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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. 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.
    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. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Stern, Helman I. & Gertsbakh, Ilya B., 2019. "Using deficit functions for aircraft fleet routing," Operations Research Perspectives, Elsevier, vol. 6(C).
    8. Saltzman, Robert M. & Stern, Helman I., 2022. "The multi-day aircraft maintenance routing problem," Journal of Air Transport Management, Elsevier, vol. 102(C).

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