# The Optimization of Bus Departure Time Based on Uncertainty Theory—Taking No. 207 Bus Line of Nanchang City, China, as an Example

**Round 1**

*Reviewer 1 Report
*

The Authors present a contemporary problem and its solution, i.e. the uncertainty of the number of passengers at the bus station, the bus operation time, and the support for bus departure time problems.

There is presented the literature review based on a list of 27 references. Most of them, i.e. 70 %, are from 2017 to 2022. This is an interesting research with a proposed approach to the problem solution and its exemplification on a real-world case study, including data collection, calculations and analysis of results.

My comments and questions are as follows:

- The meaning of the sentence in lines 37-38 is the same as the meaning of the sentence in lines 35-37.

-The mathematical formula (3) includes the parameter *Pij*(capital letter P), while the explanation below that is about *pij *(lowercase letter p)*. *Is it the same parameter? If not, please explain the difference.

A similar comment and question is about mathematical formula (5) and parameters C and c.

- Below the mathematical formula (3) is presented the total duration of the period *F _{i}*. Itsunitshould be expressed in (hour) or (minute). Assuming that it is expressed in (hours) and considering the bus departure frequency

*f*in the period

_{j}*j*expressed in (vehicle/hour), then according to Authors, the length of the bus departure interval

*i*formulatedas F

_{i}/f

_{j}is expressed in (min). Where is this unit from?

- What is the parameter *f _{i}*in the mathematical formula (4)? The Authors defined previously

*f*.

_{j}- There are two mathematical formulas with the same number (5).

- As I understand the first mathematical formula (5) should be expressed in monetary units, i.e. Yuan. If yes, then right hand side of the equation (5) should be checked, e.g. c/d component is not expressed in (Yuan/km). Moreover, each parameter should be given the unit, e.g. *V*,*T _{B}*.

- The second mathematical formula (5) should be expressed in time units, i.e. hours. If yes, then right hand side components should be verified, e.g. the first product. Please note that time units in some of the components are expressed in hours, while the others are presented in minutes.

- Taking into consideration the above mentioned comments, formulas (6) and (7) should be verified, as well.

- The units of the parameters presented in equation (9) are not given, and *t _{ij}*is not explained. There is also

*q*explained, but it is not presented in this mathematical formula. The explanation of

_{h}*q*includes

_{TIJ}*Ti*period, which is not given in the mathematical formula (9). What is

*Ti*?

- The Authors mention about the interval between trains (see line 285), while the former considerations are about buses. What is the mathematical model about?

- The explanation of the constraint (15) is not presented.

- The subsection 3.2 starts with the steps of the model solution. Since there are some loops, e.g. step (3) with the option to return to step (2), the scheme of the proposed procedure would help to understand a relationship between steps. Since the Authors propose different tools and algorithms to solve the problem, e.g. Excel (probably Solver) and Genetic Algorithms for different steps, the scheme could also precisely indicate the application of each algorithm.

- The beginning of the model solution on the lower-level is step (1) with the input of the original data. The Authors mention about the probability density function of passenger arrival and bus running time, as well as the passenger waiting cost per unit time. What is the advised period of data collection? How to measure the passenger waiting cost per unit time considered as the input data?

- There are two subsections with the same headings, i.e. “Lower-level programming model solution” (see 3.2.1 and 3.2.2). There are also two subsections 3.2, i.e. *“*Optimization Model of Non-uniform Departure Interval” and “Model Solution”.

- What is the explanation of the statement that left hand side equals right hand side in line 316: “*t _{i}, t_{i1}, t_{i2}, … t_{ih}= T_{i}*” ?

- The Authors mention that “there are 13 vehicle departures (Table 2)” (see lines 353-354), while in Table 2 the number of departures is from 11 to 13.

- Table 4 and 5 show the Chi-Square test statistics for passenger numbers and running time at peak hours, respectively. There are used the same symbols for different measures, e.g. *f _{i}*denotes a real swipe amount of bus passengers in Table 4 and actual number of vehicles in the running time period in Table 5. It can result in a misunderstanding; to avoid this ambiguity each parameter should have its unique symbol.

- The mathematical formulas (17) and (18) should be verified, including the verbal descriptions of nominators and denominators. The obtained values B_{1}and B_{2}are not presented.

- Information presented in Table 7 is not precisely described.

- The manuscript lacks a precise link between the mathematical model presented in section 3 and its application described in section 4.

- The Authors conclude that “The problem of bus line departure frequency andâ€¨scheduling has a positive effect on improving the efficiency of public transportation, reducing operating costs, and promoting the sustainable development of the public transportation system” (see lines 469-471). Could the Authors expand on this thread and point to the results of calculations that support this statement?

