Journal of Industrial Engineering Research in Production Systems

Journal of Industrial Engineering Research in Production Systems

Presentation of an Optimal Fleet Sizing Model in a Multimodal Automotive Distribution System under Uncertainty

Document Type : Research Paper

Authors
Ramin Nazarinia 1
Ali Husseinzadeh Kashan 2
1 Department of Economic and Social Systems, Faculty of Industrial Engineering and Systems, Tarbiat Modares University, Tehran, Iran
2 Department of Industrial Engineering, Faculty of Industrial and System Engineering, Tarbiat Modares University, Iran
10.22084/ier.2026.32029.2221
Abstract
Given the increasing role of transportation in modern societies, an efficient transportation fleet has become a critical factor in enhancing the performance of distribution systems. Effective fleet management directly impacts costs, transit times, reliability, flexibility, safety, and the environment. Consequently, optimal fleet sizing in organizations that heavily depend on transportation is essential for cost control and reduction. This study proposes a model for optimal fleet sizing in a multi-modal automotive distribution system, considering uncertainties in demand and travel time. The problem is formulated with the objective of minimizing total costs, including purchasing, hiring, operating, and maintenance expenses, and is developed under real-world constraints and conditions. The model considers not only the purchase of trailers and car carriers but also the possibility of entering into short-term and long-term hire agreements. Results for the studied company indicate that the maximum purchase budget is used to provide owned fleets. Moreover, implementing the proposed model could reduce the company’s total purchasing, hiring, operating, and maintenance costs by approximately 21.34% compared to current practices.
Keywords
Optimization
Stochastic Programming
Fleet Sizing
Transportation
Automotive Distribution
Subjects
[1]    Redmer, A. (2015). Strategic vehicle fleet management-the composition problem. LogForum. 2015; 11 (1): 119-26. ISSN 1895-2038. DOI 10.17270. J. LOG, 11.‏
[2]    Redmer, A. (2022). Strategic vehicle fleet management–a joint solution of make-or-buy, composition and replacement problems. Journal of Quality in Maintenance Engineering, 28(2), 327-349.‏
[3]    Redmer, A. (2016). Strategic vehicle fleet management-the replacement problem. LogForum, 12(1).‏
[4]    Hoff, A., Andersson, H., Christiansen, M., Hasle, G., & Løkketangen, A. (2010). Industrial aspects and literature survey: Fleet composition and routing. Computers & Operations Research, 37(12), 2041-2061.‏
[5]    Brealey, R. A., Myers, S. C., Allen, F., & Edmans, A. (2025). Principles of corporate finance (99th ed.). McGraw Hill.
[6]    Chaowasakoo, P., Seppälä, H., & Koivo, H. (2018). Age-based maintenance for a fleet of haul trucks. Journal of Quality in Maintenance Engineering, 24(4),511-528. https://doi.org/https://doi.org/10.1108/JQME-03-2017-0016.
[7]    Stojanović, Đ., Nikoličić, S., & Miličić, M. (2011). Transport fleet sizing by using make and buy decision-making. Economic Annals, 56(190), 77-102.‏
[8]    مسیحی, الیپس, & مفاخری. (2015). مدلسازی و حل مسئله تعیین تعداد واگن های باری با در نظر گرفتن اهداف چندگانه و ناوگان ریلی ناهمگون توسط الگوریتم های فراابتکاری. فصلنامه مهندسی حمل و نقل, 6(4), 685-702.
[9]    فرازمند, مینو, پیشوایی, & میر سامان. (2018). مدل طراحی شبکه حمل‌ونقل ترکیبی تحت شرایط عدم قطعیت (موردمطالعه: حمل‌ونقل سیمان در کشور ایران). چشم‌انداز مدیریت صنعتی, 8(3), 115-139.
[10] G. B. Dantzig & D. R. Fulkerson, 1954. "Minimizing the number of tankers to meet a fixed schedule," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 1(3), pages 217-222, September.
