Vehicle Scheduling Problem with Multiple Type of Vehicles and a Single Depot

The vehicle scheduling problem, arising in public transport bus companies, addresses the task of assigning buses to cover a given set of timetabled trips with consideration of practical requirements such as multiple depots and vehicle types as well as further extensions. An optimal schedule is characterized by minimal fleet size and/or minimal operational costs. Various publications were released as a result of extensive research in the last decades on this topic. Several modeling approaches as well as specialized solution strategies were presented for the problem and its extensions. This paper discusses the modeling approaches for different kinds of vehicle scheduling problems and gives an up-to-date and comprehensive overview on the basis of a general problem definition. Although we concentrate on the presentation of modeling approaches, also the basic ideas of solution approaches are given.

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“…This approach was published for the single depot case (SD-MVT-VSP) in (Bodin et al 1983) and also used in (Costa et al 1995).…”

Section: Multiple Vehicle Types and Vehicle Type Groupsmentioning

confidence: 97%

An overview on vehicle scheduling models

2009

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“…Considering the example mentioned in Section 2 again, the sequence of trips (8,2,11,6) is a path in the initial timetable rather than a route, because trip 8 and trip 2 are incompatible but restrictively compatible. However, (8,2,11,6) is also a route in the modified timetable. The notations for the path-based model are presented in Table 2.…”

Section: The Path-based Model For Vspvt-ltmentioning

confidence: 99%

“…Generally, the connection-based model is hard to solve by optimization software when thousands of trips have to be scheduled. Costa et al [11] and Hadjar et al [12] formulated the VSP as a Set Portioning Problem which can be solved successfully by column generation. Bodin et al [13] and Freling and Paixão [14] discussed the vehicle scheduling problem with time constraint, and they constructed a special connection-based network with inserting additional arcs or alternative graphs with different levels to handle the time constraint.…”

Section: Introductionmentioning

confidence: 99%

Optimizing Vehicle Scheduling Based on Variable Timetable by Benders-and-Price Approach

Lan

Song

et al. 2019

Journal of Advanced Transportation

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In practice, vehicle scheduling is planned on a variable timetable so that the departure times of trips can be shifted in tolerable ranges, rather than on a fixed timetable, to decrease the required fleet size. This paper investigates the vehicle scheduling problem on a variable timetable with the constraint that each vehicle can perform limited trips. Since the connection-based model is difficult to solve by optimization software for a medium-scale or large-scale instance, a designed path-based model is developed. A Benders-and-Price algorithm by combining the Benders decomposition and column generation is proposed to solve the LP-relaxation of the path-based model, and a bespoke Branch-and-Price is used to obtain the integer solution. Numerical experiments indicate that a variable timetable approach can reduce the required fleet size with a tolerable timetable deviation in comparison with a fixed timetable approach. Moreover, the proposed algorithm is greatly superior to GUROBI in terms of computational efficiency and guarantees the quality of the solution.

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