Based on the above-mentioned comments a revision of the text should be carried out, including English corrections (punctuation, spelling, grammar), e.g. heading of the 4.2.1 subsection starts with a lower case letter instead of a capital letter; there is a capital letter in the middle of the sentence, e.g. in line 122 „…uncertainty; Problems …”.

*Author Response*

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Author Response File: Author Response.pdf

*Reviewer 2 Report
*

The paper deals with an optimization method of bus departure time based on uncertainty theory.

1. Before submitting a revision be sure that your manuscript is properly prepared and formatted. For example, P8 Line 274 276 , Line 292 Is this sentence completeï¼Ÿ

2. You have mentioned that the uncertain theory has been widely and successfully applied in the fields of transportation and logistics, but the results of using the uncertainty theory to study the bus line allocation problems are few. So, what is the scientific problem to be solved in this article? Uncertain theory is only a method and approach. It is suggested to summarize the contributions in the previous sections.

3. This paper discusses the optimization of the train departure time of the single line, evades many of the core variables of the article, and the model is more ideal. You can read more articles on the same scientific issues in urban rail transit, railway and other major industries.

4. Can you fully consider the coupling factors of passenger travel demand and vehicle scheduling, the location, environment, platform capacity, passenger waiting time and other attributes of the station, and modify the parameters of the modelï¼ŸRelevant papers research in the industry such as “Autonomous Shuttle Bus Service Timetabling and Vehicle Scheduling Using Skip-Stop Tactic.”ï¼Œ“Modelling cascade dynamics of passenger flow congestion in urban rail transit network induced by train delay” and so on. Update references synchronously.

5. A detailed discussion and analysis is very important. It is suggested to add the discussion part of the final conclusion and model parameters, and the design of the discussion part is based on the contribution points of the article.

*Author Response*

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Author Response File: Author Response.pdf

*Reviewer 3 Report
*

In this paper, the authors conducted optimization of the bus departure time using a bus line in the Chinese city of Nanchang based on the uncertainty theory. The paper has an interesting research topic, but not fit for publication in its current form. My recommendation is to return the paper to the authors with an invitation to re-resubmit the paper after major revision.

My specific comments are as follows:

1) Line 35-37: What do you by “vehicle configuration” and “enterprise”? These terms appear to be vague and need to be specified.

2) Line 39: What exactly does “bus configuration” mean? Does it mean the planning of bus routes, bus stops or else?

3) Line 41: Again, the authors used “number of vehicles configured”, which is vague and confusing. The authors need to provide a cleared explanation for “vehicle configuration/vehicle configured” before using these terms repeatedly in the manuscript.

4) Besides, is there any relationship between “vehicle configuration” and “bus line allocation” and “vehicle allocation”? In other words, are these terms refer to the same thing? If so, this needs to be clearly specified and it’s recommended that the authors stick to one term consistently throughout the manuscript instead of using multiple terms referring to the same thing.

5) The authors need to provide more details where to obtain the relevant transit data (i.e., the IC-card data). Is the data open-source? If so, where can readers obtain/download such transit data (for the sake of replicability)?

6) Figure 2: The name of the bus stops should be added. Besides, basic map elements such as north arrow and scale bar should also be added. The authors may also consider dropping many of the irrelevant location names in the map and keep only the essential facilities around the bus lines in order to improve the legibility of the map.

7) Line 151 – 167: No need to cite [15] after every definition, just state at the very beginning of Section 2.1 that all five definitions are based on [15]. Also, add a paragraph at the beginning of Section 2.1 to introduce the purpose of this section. It’s confusing to see five definitions at the very beginning of this section without understanding any purpose for this part.

8) Line 210: How did the waiting time cost per passenger get calculated? The authors need to provide more details here. Besides, studies have monetized the transit travel time cost in the past, which can serve as good reference here (El-Geneidy et al., 2016; Liu and Kwan, 2020). The authors may want to highlight how the proposed methods used in your own paper is similar to/different from these past studies.

· El-Geneidy, A., Levinson, D., Diab, E., Boisjoly, G., Verbich, D. and Loong, C., 2016. The cost of equity: Assessing transit accessibility and social disparity using total travel cost. Transportation Research Part A: Policy and Practice, 91, pp.302-316. https://doi.org/10.1016/j.tra.2016.07.003

· Liu, D. and Kwan, M.P., 2020. Measuring job accessibility through integrating travel time, transit fare and income: a study of the Chicago metropolitan area. Tijdschrift voor economische en sociale geografie, 111(4), pp.671-685. https://doi.org/10.1111/tesg.12415

9) Line 217-233: How were all the costs (e.g., bus parking cost, operating costs) calculated exactly? What are the bases for calculating these costs? Where did the authors obtain the relevant data? More details are required.

