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Constructing an Optimal Fleet for a Transportation Schedule

Author

Listed:
  • I. Gertsbach

    (Ben Gurion University of the Negev, Beer Sheva, Israel)

  • Yu. Gurevich

    (Ben Gurion University of the Negev, Beer Sheva, Israel)

Abstract

A schedule is a set of passages; a passage is a 4-tuple p = ( p 1, p 2, p 3, p 4) where p 1, p 2 denote departure and arrival terminals, p 3, p 4 departure and arrival times. A fleet is a partition of the schedule into chains; each chain is a finite or infinite sequence of passages p 1 , p 2 , ... having the property p n 2 = p n +1 1 and p n 4 (le) p n +1 3. The fleet-size is the minimal possible dimension (i.e., the number of chains) of the fleets. The deficit function d ( t , a ) for a terminal a is the difference between the number of departures and arrivals occurring at a during the interval [0, t ]. It is proved that the fleet-aim is equal to (sum) a max t (ge)0 d ( t , a ). A general method for constructing all optimal fleets is described. A special case of periodic schedules is studied and it is proved that a periodic schedule can be decomposed into an optimal periodic fleet. Applications of the deficit function technique to practical scheduling when passages have tolerances for departure times are discussed.

Suggested Citation

  • I. Gertsbach & Yu. Gurevich, 1977. "Constructing an Optimal Fleet for a Transportation Schedule," Transportation Science, INFORMS, vol. 11(1), pages 20-36, February.
    • Handle: RePEc:inm:ortrsc:v:11:y:1977:i:1:p:20-36
    DOI: 10.1287/trsc.11.1.20
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    Cited by:

    1. Klosterhalfen, S.T. & Kallrath, J. & Fischer, G., 2014. "Rail car fleet design: Optimization of structure and size," International Journal of Production Economics, Elsevier, vol. 157(C), pages 112-119.
    2. Kayhan Alamatsaz & Sadam Hussain & Chunyan Lai & Ursula Eicker, 2022. "Electric Bus Scheduling and Timetabling, Fast Charging Infrastructure Planning, and Their Impact on the Grid: A Review," Energies, MDPI, vol. 15(21), pages 1-39, October.
    3. Saltzman, Robert M. & Stern, Helman I., 2022. "The multi-day aircraft maintenance routing problem," Journal of Air Transport Management, Elsevier, vol. 102(C).
    4. Bojovic, Nebojsa J., 2002. "A general system theory approach to rail freight car fleet sizing," European Journal of Operational Research, Elsevier, vol. 136(1), pages 136-172, January.
    5. 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.
    6. Liu, Tao & Ceder, Avishai (Avi), 2018. "Integrated public transport timetable synchronization and vehicle scheduling with demand assignment: A bi-objective bi-level model using deficit function approach," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 935-955.
    7. Kallrath, J. & Klosterhalfen, S.T. & Walter, M. & Fischer, G. & Blackburn, R., 2017. "Payload-based fleet optimization for rail cars in the chemical industry," European Journal of Operational Research, Elsevier, vol. 259(1), pages 113-129.
    8. 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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