Improving Vehicle Scheduling Support by Efficient Algorithms

  • Taïeb Mellouli
Conference paper
Part of the Operations Research Proceedings book series (ORP, volume 1996)

Abstract

In this paper, the minimum fleet size problem is investigated: Find the minimum number of vehicles to serve a set of trips of a given timetable for a transportation system. First, we present an algorithm for the basic problem requiring only linear-time after suitably sorting input data. This improves a quadratic-time greedy algorithm developed in [Su95]. Our algorithm was implemented and tested with real-life data indicating a good performance. Generated diagrams on vehicle standing times are shown to be useful for various tasks. Second, Min-Max-results for the minimum fleet size problem are discussed. We argue that Dilworth’s chain decomposition theorem works only if unrestricted deadheading, i.e., adding non-profit ‘empty’ trips, is permitted and thus its application to the case of railway or airline passenger traffic is misleading. To remedy this lack, we consider a particular network flow model for the no deadheading case, formulate a Min-Max-result, and discuss its implications- along with efficient algorithms-for vehicle as well as trip and deadhead trip scheduling.

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References

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    Ahuja, R.K., Magnanti, T.L., and Orlin, J.B., L.: Network Flows. Prentice Hall, NJ, 1993.Google Scholar
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    Bartlett, T.E.: “An algorithm for the minimum number of transport units to maintain a fixed schedule” Bartlett, T.E. and Charnes, A.: “Part II: Generalizations and Analysis”. Nav. Res. Log.Q., 4,139–149 and 207–220, 1957.CrossRefGoogle Scholar
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    Ford, L.R. and Fulkerson, D.R.: Flows in Networks. Princeton U.P., Princeton, NJ, 1962.Google Scholar
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    Mellouli, T. and Suhl, L.: “Supporting Planning and Operation Time Control in Transportation Systems”. Symposium on Operations Research (SOR’96). Braunschweig, Germany, 1996.Google Scholar
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    Suhl, L.: Computer-Aided Scheduling: An Airline Perspective. Gabler - DUV, Wiesbaden, 1995.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Taïeb Mellouli
    • 1
  1. 1.Dept. of Business Computing Decision Support & OR LaboratoryUniversity of PaderbornGermany

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