Improving Vehicle Scheduling Support by Efficient Algorithms
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.
KeywordsGreedy Algorithm Terminal Station Minimum Flow Greedy Approach Vehicle Schedule
Unable to display preview. Download preview PDF.
- [AhMaOr93]Ahuja, R.K., Magnanti, T.L., and Orlin, J.B., L.: Network Flows. Prentice Hall, NJ, 1993.Google Scholar
- [Ba57, BaCh57]
- [FoFu62]Ford, L.R. and Fulkerson, D.R.: Flows in Networks. Princeton U.P., Princeton, NJ, 1962.Google Scholar
- [MeSu96]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
- [Su95]Suhl, L.: Computer-Aided Scheduling: An Airline Perspective. Gabler - DUV, Wiesbaden, 1995.Google Scholar