10) Section 4.1 Case Introduction: The authors provided the data the number of passengers boarding and getting off each bus stops. However, it’d be interesting to know what kind passengers are mostly using this bus line. Also, it’d also interesting to know the percentage of residents, living within walking distance to the bus stop, that used this line as well as the socioeconomic background the residents (e.g., at the housing neighborhood level) living near those bus stops.

11) Line 352-353: What is the basis for the peak hours (7:00-8:00 a.m. and 17:30-18:30 p.m.) for Bus 207? Any source to support this or it’s based on pure assumption?

12) Line 353: It should be either 7:00-8:00 a.m., and 5:30-6:30 p.m. or 7:00-8:00 and 17:30-18:30. a.m./p.m. only appears in 12-hour clock not 24-hour clock.

13) Line 354-363: The major sites of social activities including schools, hospitals and tourist attractions mentioned in the text (e.g., Nanchang Railway Station; Nanchang No. 14 Middle School; Second People's Hospital; Shengjin Tower) should all be marked in Figure 2 when displaying the bus route so that the readers may understand where exactly those sites are located in relation to the bus route.

14) Line 510-529: In addition to some of the limitations with this study mentioned by the authors, another limitation the authors may want to elaborate upon is social (in)equity and housing along the bus line. First of all, the transit optimization should ultimately serve the interests of the socially vulnerable and improve social inequity. Although this paper is more focused on the methodological side of the transit optimization, it would really help if the authors can bring up the potential implication on social (in)equity of the proposed method. Besides, speaking of social (in)equity, the captive riders of public transport are often middle-to-low-income residents with high-income residents (the choice riders) often choosing to drive to reach various destinations. Housing price/cost is often a good indicator for the income level of residents living there and the probability of residents’ transit utility. Moreover, the optimization of transit location should consider the very people living along the transit lines, which can be relatively accurately reflected by housing costs/prices. There are existing studies that have examined the housing and transit costs (Liu et al., 2021; Renne et al., 2016), which may be used by the authors when elaborating upon this point. Overall, the transit optimization is often a social equity issue that should be discussed along with the housing since they are often intertwined with each other in affecting (in)equity.

· Kramer, A., 2018. The unaffordable city: Housing and transit in North American cities. Cities, 83, pp.1-10. https://doi.org/10.1016/j.cities.2018.05.013

· Liu, D., Kwan, M.P., Kan, Z. and Song, Y., 2021. An integrated analysis of housing and transit affordability in the Chicago metropolitan area. The Geographical Journal, 187(2), pp.110-126. https://doi.org/10.1111/geoj.12377

· Renne, J.L., Tolford, T., Hamidi, S. and Ewing, R., 2016. The cost and affordability paradox of transit-oriented development: A comparison of housing and transportation costs across transit-oriented development, hybrid and transit-adjacent development station typologies. Housing Policy Debate, 26(4-5), pp.819-834. https://doi.org/10.1080/10511482.2016.1193038

15) Finally, the authors should do a thorough proofreading of the entire manuscript before re-submission to avoid unnecessary wording and grammatical issues.

*Author Response*

Please see the attachment.

Author Response File: Author Response.pdf

**Round 2**

*Reviewer 2 Report
*

Please carefully check the English grammar of the manuscript and the use of articles.

*Author Response*

Thank you so much for the comments. We have revised the manuscript according reviewers. The revised manuscript has been resubmitted. We hope the revised paper is now clearer and more useful to researchers and practitioners. Please feel free to contact me if you have any questions. Thanks.

# Question 1: Please carefully check the English grammar of the manuscript and the use of articles.

*Response 2-1: *

Thanks for the reviewer’s comments. We have carefully checked the English grammar of the manuscript and the use of articles. We think the revised paper is now clearer and more useful to researchers and practitioners. The detailed revisions can be seen in the resubmitted manuscript.

*Reviewer 3 Report
*

I appreciate the authors’ efforts in addressing my comments. The revised manuscript has been improved and I am now largely satisfied with authors’ revision. Therefore, I would recommend accepting the paper for publication after doing a thorough proofreading to avoid any wording/grammatical/format issue.

*Author Response*

Thank you so much for the comments. We have done a thorough proofreading carefully, checked the English grammar of the manuscript. We think the revised paper is now clearer and more useful to researchers and practitioners. The detailed revisions can be seen in the resubmitted manuscript. Please feel free to contact me if you have any questions.

Author Response File: Author Response.pdf