Sustainable Time-Dependent Cheapest Path Problem with Integrated Collaborative Stakeholders’ Perspectives

Round 1

Reviewer 1 Report

The main content of this paper is to introduce a sustainable time-dependent shortest and cheapest path planning problem, and propose a modified cost function and an integrated multi-standard decision-making method to solve the problem. The paper also demonstrates the applicability of the method through two practical cases and the improved Dijkstra algorithm.

The salient points of this paper include: First, a novel problem is proposed, which takes sustainability-related costs as a variable element in path planning and integrates them into the cost function. Second, a multi-criteria decision-making method is used to balance the importance of different variable cost elements, and the flexibility and applicability of the method are enhanced. Thirdly, the feasibility and effectiveness of the method are demonstrated through practical cases and algorithms. The article can be improved in the following areas: First, when introducing the problem and methodology, the background of the problem and the importance of practical application can be explained more clearly, so that readers can better understand the motivation and significance of the research. Second, in the actual case, more case details and result analysis can be provided to further verify the effectiveness and applicability of the method. Thirdly, in the discussion, the limitations of the method and potential improvement directions can be explored in more depth, so that readers can better understand the limitations of the method and the direction of future research.

The literature review may be improved by citing more relevant papers. Just list several as follows.

Ship imaging trajectory extraction via an aggregated you only look once (YOLO) model

A hybrid visualization model for knowledge mapping: scientometrics, SAOM, and SAO

Overall, the article proposes an interesting and promising approach to solving the problem of sustainable pathway planning, and demonstrates its feasibility through practical examples. However, there are some aspects that could be further improved and explored.

Good

Author Response

Reviewers

Sustainability journal

April 16, 2024

Sustainable Time-Dependent Cheapest Path Problem with integrated collaborative stakeholders’ perspective

Dear Reviewers,

We are pleased to resubmit for publication the revised version of “Sustainable Time-Dependent Cheapest Path Problem with integrated collaborative stakeholders’ perspective”. We thank Editors and the Reviewers for interest in our work and for helpful comments that will greatly improve the manuscript. We have tried to do our best to respond to the points raised. The Reviewers have brought up some good points and we appreciate the opportunity to clarify our research objectives and results.

As indicated below, we have checked all the general and specific comments provided and have made necessary changes accordingly to their indications.

Reviewer #1:

“The main content of this paper is to introduce a sustainable time-dependent shortest and cheapest path planning problem, and propose a modified cost function and an integrated multi-standard decision-making method to solve the problem. The paper also demonstrates the applicability of the method through two practical cases and the improved Dijkstra algorithm.

The salient points of this paper include: First, a novel problem is proposed, which takes sustainability-related costs as a variable element in path planning and integrates them into the cost function. Second, a multi-criteria decision-making method is used to balance the importance of different variable cost elements, and the flexibility and applicability of the method are enhanced. Thirdly, the feasibility and effectiveness of the method are demonstrated through practical cases and algorithms. The article can be improved in the following areas: First, when introducing the problem and methodology, the background of the problem and the importance of practical application can be explained more clearly, so that readers can better understand the motivation and significance of the research.”

Thank you for this feedback. We have updated the manuscript, hopefully to provide more context and highlight the importance of practical application in more details. Among others, this is reflected the updated text:

“… However, the above-mentioned research mainly considers time variable cost as travel time, emissions and/or monetary cost, separately while the potential to involve diverse stakeholders in the assessment of the overarching cost estimation could be of an added value. The latter might particularly be relevant in supporting various co-creation aspects, integration of citizen initiatives outcomes and potentially enhancing the societal aspects of route sustainability [5,7,48,49]. Hence, in this paper we explore in more detail the possibility to modify adaptive route planning to integrate route sustainability into arc traversal cost that varies over time. Integration of the route sustainability is based on the adoption of multi-criterial decision-making to evaluate sustainability cost in regard to the route’s spatial and temporal context. Next to this, we test the performance of the suggested adaptive route planning approach on road network where the route’s spatial context is extracted from traffic sign database….

“Second, in the actual case, more case details and result analysis can be provided to further verify the effectiveness and applicability of the method.”

