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Minimum Cost Schedules for a Public Transportation Route---I. Theory

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  • V. F. Hurdle

    (University of California, Berkeley, California)

Abstract

A fleet of vehicles carries passengers in one direction on a public transit route, then returns empty to the dispatch point after a round trip travel time T . The arrival rate of passengers is a known, deterministic, continuous, function of time and the objective is to devise a schedule that minimizes the total cost for passenger waiting time and vehicle operation. It is shown that the optimal dispatch rate at any time t is either equal to the arrival rate at t + kT where k is some integer (not necessarily positive) or proportional to the square root of the average of the passenger arrival rates at t - mT , t - ( m - 1) T , ..., t , ..., t + nT where m and n are nonnegative integers (sometimes both zero). Furthermore, the optimal dispatch rate, expressed as a function of time, can be discontinuous only at t q + jT and at t d , where t q is a time when a queue of waiting passengers forms, t d is a time when a queue disappears, and j is an integer.

Suggested Citation

  • V. F. Hurdle, 1973. "Minimum Cost Schedules for a Public Transportation Route---I. Theory," Transportation Science, INFORMS, vol. 7(2), pages 109-137, May.
    • Handle: RePEc:inm:ortrsc:v:7:y:1973:i:2:p:109-137
    DOI: 10.1287/trsc.7.2.109
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    Cited by:

    1. Chen, Zhiwei & Li, Xiaopeng & Zhou, Xuesong, 2020. "Operational design for shuttle systems with modular vehicles under oversaturated traffic: Continuous modeling method," Transportation Research Part B: Methodological, Elsevier, vol. 132(C), pages 76-100.
    2. Yan, Shangyao & Chen, Hao-Lei, 2002. "A scheduling model and a solution algorithm for inter-city bus carriers," Transportation Research Part A: Policy and Practice, Elsevier, vol. 36(9), pages 805-825, November.
    3. Tian, Xiaopeng & Niu, Huimin, 2020. "Optimization of demand-oriented train timetables under overtaking operations: A surrogate-dual-variable column generation for eliminating indivisibility," Transportation Research Part B: Methodological, Elsevier, vol. 142(C), pages 143-173.
    4. Langevin, André & Mbaraga, Pontien & Campbell, James F., 1996. "Continuous approximation models in freight distribution: An overview," Transportation Research Part B: Methodological, Elsevier, vol. 30(3), pages 163-188, June.

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