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Planning approximations to the average length of vehicle routing problems with time window constraints

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  • Figliozzi, Miguel Andres

Abstract

This paper studies approximations to the average length of vehicle routing problems (VRP) with time window, route duration, and capacity constraints. The approximations are valuable for the strategic and planning analysis of transportation and logistics problems. Using asymptotic properties of vehicle routing problems and the average probability of successfully sequencing a customer with time windows a new expression to estimate VRP distances is developed. The increase in the number of routes when time constraints are added is modeled probabilistically. This paper introduces the concept of the average probability of successfully sequencing a customer with time windows. It is proven that this average probability is a unique characteristic of a vehicle routing problem. The approximation proposed is tested in instances with different customer spatial distributions, depot locations and number of customers. Regression results indicate that the proposed approximation is not only intuitive but also predicts the average length of VRP problems with a high level of accuracy.

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  • Figliozzi, Miguel Andres, 2009. "Planning approximations to the average length of vehicle routing problems with time window constraints," Transportation Research Part B: Methodological, Elsevier, vol. 43(4), pages 438-447, May.
    • Handle: RePEc:eee:transb:v:43:y:2009:i:4:p:438-447
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    Cited by:

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    2. Schaumann, Sarah K. & Bergmann, Felix M. & Wagner, Stephan M. & Winkenbach, Matthias, 2023. "Route efficiency implications of time windows and vehicle capacities in first- and last-mile logistics," European Journal of Operational Research, Elsevier, vol. 311(1), pages 88-111.
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    7. Xu, Jiuping & Yan, Fang & Li, Steven, 2011. "Vehicle routing optimization with soft time windows in a fuzzy random environment," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 47(6), pages 1075-1091.
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    11. Ansari, Sina & Başdere, Mehmet & Li, Xiaopeng & Ouyang, Yanfeng & Smilowitz, Karen, 2018. "Advancements in continuous approximation models for logistics and transportation systems: 1996–2016," Transportation Research Part B: Methodological, Elsevier, vol. 107(C), pages 229-252.
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    18. Edward G. Anderson & David R. Keith & Jose Lopez, 2023. "Opportunities for system dynamics research in operations management for public policy," Production and Operations Management, Production and Operations Management Society, vol. 32(6), pages 1895-1920, June.
    19. Gonzales, Eric J., 2016. "Demand responsive transit systems with time-dependent demand: User equilibrium, system optimum, and management strategyAuthor-Name: Amirgholy, Mahyar," Transportation Research Part B: Methodological, Elsevier, vol. 92(PB), pages 234-252.
    20. Larsen, Christian & Turkensteen, Marcel, 2014. "A vendor managed inventory model using continuous approximations for route length estimates and Markov chain modeling for cost estimates," International Journal of Production Economics, Elsevier, vol. 157(C), pages 120-132.
    21. Merchán, Daniel & Winkenbach, Matthias & Snoeck, André, 2020. "Quantifying the impact of urban road networks on the efficiency of local trips," Transportation Research Part A: Policy and Practice, Elsevier, vol. 135(C), pages 38-62.
    22. Turkensteen, Marcel & Klose, Andreas, 2012. "Demand dispersion and logistics costs in one-to-many distribution systems," European Journal of Operational Research, Elsevier, vol. 223(2), pages 499-507.
    23. Li, Yifu & Zhou, Chenhao & Yuan, Peixue & Ngo, Thi Tu Anh, 2023. "Experience-based territory planning and driver assignment with predicted demand and driver present condition," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 171(C).
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