Mathematical Modeling of the Vehicle Routing Problem with Relaxed Time Windows and Delay Penalties
DOI:
10.33395/sinkron.v9i3.14977Keywords:
Vehicle Routing Problem; Relaxed Time Windows; Delay Penalties; Logistics Distribution; Combinatorial OptimizationAbstract
The Vehicle Routing Problem with Relaxed Time Windows (VRP-RTW) is an extension of the classic Vehicle Routing Problem (VRP) that incorporates flexibility in service time windows. In VRP-RTW, vehicles are allowed to arrive later than the specified time window. However, a violation will be imposed for exceeding the specified time limit. in the form of fines or similar penalties. This research aims to design a mathematical model for VRP-RTW to minimize total travel costs and delay penalties, while ensuring that all customers are served within the capacity limits of the available vehicles. This research uses literature review methods and mathematical formulation approaches to describe the logistics distribution problem. The developed model considers several constraints, such as vehicle capacity, route balance, and service time limitations. The results of this research are expected to contribute to more efficient and flexible logistics distribution decision-making and serve as a basis for the development of vehicle route optimization models that can be applied in real-world scenarios.
Downloads
References
Bräysy, O., & Gendreau, M. (2005). Vehicle routing problem with time windows, Part I: Route construction and local search algorithms. Transportation Science, 39(1), 104–118.
Chai, S. W., Kamaluddin, M. R., & Rashid, M. F. F. A. (2022). Optimisation of vehicle routing problem with time windows using Harris Hawks optimiser. Journal of Mechanical Engineering and Sciences, 16(3), 9056–9065. https://doi.org/10.15282/jmes.16.3.2022.08.0717
Golabek, L., Stokłosa, J., Dziwulski, J., & Wyrwisz, J. (2021). Optimization of Logistics and Distribution of the Supply Chain, Taking into Account Transport Costs, Inventory and Customer Demand. European Research Studies Journal, XXIV(Special Issue 1-Part 2), 545–556. https://doi.org/10.35808/ersj/2284
Jazemi, R., Alidadiani, E., Ahn, K., & Jang, J. (2023). A Review of Literature on Vehicle Routing Problems of Last-Mile Delivery in Urban Areas. Applied Sciences, 13(24), 13015. https://doi.org/10.3390/app132413015
Liu, X., Chen, Y.-L., Por, L. Y., & Ku, C. S. (2023). A Systematic Literature Review of Vehicle Routing Problems with Time Windows. Sustainability, 15(15), 12004. https://doi.org/10.3390/su151512004
Mawengkang, H., Syahputra, M. R., Sutarman, S., & Salhi, A. (2024). A Non-Linear Optimization Model for the Multi-Depot Multi-Supplier Vehicle Routing Problem with Relaxed Time Windows. Vehicles, 6(3), 1482–1495. https://doi.org/10.3390/vehicles6030070
Sitompul, C., & Horas, O. M. (2021). A Vehicle Routing Problem with Time Windows Subject to the Constraint of Vehicles and Good’s Dimensions. International Journal of Technology, 12(4), 865. https://doi.org/10.14716/ijtech.v12i4.4294
Toth, P., & Vigo, D. (2002). An Overview of Vehicle Routing Problems. In The Vehicle Routing Problem (pp. 1–26). Society for Industrial and Applied Mathematics. https://doi.org/10.1137/1.9780898718515.ch1
Voigt, S., Frank, M., Fontaine, P., & Kuhn, H. (2023). The Vehicle Routing Problem with Availability Profiles. Transportation Science, 57(2), 531–551. https://doi.org/10.1287/trsc.2022.1182
Downloads
|
How to Cite
Issue
Section
License
Copyright (c) 2025 Rosa Fitrie, Saib Suwilo, Herman Mawengkang
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Muhammad Khoiruddin harahap
Google Scholar 
Moraref
PKP Index
Garuda Kemdikbud
Indonesia OneSearch
OCLC Worldcat
Dimensions
Index Copernicus
Scilit