[11] Sayarshad, H. R., Javadian, N., Tavakkoli-Moghaddam, R., & Forghani, N. (2010). Solving multi-objective optimization formulation for fleet planning in a railway industry. Annals of Operations Research, 181, 185-197.‏
[12] Sayarshad, H. R., & Tavakkoli-Moghaddam, R. (2010). Solving a multi periodic stochastic model of the rail–car fleet sizing by two-stage optimization formulation. Applied Mathematical Modelling, 34(5), 1164-1174.‏
[13] Loxton, R., Lin, Q., & Teo, K. L. (2012). A stochastic fleet composition problem. Computers & Operations Research, 39(12), 3177-3184.‏
[14] Yaghini, M., & Khandaghabadi, Z. (2013). A hybrid metaheuristic algorithm for dynamic rail car fleet sizing problem. Applied Mathematical Modelling, 37(6), 4127-4138.‏
[15] Klosterhalfen, S. T., Kallrath, J., & Fischer, G. (2014). Rail car fleet design: Optimization of structure and size. International Journal of Production Economics, 157, 112-119.‏
[16] Milenković, M. S., Bojović, N. J., Švadlenka, L., & Melichar, V. (2015). A stochastic model predictive control to heterogeneous rail freight car fleet sizing problem. Transportation Research Part E: Logistics and Transportation Review, 82, 162-198.‏
[17] Lei, C., Lin, W. H., & Miao, L. (2016). A two-stage robust optimization approach for the mobile facility fleet sizing and routing problem under uncertainty. Computers & Operations Research, 67, 75-89.‏
[18] Hu, L., Zhu, J. X., Wang, Y., & Lee, L. H. (2018). Joint design of fleet size, hub locations, and hub capacities for third-party logistics networks with road congestion constraints. Transportation Research Part E: Logistics and Transportation Review, 118, 568-588.‏
[19] Mohtasham, M., Mirzaei-Nasirabad, H., Askari-Nasab, H., & Alizadeh, B. (2021). Truck fleet size selection in open-pit mines based on the match factor using a MINLP model. Mining Technology, 130(3), 159-175.‏
[20] Manguino, J. L., & Ronconi, D. P. (2022). Step cost functions in a fleet size and mix vehicle routing problem with time windows. Annals of Operations Research, 1-26.‏
[21] Theuws, L. (2023). Determining optimal fleet composition under uncertainty (Doctoral dissertation, Tilburg University).‏
[22] Karmanesh, Y., Bagheri, M., Hasany, R. M., & Pishvaee, M. S. (2024). Two-stage stochastic programming approach for fleet sizing and allocating rail wagon under uncertain demand. Computers & Industrial Engineering, 188, 109878.‏
[23] Eberhardt, K., Diehlmann, F., Lüttenberg, M., Kaiser, F. K., & Schultmann, F. (2025). A combined fleet size and mix vehicle routing model for last-mile distribution in disaster relief. Progress in Disaster Science, 26, 100411. https://doi.org/https://doi.org/10.1016/j.pdisas.2025.100411.
[24] Breyer, N., Lidén, T., Tadaros, M., & Yu, L. (2026). A computational framework for dimensioning a railway freight transportation plan. Journal of Rail Transport Planning & Management, 38, 100585. https://doi.org/https://doi.org/10.1016/j.jrtpm.2026.100585.
[25] Ng, M., Mahmassani, H., Tong, D., Verbas, O., & Cokyasar, T. (2026). Joint Optimization of Multimodal Transit Frequency and Shared Autonomous Vehicle Fleet Size with Hybrid Metaheuristic and Nonlinear Programming. https://doi.org/10.48550/arXiv.2412.19401.
[26] Asghari, M., Fathollahi-Fard, A. M., Mirzapour Al-E-Hashem, S. M. J., & Dulebenets, M. A. (2022). Transformation and linearization techniques in optimization: A state-of-the-art survey. Mathematics, 10(2), 283.‏
[27] Birge, J. R. and François Louveaux (2006) Introduction to stochastic programming, Second Edition, Analysis.
Journal of Industrial Engineering Research in Production Systems
Volume 13, Issue 27
September 2026
Pages 117-135