Abstract

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.

Highlights

  • In the planning process of public bus transport, timetabling problem, and vehicle scheduling problem (VSP) are dealt with by a sequential approach where the solution of previous subproblem is taken as input of the following subproblem, because of the complexity of solving the integrated model of the two planning processes [1]

  • Considering the inefficiency of using GUROBI to solve the connection-based model for VSPVT-LT when the size of instances is relatively large, this paper formulated a pathbased model, which can be solved by a bespoke approach working in two phases

  • Benders decomposition is used to decompose the original model into a timetabling problem in Benders master problem (BMP) and a VSP in Benders subproblem (BSP)

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Summary

Introduction

In the planning process of public bus transport, timetabling problem, and vehicle scheduling problem (VSP) are dealt with by a sequential approach where the solution of previous subproblem is taken as input of the following subproblem, because of the complexity of solving the integrated model of the two planning processes [1]. Both the timetabling problem and VSP have been well-studied. Liu et al [20] provided a new biobjective, bilevel mathematical programming model, and a novel deficit-function-based sequential search approach by combining a network-flow technique and a shifting departure time procedure, presented to solve the problem to achieve a set of Pareto-efficient solutions.

The Problem Description and Notations
The Path-Based Model for VSPVT-LT
Solution Method
Numerical Experiments
Conclusions and Future Works
Full Text
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