Data-driven bus timetabling with spatial-temporal travel time
| DOI | https://doi.org/10.1108/IMDS-10-2021-0629 |
| Published date | 04 January 2022 |
| Date | 04 January 2022 |
| Pages | 2281-2298 |
| Subject Matter | Information & knowledge management,Information systems,Data management systems,Knowledge management,Knowledge sharing,Management science & operations,Supply chain management,Supply chain information systems,Logistics,Quality management/systems |
| Author | Xiang Li,Ming Yang,Hongguang Ma,Kaitao (Stella) Yu |
Data-driven bus timetabling with
spatial-temporal travel time
Xiang Li, Ming Yang and Hongguang Ma
School of Economics and Management, Beijing University of Chemical Technology,
Beijing, China, and
Kaitao (Stella) Yu
Canada International School of Beijing, Beijing, China
Abstract
Purpose –Travel time at inter-stops is a set of important parameters in bus timetabling, which is usually
assumed to be normal (log-normal) random variable in literature. With the development of digital technology
and big data analytics ability in the bus industry, practitioners prefer to generate deterministic travel time
based on the on-board GPS data under maximum probability rule and mean value rule, which simplifies the
optimization procedure, but performs poorly in the timetabling practice due to the loss of uncertain nature on
travel time. The purpose of this study is to propose a GPS-data-driven bus timetabling approach with
consideration of the spatial-temporal characteristic of travel time.
Design/methodology/approach –The authors illustrate that the real-life on-board GPS data does not
support the hypothesis of normal (log-normal) distribution on travel time at inter-stops, thereby formulating
the travel time as a scenario-based spatial-temporal matrix, where K-means clustering approach is utilized to
identify the scenarios of spatial-temporal travel time from daily observation data. A scenario-based robust
timetabling model is finally proposedto maximize the expected profit of the bus carrier. The authors introduce
a set of binary variables to transform the robust model into an integer linear programming model, and speed up
the solving process by solution space compression, such that the optimal timetable can be well solved
by CPLEX.
Findings –Case studies based on the Beijing bus line 628 are given to demonstrate the efficiency of the
proposed methodology. The results illustrate that: (1) the scenario-based robust model could increase the
expected profits by 15.8% compared with the maximum probability model; (2) the scenario-based robust model
could increase the expected profit by 30.74% compared with the mean value model; (3) the solution space
compression approach could effectively shorten the computing time by 97%.
Originality/value –This study proposes a scenario-based robust bus timetabling approach driven by GPS
data, which significantly improves the practicality and optimality of timetable, and proves the importance of
big data analytics in improving public transport operations management.
Keywords Bus timetabling, GPS data, Scenario-based robust model, Spatial-temporal travel time
Paper type Research paper
1. Introduction
Bus has always been an important mode of urban public transportation. However, with the
development of urban rail transit, online car-hailing and bike sharing, the passenger volume
of bus transport declines significantly in recent years. Taking Beijing bus for example, the
passenger volume in 2019 was 35.64 billion, which is 36.53% lower than that in 2012 [1]. Even
worse, under the influence of COVID-19, the passenger volume in 2020 decreased by 30%
compared with that in 2019 [2]. Along with the decline of passenger volume, the rise of fuel
price and labor cost make the total operations cost rapidly increase. Statistical data, still from
Beijing, shows that the total operations cost of bus carriers in 2019 was 20.83 billion RMB,
25.2% higher than that in 2013 [3]. Although the government provides certain subsidies (Ding
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This work was supported by grants from the National Natural Science Foundation of China (Nos.
71 722 007 and 71 931 001), the Key Program of NSFC-FRQSC Joint Project (NSFC No. 72 061 127 002 and
FRQSC No. 295 837), the Funds for First-class Discipline Construction (XK1802-5) and the Fundamental
Research Funds for the Central Universities (buctrc201926).
