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

Zekang Lan,Shiwei He,Sijia Hao,Rui Song

doi:10.1155/2019/2781590

Zekang Lan, Shiwei He + Show 2 more

Open Access

https://doi.org/10.1155/2019/2781590

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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)

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