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Technical Note—Optimizing the Schedule for a Fixed Vehicle Path with Convex Inconvenience Costs

Author

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  • Yvan Dumas

    (GERAD and École des Hautes Études Commerciales, Montréal, Canada H3T 1V6)

  • François Soumis

    (GERAD and École Polytechnique de Montréal, Montréal, Canada H3C 3A7)

  • Jacques Desrosiers

    (GERAD and École des Hautes Études Commerciales, Montréal, Canada H3T 1V6)

Abstract

We present an algorithm that solves the problem of finding the vehicle schedule which minimizes total inconveniences for travel along a fixed path, where service times at nodes are constrained by time windows and where inconvenience is modeled using convex functions of the service times. This problem occurs as the last step or as a sub-problem in many common approaches to solving routing and scheduling problems. We show that the complexity of the algorithm, expressed as a number of unidimensional minimizations, is on the order of the number of nodes for convex inconvenience functions. For linear and quadratic functions, this complexity is linear in the number of nodes. We present extensions to the case where linear costs are applied to waiting time, and also to the case where the service time variables are discrete.

Suggested Citation

  • Yvan Dumas & François Soumis & Jacques Desrosiers, 1990. "Technical Note—Optimizing the Schedule for a Fixed Vehicle Path with Convex Inconvenience Costs," Transportation Science, INFORMS, vol. 24(2), pages 145-152, May.
    • Handle: RePEc:inm:ortrsc:v:24:y:1990:i:2:p:145-152
    DOI: 10.1287/trsc.24.2.145
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    Citations

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    Cited by:

    1. Qie He & Stefan Irnich & Yongjia Song, 2018. "Branch-Cut-and-Price for the Vehicle Routing Problem with Time Windows and Convex Node Costs," Working Papers 1804, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    2. Fagerholt, Kjetil, 2001. "Ship scheduling with soft time windows: An optimisation based approach," European Journal of Operational Research, Elsevier, vol. 131(3), pages 559-571, June.
    3. Stojkovic, Goran & Soumis, François & Desrosiers, Jacques & Solomon, Marius M., 2002. "An optimization model for a real-time flight scheduling problem," Transportation Research Part A: Policy and Practice, Elsevier, vol. 36(9), pages 779-788, November.
    4. R A Russell & T L Urban, 2008. "Vehicle routing with soft time windows and Erlang travel times," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(9), pages 1220-1228, September.
    5. Anastasios D. Vareias & Panagiotis P. Repoussis & Panagiotis P. Repoussi, 2019. "Assessing Customer Service Reliability in Route Planning with Self-Imposed Time Windows and Stochastic Travel Times," Service Science, INFORMS, vol. 53(1), pages 256-281, February.
    6. Fu, Liping, 2002. "Scheduling dial-a-ride paratransit under time-varying, stochastic congestion," Transportation Research Part B: Methodological, Elsevier, vol. 36(6), pages 485-506, July.
    7. K Fagerholt & G Laporte & I Norstad, 2010. "Reducing fuel emissions by optimizing speed on shipping routes," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(3), pages 523-529, March.
    8. Kishore Bhoopalam, A. & Agatz, N.A.H. & Zuidwijk, R.A., 2017. "Planning of Truck Platoons: a Literature Review and Directions for Future Research," ERIM Report Series Research in Management ERS-2017-010-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.
    9. Christian Tilk & Michael Drexl & Stefan Irnich, 2018. "Nested Branch-and-Price-and-Cut for Vehicle Routing Problems with Multiple Resource Interdependencies," Working Papers 1801, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    10. Bhoopalam, Anirudh Kishore & Agatz, Niels & Zuidwijk, Rob, 2018. "Planning of truck platoons: A literature review and directions for future research," Transportation Research Part B: Methodological, Elsevier, vol. 107(C), pages 212-228.
    11. Matteo Salani & Maria Battarra, 2018. "The opportunity cost of time window violations," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 7(4), pages 343-361, December.
    12. Tilk, Christian & Drexl, Michael & Irnich, Stefan, 2019. "Nested branch-and-price-and-cut for vehicle routing problems with multiple resource interdependencies," European Journal of Operational Research, Elsevier, vol. 276(2), pages 549-565.
    13. K Fagerholt & B A Foss & O J Horgen, 2009. "A decision support model for establishing an air taxi service: a case study," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(9), pages 1173-1182, September.
    14. Desaulniers, Guy & Lavigne, June & Soumis, Francois, 1998. "Multi-depot vehicle scheduling problems with time windows and waiting costs," European Journal of Operational Research, Elsevier, vol. 111(3), pages 479-494, December.
    15. Mitrovic-Minic, Snezana & Laporte, Gilbert, 2004. "Waiting strategies for the dynamic pickup and delivery problem with time windows," Transportation Research Part B: Methodological, Elsevier, vol. 38(7), pages 635-655, August.
    16. Mohammad Mahdi Ahmadian & Amir Salehipour, 2021. "The just-in-time job-shop scheduling problem with distinct due-dates for operations," Journal of Heuristics, Springer, vol. 27(1), pages 175-204, April.
    17. Tal Grinshpoun & Elad Shufan & Hagai Ilani & Vadim Levit & Haya Brama, 2023. "Graph representation of the fixed route dial-a-ride problem," Journal of Scheduling, Springer, vol. 26(5), pages 479-495, October.
    18. Gerardo Berbeglia & Jean-François Cordeau & Irina Gribkovskaia & Gilbert Laporte, 2007. "Static pickup and delivery problems: a classification scheme and survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 1-31, July.
    19. Hideki Hashimoto & Mutsunori Yagiura & Shinji Imahori & Toshihide Ibaraki, 2013. "Recent progress of local search in handling the time window constraints of the vehicle routing problem," Annals of Operations Research, Springer, vol. 204(1), pages 171-187, April.
    20. Ahmadian, Mohammad Mahdi & Salehipour, Amir & Cheng, T.C.E., 2021. "A meta-heuristic to solve the just-in-time job-shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 288(1), pages 14-29.
    21. Qie He & Stefan Irnich & Yongjia Song, 2019. "Branch-and-Cut-and-Price for the Vehicle Routing Problem with Time Windows and Convex Node Costs," Transportation Science, INFORMS, vol. 53(5), pages 1409-1426, September.
    22. Marielle Christiansen & Kjetil Fagerholt, 2002. "Robust ship scheduling with multiple time windows," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(6), pages 611-625, September.
    23. Remy Spliet & Said Dabia & Tom Van Woensel, 2018. "The Time Window Assignment Vehicle Routing Problem with Time-Dependent Travel Times," Transportation Science, INFORMS, vol. 52(2), pages 261-276, March.

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