Thank you for this feedback. We have now complemented the existing text with more details regarding the case, particularly in the aspects of model complexity and results analysis. This is also, hopefully, reflected in the manuscript modifications including the descriptions provided below:

“… Furthermore, while the computational complexity of the original Dijkstra's algorithm is where  indicates the number of vertices and of arcs, for the modified Dijkstra algorithm, where FIFO property is satisfied, the complexity is where the  represents the maximum number of time intervals considered… “

“ The results show that routing time-dependency and route sustainability can be successfully modelled using the suggested approach. Furthermore, the obtained alternative route suggestion was rendered as acceptable solution to all stakeholder, highlighting possibility to integrate conflicting perspectives to navigate jointly towards a solution. This is particularly illustrated in the fact that the suggested solution resulted in a bit longer route (conflicting the interest of the logistics service provider) and that it did not forcibly avoid all locations with high sustainability cost (e.g., one school was visited). Nonetheless, the solution acceptable to all was found (including the school, that was itself a delivery location, where a prolonged working hours were avoided and compromise to receive deliveries during the school hours but avoiding the school star and end times was achieved). Moreover, the suggested approach is adaptable across various domains and/or stakeholders, as the relative importance of the sustainability elements can be reconsidered in light of the organization(s) and local specific context.”

“Thirdly, in the discussion, the limitations of the method and potential improvement directions can be explored in more depth, so that readers can better understand the limitations of the method and the direction of future research.”

Thank you for this feedback. The revised manuscript now contains explanation regarding the potential improvements and limitations as follows:

“In addition, in certain dynamic contexts, e.g., change of the geospatial characteristics (e.g., new educational facility is open) or the type of sustainability cost that was not relevant for a given community so far is introduced (e.g., new urban blue/green area), this might require revisiting the results of pairwise comparisons among the stake-holders over time. Which is an repetitive step that might be good to consider to be conducted in any case in a circular manner (e.g., every 5 to 10 years) to make sure that the assessment reflect well the attitudes of different stakeholders towards sustainability. Furthermore, while the availability of verified spatial routing context data may pose limitations in certain areas, it is anticipated that the availability of such, and sim-ilar, data sources will proliferate in the near future. Next to this, regular updating and verification of these data sources might pose a challenge and preferably an automated manner to do so would be a valuable to consider. In addition, to draw broader conclusions regarding the acceptability of sustainability-related costs in the total route cost, it would be advantageous to evaluate the proposed approach across a more extensive array of use cases encompassing a diverse set of sustainability elements. Moreover, exploring the applicability of the adaptive routing approach beyond urban settings, or within broader city areas, could potentially be an intriguing avenue for future research. “

“The literature review may be improved by citing more relevant papers. Just list several as follows.

Ship imaging trajectory extraction via an aggregated you only look once (YOLO) model

A hybrid visualization model for knowledge mapping: scientometrics, SAOM, and SAO

Overall, the article proposes an interesting and promising approach to solving the problem of sustainable pathway planning, and demonstrates its feasibility through practical examples. However, there are some aspects that could be further improved and explored..”

The revised manuscript includes updated literature review, with some additional sources included, and additional contextualisation of the proposed research. In this context, we retained from expanding the literature review to other transportation modes, as this would require broad review to ensure that potential context across all transport modes is included. However, we will consider in our future research preparing an literature review paper where this broader context could be reflected in an appropriate and systematic manner.

Additional literature references include, among others:

45. Kilani, M.; Proost, S.; Van Der Loo, S. Road Pricing and Public Transport Pricing Reform in Paris: Comple-ments or Substitutes? Economics of Transportation 2014, 3, 175–187, doi:10.1016/j.ecotra.2014.04.003.
46. Lindsey, R. Road Pricing and Investment. Economics of Transportation 2012, 1, 49–63, doi:10.1016/j.ecotra.2012.07.001.
47. Fransen, K.; Versigghel, J.; Guzman Vargas, D.; Semanjski, I.; Gautama, S. Sustainable Mobility Strategies Deconstructed: A Taxonomy of Urban Vehicle Access Regulations. Eur. Transp. Res. Rev. 2023, 15, 3, doi:10.1186/s12544-023-00576-3.

We appreciate your careful evaluation of our work and hope that this revision meets with your approval. We have included both the revised manuscript and a “compare documents” version that highlights the changes from the original submission.

Thank you again for your interest in our work. We await your review of our revised manuscript.

