Global Optimization for Bus Line Timetable Setting Problem

Qun Chen

doi:10.1155/2014/636937

Abstract

This paper defines bus timetables setting problem during each time period divided in terms of passenger flow intensity; it is supposed that passengers evenly arrive and bus runs are set evenly; the problem is to determine bus runs assignment in each time period to minimize the total waiting time of passengers on platforms if the number of the total runs is known. For such a multistage decision problem, this paper designed a dynamic programming algorithm to solve it. Global optimization procedures using dynamic programming are developed. A numerical example about bus runs assignment optimization of a single line is given to demonstrate the efficiency of the proposed methodology, showing that optimizing buses’ departure time using dynamic programming can save computational time and find the global optimal solution.

Highlights

The transit planning process includes four basic components which are usually performed in sequence: (1) network route design, (2) setting frequencies and timetables, (3) scheduling vehicles to trips, and (4) assignment of drivers
Trip frequency scheduling is the determination of trip frequencies for an operation period, normally a daily operation
Ρ can be approximately given according to the forecasting of future bus operation; τ is the average number of in-vehicle passengers; C is the capacity of the vehicle; L is the length of the bus line; qT(l) ij is the number of passengers going from stop i to stop j during time period T(l), and here i < j is because this paper only studies the case of one direction (1 → n); dij is the distance between stops i and j

Summary

Introduction

The transit planning process includes four basic components which are usually performed in sequence: (1) network route design, (2) setting frequencies and timetables, (3) scheduling vehicles to trips, and (4) assignment of drivers. Van Oudheusden and Zhu (1995) [14] developed an integer programming model for trip frequency scheduling and presented two heuristic solution methods, one of which was based on linear programming and the other was a straightforward derivation of common bus operation practice; but they could not guarantee the global optimal solution. The majority of previous solution methods for transit frequencies and timetable setting problems relied on problembased heuristics or design guidelines, which could not guarantee the best solution in mathematics. The final section concludes the paper and discusses future research issues

The Bus Timetable Setting Problem

Optimization Procedures Using Dynamic Programming

Dynamic Programming Algorithms for Solving the Bus

A Numerical Example

Conclusions and Prospect