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Homogeneous optimal fleet

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  • Gertsbakh, I.
  • Gurevich, Yuri

Abstract

The structure of chains in the optimal chain decomposition of a periodic schedule S is investigated. A finite oriented graph termed the Linis Graph (LG) is defined which serves as the key for this investigation. The edges of the LG are trip-types of S and the vertices of the LG represent terminals. It is proved that there is an Euler cycle for a connected LG satisfying natural precedence relations between arrival and departure times. Expansion of this cycle in a real time gives a "master-chain" of trips which, being repeated periodically, gives an infinite periodic chain. Time-shifted periodic replication of this chain allows obtaining a group of twin-type periodic chains forming an optimal fleet over S. It is proved that if the LG has m connected components then there is an optimal fleet consisting of m groups of similar periodic chains. It is shown that if the graph of terminals is connected and the LG is disconnected then it is possible to obtain a twin-type fleet over S by adding to S "dummy" trip-types. A general approach to constructing a twin-type fleet of minimal size for this case is described. The relation of the theory developed to the so-called center problem is discussed.

Suggested Citation

  • Gertsbakh, I. & Gurevich, Yuri, 1982. "Homogeneous optimal fleet," Transportation Research Part B: Methodological, Elsevier, vol. 16(6), pages 459-470, December.
    • Handle: RePEc:eee:transb:v:16:y:1982:i:6:p:459-470
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    Cited by:

    1. Saltzman, Robert M. & Stern, Helman I., 2022. "The multi-day aircraft maintenance routing problem," Journal of Air Transport Management, Elsevier, vol. 102(C).
    2. Liu, Tao & (Avi) Ceder, Avishai, 2017. "Deficit function related to public transport: 50 year retrospective, new developments, and prospects," Transportation Research Part B: Methodological, Elsevier, vol. 100(C), pages 1-19.
    3. Stern, Helman I. & Gertsbakh, Ilya B., 2019. "Using deficit functions for aircraft fleet routing," Operations Research Perspectives, Elsevier, vol. 6(C).

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