Sincerely yours,

Authors

Reviewer 2 Report

1. In the abstract, innovation needs to be highlighted.

2. “Decision-making approach” is better instead of “Decision-making approach”.

3. The layout of the article needs to be noted, as some pages have a lot of blank space

4. Line 334 has wrong spellings.

5. Line 445 has bold font.

6. The t_ns in the first row of Table 2 is centered

Minor editing of English language required

Author Response

Reviewers

Sustainability journal

April 16, 2024

Sustainable Time-Dependent Cheapest Path Problem with integrated collaborative stakeholders’ perspective

Dear Reviewers,

We are pleased to resubmit for publication the revised version of “Sustainable Time-Dependent Cheapest Path Problem with integrated collaborative stakeholders’ perspective”. We thank Editors and the Reviewers for interest in our work and for helpful comments that will greatly improve the manuscript. We have tried to do our best to respond to the points raised. The Reviewers have brought up some good points and we appreciate the opportunity to clarify our research objectives and results.

As indicated below, we have checked all the general and specific comments provided and have made necessary changes accordingly to their indications.

Reviewer #2:

 “1. In the abstract, innovation needs to be highlighted.”

Thank you for this suggestion. The abstract is now updated to reflect in more details the suggested contribution and innovation of this manuscript by including the explanation as follows:

 “…To address this issue, the paper suggests twofold contribution. First, we describe the Sustainable Time-Dependent Cheapest Path Problem and define complex cost function, that based on the multi-criteria decision-making approach integrates views of different stakeholders and sustainability elements into route cost calculation. Second, we show that the modified problem satisfies FIFO (First-in-First-Out) property and demonstrate the applicability of the suggested approach on real-life scenario where route sustainability is extracted from the traffic sign information system available in Flanders, Belgium. “

2. “Decision-making approach” is better instead of “Decision-making approach”.

Thank you for this suggestion. The manuscript is now updated and only “Decision-making approach” is used across the text.

3. The layout of the article needs to be noted, as some pages have a lot of blank space

Thank you for this feedback. We have updated the manuscript layout and are very much open to the updating it in addition before the (hopefully) publication, as per suggestions from the editorial team on the improved formation and the final layout.

4. Line 334 has wrong spellings.

Thank you for noting this. It is now corrected.

5. Line 445 has bold font.

Thank you for noting this. It is now corrected.

6. The tns in the first row of Table 2 is centered”

Thank you for noting this. It is now corrected.

We appreciate your careful evaluation of our work and hope that this revision meets with your approval. We have included both the revised manuscript and a “compare documents” version that highlights the changes from the original submission.

Thank you again for your interest in our work. We await your review of our revised manuscript.

Sincerely yours,

Authors

Author Response File: Author Response.pdf

Reviewer 3 Report

Report on

Sustainable Time-Dependent Cheapest Path Problem with integrated
collaborative stakeholders’ perspective

Main comment
=============

The analysis is related to the development of route optimization
that takes into account sustainability. This is motivated by the
fact that different stakeholders can have different evaluation of
the transport cost. Some examples are given to make a link with
real life.

I find an ambiguity, however, how the authors set this research
question. More precisely, all that is described as road
sustainability (Lines 175-183 or 305-314) can be handled as
constraints using standard optimization techniques.

I think that the authors should be rigorous in setting the
objective of their research and how it addresses questions that
cannot be dealt with (or is less difficult or yields better
results) using other standard techniques.

Furthermore, the main problem looks similar to what is discussed
in the (large) literature on road pricing, in particular when I
try to comment on Figure 2 (left panel):

- Lindsey, R. (2012). Road pricing and investment. Economics of
  transportation, 1(1-2), 49-63.

- Kilani, M., Proost, S., & Van der Loo, S. (2014). Road pricing
  and public transport pricing reform in Paris: complements or
  substitutes?. Economics of Transportation, 3(2), 175-187.


