & Kumar, A. (2023). Modified Wild Horse Optimizer for Constrained System Reliability Optimization. Axioms, 12(7), 693. https://doi.org/10.3390/axioms12070693
Huang, N., Li, J., Zhu, W., & Qin, H. (2021). The multi-trip vehicle routing problem with time windows and unloading queue at depot. Transportation Research Part E: Logistics and Transportation Review, 152, 102370. https://doi.org/10.1016/j.tre.2021.102370
Rezaei Kallaj, M., Abolghasemian, M., Moradi Pirbalouti, S., Sabk Ara, M., & Pourghader Chobar, A. (2021). Vehicle routing problem in relief supply under a crisis condition considering blood types. Mathematical Problems in Engineering, 2021, 1-10. https://doi.org/10.1155/2021/7217182
Shiri, M., Ahmadizar, F., Thiruvady, D., & Farvaresh, H. (2023). A sustainable and efficient home health care network design model under uncertainty. Expert Systems with Applications, 211, 118185. https://doi.org/10.1016/j.eswa.2022.118185
Wang, Y., Zhe, J., Wang, X., Sun, Y., & Wang, H. (2022). Collaborative multidepot vehicle routing problem with dynamic customer demands and time windows. Sustainability, 14(11), 6709. https://doi.org/10.3390/su14116709
Hasanpour Jesri, Z. S., Eshghi, K., Rafiee, M., & Van Woensel, T. (2022). The Multi-Depot Traveling Purchaser Problem with Shared Resources. Sustainability, 14(16), 10190. https://doi.org/10.3390/su141610190
Nozari, H., Tavakkoli-Moghaddam, R., & Gharemani-Nahr, J. (2022). A neutrosophic fuzzy programming method to solve a multi-depot vehicle routing model under uncertainty during the covid-19 pandemic. International Journal of Engineering, 35(2), 360-371. https://doi.org/10.5829/IJE.2022.35.02B.12
Jiao, L., Peng, Z., Xi, L., Guo, M., Ding, S., & Wei, Y. (2023). A multi-stage heuristic algorithm based on task grouping for vehicle routing problem with energy constraint in disasters. Expert Systems with Applications, 212, 118740. https://doi.org/10.1016/j.eswa.2022.118740
Pirabán-Ramírez, A., Guerrero-Rueda, W. J., & Labadie, N. (2022). The multi-trip vehicle routing problem with increasing profits for the blood transportation: An iterated local search metaheuristic. Computers & Industrial Engineering, 170, 108294. https://doi.org/10.1016/j.cie.2022.108294
Navazi, F., Tavakkoli-Moghaddam, R., Sazvar, Z., & Memari, P. (2019). Sustainable design for a bi-level transportation-location-vehicle routing scheduling problem in a perishable product supply chain. In Service Orientation in Holonic and Multi-Agent Manufacturing: Proceedings of SOHOMA 2018 (pp. 308-321). Springer International Publishing. https://doi.org/10.1007/978-3-030-03003-2_24
Asefi, A. H., Bozorgi-Amiri, A., & Ghezavati, V. (2020). Location-Routing Problem in Humanitarian Relief Chain Considering the Reliability of Road Network. Emergency Management, 9(1), 29-41. https://dorl.net/dor/20.1001.1.23453915.1399.9.1.3.6
Norouzi, N., Tavakkoli-Moghaddam, R., Ghazanfari, M., Alinaghian, M., & Salamatbakhsh, A. (2012). A new multi-objective competitive open vehicle routing problem solved by particle swarm optimization. Networks and Spatial Economics, 12, 609-633. https://doi.org/10.1007/s11067-011-9169-4
Al-Qudaimi, A., Kaur, K., & Bhat, S. (2021). Triangular fuzzy numbers multiplication: QKB method. Fuzzy Optimization and Modeling Journal, 2(2), 34-40. https://doi.org/ 10.30495/fomj.2021.1934118.1032
Liang, T. F. (2006). Distribution planning decisions using interactive fuzzy multi-objective linear programming. Fuzzy Sets and Systems, 157(10), 1303-1316. https://doi.org/10.1016/j.fss.2006.01.014
Wang, R. C., & Liang, T. F. (2005). Applying possibilistic linear programming to aggregate production planning. International journal of production economics, 98(3), 328-341. https://doi.org/10.1016/j.ijpe.2004.09.011
Zimmermann, H. J. (1978). Fuzzy programming and linear programming with several objective functions. Fuzzy sets and systems, 1(1), 45-55. https://doi.org/10.1016/0165-0114(78)90031-3
Lai, Y. J., & Hwang, C. L. (1992). A new approach to some possibilistic linear programming problems. Fuzzy sets and systems, 49(2), 121-133. https://doi.org/10.1016/0165-0114(92)90318-X
Selim, H., & Ozkarahan, I. (2008). A supply chain distribution network design model: an interactive fuzzy goal programming-based solution approach. The International Journal of Advanced Manufacturing Technology, 36, 401-418. https://doi.org/10.1007/s00170-006-0842-6
Torabi, S. A., & Hassini, E. (2008). An interactive possibilistic programming approach for multiple objective supply chain master planning. Fuzzy sets and systems, 159(2), 193-214. https://doi.org/10.1016/j.fss.2007.08.010
Werners, B. M. (1988). Aggregation models in mathematical programming. In Mathematical models for decision support (pp. 295-305). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-83555-1_19
Diaz-Madronero, M., Peidro, D., & Mula, J. (2014). A fuzzy optimization approach for procurement transport operational planning in an automobile supply chain. Applied Mathematical Modelling, 38(23), 5705-5725. https://doi.org/10.1016/j.apm.2014.04.053
Lai, Y. J., Hwang, C. L., Lai, Y. J., & Hwang, C. L. (1994). Fuzzy multiple objective decision making (pp. 139-262). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-57949-3_3
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Decision Making: Applications in Management and Engineering
This work is licensed under a Creative Commons Attribution 4.0 International License.
