# Timetable optimization for single bus line involving fuzzy travel time

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## Abstract

Timetable optimization is an important step for bus operations management, which essentially aims to effectively link up bus carriers and passengers. Generally speaking, bus carriers attempt to minimize the total travel time to reduce its operation cost, while the passengers attempt to minimize their waiting time at stops. In this study, we focus on the timetable optimization problem for a single bus line from both bus carriers’ perspectives and passengers’ perspectives. A bi-objective optimization model is established to minimize the total travel time for all trips along the line and the total waiting time for all passengers at all stops, in which the bus travel times are considered as fuzzy variables due to a variety of disturbances such as weather conditions and traffic conditions. A genetic algorithm with variable-length chromosomes is devised to solve the proposed model. In addition, we present a case study that utilizes real-life bus transit data to illustrate the efficacy of the proposed model and solution algorithm. Compared with the timetable currently being used, the optimal bus timetable produced from this study is able to reduce the total travel time by 26.75% and the total waiting time by 9.96%. The results demonstrate that the established model is effective and useful to seek a practical balance between the bus carriers’ interest and passengers’ interest.

## Keywords

Timetable optimization Fuzzy variable Travel time Waiting time Genetic algorithm## Notes

### Funding

This work was partly supported by Grants from the National Natural Science Foundation of China (No. 71722007), partly by the Welsh Government and Higher Education Funding Council for Wales through the S\(\hat{\text {e}}\)r Cymru National Research Network for Low Carbon, Energy and Environment (NRN-LCEE), and partly by a S\(\hat{\text {e}}\)r Cymru II COFUND Fellowship, UK.

### Compliance with ethical standards

### Conflict of interest

All authors declare that they have no conflict of interest in this research.

### Human and animal rights

This article does not contain any studies with human or animal participants performed by the author.

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