The current issue and full text archive of this journal is available on Emerald Insight at:
https://www.emerald.com/insight/0263-5577.htm
Received 16 October 2021
Revised 2 December 2021
Accepted 15 December 2021
Industrial Management & Data
Systems
Vol. 122 No. 10, 2022
pp. 2281-2298
© Emerald Publishing Limited
0263-5577
DOI 10.1108/IMDS-10-2021-0629
et al., 2020) for bus carriers in accordance to passenger volume, it is not enough to make up for
the loss caused by the increased operations cost. Under such a dilemma, bus carriers are
seeking to increase passenger volume and control operations cost by improving operations
management.
Timetabling is a critical step in bus operations management, which is the basis for vehicle
scheduling and crew scheduling. In the process of timetabling, travel time at inter-stops is a
set of critical parameters, which is generally assumed to be normal (log-normal) random
variable with given distribution (Ma et al., 2016;Srinivasan et al., 2014) in the existing
literature. In this paper, we consider that the spatial-temporal travel time contains 2,220
pieces [4]. Based on the real-life GPS data collected from Beijing bus line 628 from October 12,
2016 to March 27, 2017, we take Chi-square test on the normal and log-normal distribution
hypotheses. Among the 2,220 hypothesis tests, the accept rate of normal (log-normal)
distribution is only 58.38% (55.23%). These super-under fitting results motivate us to explore
the bus timetabling method driven by data instead of hypothesized random information.
Timetabling methods are generally divided into two categories, i.e. headway-based
method and timetable-based method. The headway-based method determines the
dispatching frequencies or headway among adjacent trips, while the timetable-based
method determines the specific departure time and arrival time of trips at stops. This paper
focuses on developing a data-driven headway-based timetabling method within the
framework of scenario-based robust optimization (Mulvey et al., 1995;Yan and Tang,
2008,2009). The scenario-based robust optimizations are based on using mean–variance as a
measure of solution robustness. The solution of scenario-based robust model can perform
well even at the low-probability regions of the probability distribution. To the best of our
knowledge, there is no bus timetabling research with scenario-based spatial-temporal travel
time, although the scenario-based robust optimization has been widely studied in
transportation fields, e.g. train timetabling (Hassannayebi et al., 2017), vehicle routing
(Sun, 2014) and emergency transportation network design (Rezaei-Malek et al., 2016). In this
paper, the K-means clustering approach is utilized to identify the scenarios of spatial-
temporal travel time. Then a scenario-based robust timetabling model is developed to
maximize the expected profit of bus carriers. By introducing a set of binary variables, we
transform the model into a mixed integer linear programming model. To be easily solved by
commercial software, time window constraints and empirical constraints are formulated to
compress the solution space. Case studies on Beijing bus line 628 is given to demonstrate the
efficiency of the proposed methodology. The computation results show that the proposed
model is able to produce a satisfactory timetable that outperforms the deterministic models
with maximum probability rule and mean value rule, in terms of raising the expected profit
by 15.80 and 30.74%, respectively. Meanwhile, the solution space compression approach
shows its speedy solution ability by shortening the computing time by 97%.
The contributions of this study are three-fold: (1) Most of the previous bus timetabling
studies are built on the hypothesized random information of travel time. The hypothesis test
based on the real-life GPS data reveals that the travel time has a high degree of nonstochastic
uncertainty; (2) Adhering to the principle of data-driven decision making, this paper proposes
a robust bus timetabling approach with scenarios of spatial-temporal travel time derived
from GPS data, which significantly improves the practicality and optimality of timetable;
(3) The case studies on a real-life bus line prove the importance of big data analytics in
improving public transport operations management.
The remainder of this paper is structured as follows. Section 2 reviews the relevant
literature and concludes the research gap. Section 3 conducts data analysis on travel time.
Section 4 formulates the scenario-based robust timetabling model. In Section 5, the proposed
model is transformed into a mixed integer linear programming, and solution space
compression approach is provided. Section 6 presents a real-life case study to illustrate the
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