Joint Optimization for the Locations of Time Control Points and Corresponding Slack Times for a Bus Route

Abstract

Bus holding strategy is an effective way for alleviating inevitable disruptions along a bus route, including decisions on the control point locations and slack duration. However, at present, the locations of the control points and corresponding slack times are largely determined by engineering experience and therefore lack theoretical optimization. The aim of this study is to develop a model which can jointly optimize the locations of the control points and corresponding slack times under a given number of control points. As locations of the upstream control points will influence the downstream operation states, this optimization problem is modeled as a multi-stage decision process. To evaluate the stability and efficiency of a bus system, we calculate the punctuality rate and travel time at each stage by taking into account the uncertainty along the route and propose a reasonable stage-utilization cost combing these two factors. A numerical case study based on a real bus route in Harbin of China is carried out to demonstrate our approach. The impacts of the weighting factor and slack times on the optimal control point plan are also discussed.