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Minimizing the Number of Vehicles to Meet a Fixed Periodic Schedule: An Application of Periodic Posets

Author

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  • James B. Orlin

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

Abstract

In this paper we consider countably infinite partially ordered sets (posets) in which the order relations occur periodically. We show that the problem of determining the minimum number of chains (completely ordered subsets) needed to cover all of the elements may be solved efficiently as a finite network flow problem. A special case of the chain-cover problem for periodic posets is the problem of minimizing the number of individuals to meet a fixed periodically repeating set of tasks with set-up times between tasks. For example, if we interpret tasks as flights and individuals as airplanes, the resulting problem is to minimize the number of airplanes needed to fly a fixed daily repeating schedule of flights, where deadheading between airports is allowed.

Suggested Citation

  • James B. Orlin, 1982. "Minimizing the Number of Vehicles to Meet a Fixed Periodic Schedule: An Application of Periodic Posets," Operations Research, INFORMS, vol. 30(4), pages 760-776, August.
    • Handle: RePEc:inm:oropre:v:30:y:1982:i:4:p:760-776
    DOI: 10.1287/opre.30.4.760
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    Cited by:

    1. Rolf N. Van Lieshout, 2021. "Integrated Periodic Timetabling and Vehicle Circulation Scheduling," Transportation Science, INFORMS, vol. 55(3), pages 768-790, May.
    2. Campbell, Ann Melissa & Hardin, Jill R., 2005. "Vehicle minimization for periodic deliveries," European Journal of Operational Research, Elsevier, vol. 165(3), pages 668-684, September.
    3. Stern, Helman I. & Gertsbakh, Ilya B., 2019. "Using deficit functions for aircraft fleet routing," Operations Research Perspectives, Elsevier, vol. 6(C).
    4. van Lieshout, R.N., 2019. "Integrated Periodic Timetabling and Vehicle Circulation Scheduling," Econometric Institute Research Papers EI2019-27, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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