An exact algorithm for multiple depot bus scheduling

Forbes, Michael A.; Holt, J. N.; Watts, A. M.

doi:10.1016/0377-2217(94)90334-4

Cited by 70 publications

(28 citation statements)

References 7 publications

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“…Some exact algorithms, presented by Fischetti et al (1989), Forbes et al (1994) and Kliewer et al (2006), were able to solve instances with up to thousands of trips. Pepin et al (2009) presented and compared five representative heuristics: a tabu search, a large neighborhood search, a truncated column generation, a Lagrangian heuristic and a truncated branch-and-cut.…”

Section: Literature Reviewmentioning

confidence: 99%

A GRASP with efficient neighborhood search for the integrated maintenance and bus scheduling problem

Hama

Yagiura

2018

JAMDSM

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The overall planning process undertaken by a bus company is traditionally composed of five sub-processes: timetabling, vehicle scheduling, maintenance scheduling, crew scheduling, and crew rostering. Solving the full optimization problem is believed to be computationally intractable, and therefore in practice the five sub-processes are usually optimized in sequence. In this paper, we present a model that integrates the problems of vehicle scheduling and maintenance scheduling. The objective is to minimize the differences in mileage between buses, the total distance traveled, and the daily differences in the number of maintenance tasks. We propose a heuristic algorithm using the framework of greedy randomized adaptive search procedure (GRASP), and we improve the neighborhood search procedure by using an ordered list of possible trips. We compare the neighborhood search procedure with and without this mechanism and show that the ordered list reduces the number of neighbors to be checked by more than 95%, and it reduces the time to obtain solutions of the same or better quality by an average of 70%. Through computational experiments on instances generated from real-world data, we show that the proposed algorithm finds solutions that are as good as or better than those obtained by a commercial solver in less than 5% of the time required by the latter.

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Section: Literature Reviewmentioning

confidence: 99%

A GRASP with efficient neighborhood search for the integrated maintenance and bus scheduling problem

Hama

Yagiura

2018

JAMDSM

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“…The approach described in (Lamatsch 1992) uses a bundle of depot nodes per depot to model different daytimes and presents a Lagrangian relaxation of depot-related flow conservation constraints in combination with a subgradient algorithm. An exact approach for the multi-commodity model given in (Forbes et al 1994) uses a Lagrangian relaxation to run a dual simplex algorithm to obtain an LP solution. The authors of (Forbes et al 1994) also observe that the potentially fractional solution of the LP is in most cases integer or near-integer for real-life instances.…”

Section: Connection-based Modelsmentioning

confidence: 99%

“…An exact approach for the multi-commodity model given in (Forbes et al 1994) uses a Lagrangian relaxation to run a dual simplex algorithm to obtain an LP solution. The authors of (Forbes et al 1994) also observe that the potentially fractional solution of the LP is in most cases integer or near-integer for real-life instances. Because of this fact the integer solution was obtained by a standard branchand-bound algorithm.…”

Section: Connection-based Modelsmentioning

confidence: 99%

An overview on vehicle scheduling models

2009

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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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“…Such improvement is very important in the case in which the SDVSP is used as a subproblem. For example, many instances of the SDVSP have to be solved when it is used as a relaxation of more complicated scheduling problems, such as the multidepot vehicle-scheduling problem (see Dell'Amico et al 1993, Ribeiro and Soumis 1994, Forbes et al 1994. The research which has resulted in this paper is motivated by our research on the integration of vehicle and crew scheduling (see Freling 1997), where we need to solve thousands of instances of the SDVSP to get a solution for one instance of the original problem.…”

Section: Freling Wagelmans and Pinto Paix Aomentioning

confidence: 99%

Models and Algorithms for Single-Depot Vehicle Scheduling

Freling

Wagelmans

Paixão

2001

Transportation Science

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V ehicle scheduling is the process of assigning vehicles to a set of predetermined trips with fixed starting and ending times, while minimizing capital and operating costs. This paper considers modeling, algorithmic, and computational aspects of the polynomially solvable case in which there is a single depot and vehicles are identical. A quasiassignment formulation is reviewed and an alternative asymmetric assignment formulation is given. The main contributions of the paper are a new two-phase approach which is valid in the case of a special cost structure, an auction algorithm for the quasiassignment problem, a core-oriented approach, and an extensive computational study. New algorithms are compared with the most successful algorithms for the vehicle-scheduling problem, using both randomly generated and real-life data. The new algorithms show a significant performance improvement with respect to computation time. Such improvement can, for example, be very important when this particular vehicle-scheduling problem appears as a subproblem in more complex vehicle-and crew-scheduling problems.The single-depot vehicle-scheduling problem (SDVSP) is defined as follows: Given a depot and a set of trips with fixed starting and ending times, and given the travelling times between all pairs of locations, find a feasible minimum-cost schedule such that (1) each trip is assigned to a vehicle, and (2) each vehicle performs a feasible sequence of trips. All the vehicles are supposed to be identical. A schedule for a vehicle is composed of vehicle blocks, where each block is a departure from the depot, the service of a feasible sequence of trips, and the return to the depot. The cost function is usually a combination of vehicle capital (fixed) and operational (variable) cost. The SDVSP is well known to be solvable in polynomial time.Overviews of algorithms and applications for the SDVSP and some of its extensions can be found in Daduna and Paixão (1995) and in Desrosiers et al. (1995). Several network-flow-type algorithms have been proposed for the SDVSP in the literature. In particular, the SDVSP has been formulated as a linear assignment problem, a transportation problem, a minimum-cost flow problem, a quasiassignment problem, and a matching problem. We briefly discuss the most relevant algorithms. Let n be the number of trips to be covered by vehicles. Paixão and Branco (1987) propose an O n 3 quasiassignment algorithm which is specially designed for the SDVSP. Computational results indicate that this approach significantly outperforms approaches based on transportation and linear-assignment models. The quasiassignment algorithm is a modified version of the Hungarian algorithm for the linear assignment problem, including the improvements proposed by Jonker and Volgenant (1986). An extension of this algorithm can also deal with a fixed number of vehicles (see Paixão and Branco 1988). Dell'Amico (1989) (see also Dell'Amico et al. 1993) proposes an O n 3 successive shortest-path algorithm for the SDVSP, which uses the initializ...

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An exact algorithm for multiple depot bus scheduling

Cited by 70 publications

References 7 publications

A GRASP with efficient neighborhood search for the integrated maintenance and bus scheduling problem

A GRASP with efficient neighborhood search for the integrated maintenance and bus scheduling problem

An overview on vehicle scheduling models

Models and Algorithms for Single-Depot Vehicle Scheduling

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