Further points
==============

- Line 160: space after period
- Sentence over lines 174 and 175. Check punctuation.
- What values can take d_ij in Eq. (7); usually in transportation
  problems, d_ij is used to denote distance between an origin and
  a destination.
- In Fig. 1b, there are multiple alternative paths yielding the
  same distance. For example, the one in Fig 1d (as noticed by
  the authors)
- Definitely two graphs are enough to illustrate the
  point in Fig. 1 (no need for four panels)
- Can something be said on the convergence and speed of
  Algorithm in Fig.3 (as a function of the number of nodes and
  links in the network)
- In Fig. 9, the y-axis, values below 8000 do not seem to be
  useful; that can make the graph better.:w

Overall, it is OK

Author Response

Reviewers

Sustainability journal

April 16, 2024

Sustainable Time-Dependent Cheapest Path Problem with integrated collaborative stakeholders’ perspective

Dear Reviewers,

We are pleased to resubmit for publication the revised version of “Sustainable Time-Dependent Cheapest Path Problem with integrated collaborative stakeholders’ perspective”. We thank Editors and the Reviewers for interest in our work and for helpful comments that will greatly improve the manuscript. We have tried to do our best to respond to the points raised. The Reviewers have brought up some good points and we appreciate the opportunity to clarify our research objectives and results.

As indicated below, we have checked all the general and specific comments provided and have made necessary changes accordingly to their indications.

Reviewer #3:

“Main comment

The analysis is related to the development of route optimization that takes into account sustainability. This is motivated by the fact that different stakeholders can have different evaluation of the transport cost. Some examples are given to make a link with real life.

I find an ambiguity, however, how the authors set this research question. More precisely, all that is described as road sustainability (Lines 175-183 or 305-314) can be handled as constraints using standard optimization techniques.

I think that the authors should be rigorous in setting the objective of their research and how it addresses questions that cannot be dealt with (or is less difficult or yields better results) using other standard techniques.

Furthermore, the main problem looks similar to what is discussed in the (large) literature on road pricing, in particular when I try to comment on Figure 2 (left panel):

- Lindsey, R. (2012). Road pricing and investment. Economics of   transportation, 1(1-2), 49-63.

- Kilani, M., Proost, S., & Van der Loo, S. (2014). Road pricing   and public transport pricing reform in Paris: complements or   substitutes?. Economics of Transportation, 3(2), 175-187.”

We thank you for this comment and for highlighting the possibility to clarify our research and its applicability in more details. We have updated the manuscript’s literature review to include the mentioned papers and have updated the text to provide more clarity in several occasions. Hence, the updated manuscript now includes the addition of the following explanations regarding the differentiation from some of the known measures and strategies with the suggested one, including:

“… Furthermore, departing from route planning, other approaches have also been considered across the literature on how different measures and strategies can be implemented to manage road use and the various impacts that these strategies might have. Some examples include road pricing and diverse vehicle access regulations [45–47]. However, the above-mentioned research mainly considers time variable cost as travel time, emissions and/or monetary cost, separately while the potential to involve diverse stakeholders in the assessment of the overarching cost value could be of an added value. The latter might particularly be relevant in supporting various co-creation aspects, integration of citizen initiatives outcomes and potentially enhancing the societal aspects of routing sustainability [5,7,48,49]. Hence, in this paper we explore in more detail the possibility to modify adaptive route planning to integrate route sustainability into arc traversal cost that varies over time. Integration of the route sustainability is based on the adoption of multi-criterial decision-making to evaluate sustainability cost in regard to the route’s spatial and temporal context. Next to this, we test the performance of the suggested adaptive route planning approach on road network where the route’s spatial context is extracted from traffic sign database…”

“… . However, rather than regarding these as one sided decisions and “hard constrains”, imposed by one stakeholder, we consider sustainability cost as composition of different elements …

… and suggest integrating it in the overall cost calculation based on the joint perspective of various stakeholders. Hence, taking into account the different stakeholders’ views in the routing process, for example, regarding the acceptability of available routing alternatives or sustainability cost for different spatial and temporal contexts, we suggest the adoption of a decision-making approach when determining the sustainability cost...”

