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Modeling Distribution Problems with Time Windows: Part I

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  • Carlos F. Daganzo

    (University of California, Berkeley, California)

Abstract

This paper shows how distribution problems with delivery time constraints can be modeled approximately with just a few variables. Its objective is neither to develop a scheduling algorithm nor an exact predictive method; rather, it is to illustrate some trade-offs and principles that can be used for planning and algorithm development. A workday is divided into time periods. Time windows are modeled by specifying the period in which a vehicle should visit each customer. (The companion paper explores scenarios where many customers do not specify a time window, and thus, it is advantageous not to allocate all the customers to periods.) Travel distance expressions are provided for a “cluster-first, route-second” strategy, similar to some routing methods currently in use. Travel distance expressions are also provided for refinements of the strategy, including one in which tours are systematically staggered, overlapping. The consequent reductions in travel distance can be quite significant. We suggest here that more attention should be paid to the clustering part of algorithm construction, and point to ways in which the customers served by one vehicle should be selected.

Suggested Citation

  • Carlos F. Daganzo, 1987. "Modeling Distribution Problems with Time Windows: Part I," Transportation Science, INFORMS, vol. 21(3), pages 171-179, August.
    • Handle: RePEc:inm:ortrsc:v:21:y:1987:i:3:p:171-179
    DOI: 10.1287/trsc.21.3.171
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    Cited by:

    1. Jabali, Ola & Gendreau, Michel & Laporte, Gilbert, 2012. "A continuous approximation model for the fleet composition problem," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1591-1606.
    2. Waßmuth, Katrin & Köhler, Charlotte & Agatz, Niels & Fleischmann, Moritz, 2023. "Demand management for attended home delivery—A literature review," European Journal of Operational Research, Elsevier, vol. 311(3), pages 801-815.
    3. Carlsson, John Gunnar & Behroozi, Mehdi, 2017. "Worst-case demand distributions in vehicle routing," European Journal of Operational Research, Elsevier, vol. 256(2), pages 462-472.
    4. Anna Franceschetti & Ola Jabali & Gilbert Laporte, 2017. "Continuous approximation models in freight distribution management," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 413-433, October.
    5. van der Hagen, L. & Agatz, N.A.H. & Spliet, R. & Visser, T.R. & Kok, A.L., 2022. "Machine Learning-Based Feasibility Checks for Dynamic Time Slot Management," ERIM Report Series Research in Management ERS-2022-001-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    6. Francis, Peter & Smilowitz, Karen, 2006. "Modeling techniques for periodic vehicle routing problems," Transportation Research Part B: Methodological, Elsevier, vol. 40(10), pages 872-884, December.
    7. Parisa Ahani & Amílcar Arantes & Rohollah Garmanjani & Sandra Melo, 2023. "Optimizing Vehicle Replacement in Sustainable Urban Freight Transportation Subject to Presence of Regulatory Measures," Sustainability, MDPI, vol. 15(16), pages 1-18, August.
    8. Robert Klein & Michael Neugebauer & Dimitri Ratkovitch & Claudius Steinhardt, 2019. "Differentiated Time Slot Pricing Under Routing Considerations in Attended Home Delivery," Service Science, INFORMS, vol. 53(1), pages 236-255, February.
    9. Diana, Marco & Dessouky, Maged M. & Xia, Nan, 2006. "A model for the fleet sizing of demand responsive transportation services with time windows," Transportation Research Part B: Methodological, Elsevier, vol. 40(8), pages 651-666, September.
    10. Fransoo, Jan C. & Escamilla, Rafael & Ge, Jiwen, 2024. "Nanoretail operations in developing markets," Other publications TiSEM 11ea94fa-87eb-41ca-89f6-b, Tilburg University, School of Economics and Management.
    11. Jiwen Ge & Dorothee Honhon & Jan C. Fransoo & Lei Zhao, 2021. "Supplying to Mom and Pop: Traditional Retail Channel Selection in Megacities," Manufacturing & Service Operations Management, INFORMS, vol. 23(1), pages 19-35, 1-2.
    12. Klein, Robert & Koch, Sebastian & Steinhardt, Claudius & Strauss, Arne K., 2020. "A review of revenue management: Recent generalizations and advances in industry applications," European Journal of Operational Research, Elsevier, vol. 284(2), pages 397-412.
    13. Strauss, Arne & Gülpınar, Nalan & Zheng, Yijun, 2021. "Dynamic pricing of flexible time slots for attended home delivery," European Journal of Operational Research, Elsevier, vol. 294(3), pages 1022-1041.
    14. Melih Çelik & Özlem Ergun & Pınar Keskinocak, 2015. "The Post-Disaster Debris Clearance Problem Under Incomplete Information," Operations Research, INFORMS, vol. 63(1), pages 65-85, February.
    15. Koch, Sebastian & Klein, Robert, 2020. "Route-based approximate dynamic programming for dynamic pricing in attended home delivery," European Journal of Operational Research, Elsevier, vol. 287(2), pages 633-652.
    16. Fleckenstein, David & Klein, Robert & Steinhardt, Claudius, 2023. "Recent advances in integrating demand management and vehicle routing: A methodological review," European Journal of Operational Research, Elsevier, vol. 306(2), pages 499-518.
    17. Robert Klein & Jochen Mackert & Michael Neugebauer & Claudius Steinhardt, 2018. "A model-based approximation of opportunity cost for dynamic pricing in attended home delivery," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(4), pages 969-996, October.
    18. Franceschetti, Anna & Honhon, Dorothée & Laporte, Gilbert & Woensel, Tom Van & Fransoo, Jan C., 2017. "Strategic fleet planning for city logistics," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 19-40.
    19. Yang, Xinan & Strauss, Arne K., 2017. "An approximate dynamic programming approach to attended home delivery management," European Journal of Operational Research, Elsevier, vol. 263(3), pages 935-945.
    20. Langevin, André & Mbaraga, Pontien & Campbell, James F., 1996. "Continuous approximation models in freight distribution: An overview," Transportation Research Part B: Methodological, Elsevier, vol. 30(3), pages 163-188, June.

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