As well as:

“… Surely, if one has only quantitative parameters, like a community that charges passing through the pedestrian area for goods vehicles between 8-10h, 10 Euros per vehicle, and only one stakeholder as city administration, then the complete problem is simplified and only path’s length (in our case, the non-time dependable part of the route’s cost) needs to be recalculated in monetary units and the problem can be summarized to obtain the route’s cost. Another borderline example is to place traffic signs that forbid goods vehicles to enter specific zones, such as school areas, within the community. Such a solution would require, in the suggested approach, setting the sustainability cost for affected arcs to +∞ or, simply, considering the subgraph of the not affected arcs for the routing problem. However, such measures in real life exhibit a lack of flexibility, whereas the suggested approach looks at both the time of delivery and possible route alternatives. Hence, it first looks for an option where companies can still perform their activities in a manner that is acceptable for the community (as they do deliver goods to the community) and leaves more extreme conflict resolution measures as possible, but last considered, solution. Furthermore, the time-dependability of the TDCPP is a consequence of daily changes in the community during different time periods of a day, and more realistically describes real life urban conditions than traditional CPP approaches…”

“Further points

- Line 160: space after period”

Thank you for noting this. It is now corrected.

“- Sentence over lines 174 and 175. Check punctuation.”

Thank you for noting this. It is now corrected.

“- What values can take d_ij in Eq. (7); usually in transportation   problems, d_ij is used to denote distance between an origin and  a destination.”

Thank you for this feedback. Indeed, variable  can often be used to denote distance, destination location or other parameters. However, in our case, since we use decision making process the  is related to the decision variable and defined as follows:

“…Subsequently, decision-makers conduct pairwise comparisons between the elements at each level of the hierarchy relative to the next higher level. These comparisons are conducted utilizing the Saaty scale of importance [55], enabling the conversion of qualitative assessments into quantitative metrics using a numerical scale spanning from 1 to 9. Hence, each of the comparison matrices assumes the form:

where  corresponds to the pairwise comparison, within the same hierarchy level, for element  and . This matrix has positive entries everywhere and satisfies the reciprocal property ..”

We have also now added additional explanation, that clarifies the values that  can take as, based on the Saaty scale of importance, are always positive and range from 1 to 9 (and due to the symmetry as a result of the comparison consistency, values from 1/9 to 1 ). We also provide additional reference to the Saaty scale of importance so that the interested readers can explore this topic further.

“- In Fig. 1b, there are multiple alternative paths yielding the   same distance. For example, the one in Fig 1d (as noticed by  the authors)

- Definitely two graphs are enough to illustrate the   point in Fig. 1 (no need for four panels)”

Thank you for noting this. It is updated now.

“- Can something be said on the convergence and speed of  Algorithm in Fig.3 (as a function of the number of nodes and links in the network)”

Thank you for this feedback. The manuscript has been updated to include additional explanations regarding the complexity and the speed of the utilised algorithm, as per your comment, including explanations:

“… This problem has a well-known solution: Dijkstra’s algorithm [50]. Dijkstra’s algorithm processes vertices in increasing order of cost from  and stops when  is reached, resulting in a worst-case scenario running time on a graph with  vertices and  arcs to be ...”

“… Furthermore, while the computational complexity of the original Dijkstra's algorithm is where  indicates the number of vertices and of arcs, for the modified Dijkstra algorithm, where FIFO property is satisfied, the complexity is where the  represents the maximum number of time intervals considered… “

“- In Fig. 9, the y-axis, values below 8000 do not seem to be   useful; that can make the graph better.:w “

Thank you for this feedback. The figure has been updated to exclude the lower values from the visualisation.

We appreciate your careful evaluation of our work and hope that this revision meets with your approval. We have included both the revised manuscript and a “compare documents” version that highlights the changes from the original submission.

Thank you again for your interest in our work. We await your review of our revised manuscript.

Sincerely yours,

Authors

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

The authors set a graph optimization problem with a complex structure of the cost function (dependent on stakeholders views) and propose an algorithm to solve it. A case study is conducted. The main limitation of the methodology, I think, is the subjectivity related to observing and affecting weights to these costs. Apart this problem (which may deserve a comment in the conclusion), the result sound useful for the literature with good opportunities for other applications.

The revised version answered most of the issues I have raised. I think that the paper can be accepted for publication after a last text check.

Small points:

- the paragraph that extends from line 79 to line 143 should be split in two or three paragraphs at least.

- the definition of x_ij in lines 152-154 is redundant.

OK

Author Response

Dear Reviewer,

Thank you for providing your feedback and review of our manuscript.

We apricate your time and effort invested in this process and contribution that your constructive comments have made towards the final version of our manuscript.

We have integrated your suggestions into the revised version of the manuscript.

With kind regards,

Authors

Author Response File: Author Response.pdf