Synthetic Demand Flow Generation Using the Proximity Factor
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe article makes a valuable contribution to the development of methodologies for modeling demand flows in logistics networks. The authors present an innovative alternative to the traditional gravity model, eliminating its key limitations such as sensitivity to zero or extreme distance values.
A major strength of the study is its clear comparative analysis of both models, including simulations and tests on real-world data. The results indicate that the proximity factor model is more stable and flexible, particularly in situations with limited access to historical data.
The article's structure is logical, and the methodology is well-justified. The authors present the theoretical foundations of the model and subject it to empirical validation, enhancing its practical value. Additionally, they clearly outline further research directions, making this study a valuable starting point for future analyses in the field of logistics and transportation.
In summary, the article provides a significant new perspective on the problem of synthetic demand flow generation and will undoubtedly serve as a valuable resource for researchers and practitioners engaged in transport and logistics modeling.
Congratulations!
Author Response
Comments 1: The article makes a valuable contribution to the development of methodologies for modeling demand flows in logistics networks. The authors present an innovative alternative to the traditional gravity model, eliminating its key limitations such as sensitivity to zero or extreme distance values.
A major strength of the study is its clear comparative analysis of both models, including simulations and tests on real-world data. The results indicate that the proximity factor model is more stable and flexible, particularly in situations with limited access to historical data.
The article's structure is logical, and the methodology is well-justified. The authors present the theoretical foundations of the model and subject it to empirical validation, enhancing its practical value. Additionally, they clearly outline further research directions, making this study a valuable starting point for future analyses in the field of logistics and transportation.
In summary, the article provides a significant new perspective on the problem of synthetic demand flow generation and will undoubtedly serve as a valuable resource for researchers and practitioners engaged in transport and logistics modeling.
Congratulations!
Response 1: Thank you for your kind comments.
Reviewer 2 Report
Comments and Suggestions for Authors1. The article was not written in accordance with the format of the journal.
2. The introduction needs to clarify the innovation of the proximity factor model, such as how its "non distance dependent sorting mechanism" solves the numerical instability of the gravity model.
3. It is necessary to clarify why the single parameter gravity model (Formula 8) was chosen as the benchmark instead of the multi parameter version, and whether it is due to the comparability of the number of parameters?
4. Does' average distance 'in Formula 5 refer to the theoretical target value or actual observation value? It is necessary to clarify the input data source for the optimization process.
5. Table 3 only tested the upper and lower limits of the average distance. It is recommended to add cases of zero distance or maximum distance to verify the robustness of the model.
6. Table 2 shows that Raleigh's RMSE-P (0.96%) is significantly lower than other cities, and it is necessary to analyze whether this is due to data size, distribution characteristics, or parameter sensitivity.
7. Further exploration is needed to verify the extremely low value of R ²=0.93% in some gravity models, such as whether it is due to distance calculation errors or model structural defects.
8. It is mentioned in the article that the FAF distance is calculated using "ton mile/ton", but later the geometric center distance is used. It needs to be explained whether the difference between the two affects the reliability of the conclusion.
9. There is a gap between the FAF data (2012-2017) and the experimental time (2023), and the impact of data timeliness on model validation needs to be discussed.
10. The conclusion needs to supplement the limitations of the proximity factor model, such as whether it relies on the assumption of uniform distribution or its applicability in multimodal transportation.
Moderate editing of English language in the entire paper
Author Response
Thank you very much for taking time to review and sharing your comments with us.
Comment 1: The article was not written in accordance with the format of the journal.
Response 1: Article is revised to MDPI format.
Comment 2: The introduction needs to clarify the innovation of the proximity factor model, such as how its "non distance dependent sorting mechanism" solves the numerical instability of the gravity model.
Response 2:The following changes have been made on Page 2, Line 37:
This makes it possible to deal with distance values between pairs of points that are zero in the calculation while also not being sensitive to extremes in distance value. This independence from distance is the major innovation of the proximity factor model compared to the gravity model. While the proximity model has been used in several applications, including the design of a public logistics network and to estimate less-than-truckload (LTL) rates, it is not empirically tested and the quality of its results have not investigated.
Comment 3: It is necessary to clarify why the single parameter gravity model (Formula 8) was chosen as the benchmark instead of the multi parameter version, and whether it is due to the comparability of the number of parameters?
Response 3: This is identified at the beginning of Section 2 (Models):
“The proximity factor only uses a single parameter. Thus, we use a single parameter version of the gravity model.” Besides, comparison between a single parameter and multiparameter model requires different sets of data practically making it impossible to compare the two models.
Comment 4: Does' average distance 'in Formula 5 refer to the theoretical target value or actual observation value? It is necessary to clarify the input data source for the optimization process.
Response 4: We used actual distances so the wording is changed to actual distances.
Before: We used the average distance between nodes for our calculations by including a circuity factor.
After: We used the actual average distance between nodes for our calculations by including a circuity factor.
Comment 5: Table 3 only tested the upper and lower limits of the average distance. It is recommended to add cases of zero distance or maximum distance to verify the robustness of the model.
Response 5: In the following portion, where we discussed the “aggregate distance”, we addressed the issue of zero distance and compared a zero distance dataset for gravity and proximity factor model. For the maximum distance case, the below discussion point for future work is added:
A comparison between the two models for maximum distances in the dataset can further solidify the robustness of the proximity factor.
Comment 6: Table 2 shows that Raleigh's RMSE-P (0.96%) is significantly lower than other cities, and it is necessary to analyze whether this is due to data size, distribution characteristics, or parameter sensitivity.
Response 6: Population data points for Raleigh and Atlanta are added to show the differences in population densities in both urban centers.
The following changes are made on Page 10, line 260: This considerable difference shows that the gravity model is biased towards the local demand, whereas the proximity factor distributes the demand evenly in the region. Figure 2 illustrates this phenomenon clearly since the density of the population center is high for Gainesville, FL, and Atlanta, GA. In contrast, the density of the center of Raleigh is low because the center is between the two main population centers, Raleigh, NC, and Durham, NC. Also, we compared the proximity factor and gravity model for the nationwide less-than-truckload (LTL) shipments.
Comment 7: Further exploration is needed to verify the extremely low value of R ²=0.93% in some gravity models, such as whether it is due to distance calculation errors or model structural defects.
Response 7: Explanation added on Page 13, line 373:
The main reason for the differences between R2 and RMSE values might be the distance calculation. Hence, we wanted to explore different distance calculations to give the gravity model a better chance.
Comment 8: It is mentioned in the article that the FAF distance is calculated using "ton mile/ton", but later the geometric center distance is used. It needs to be explained whether the difference between the two affects the reliability of the conclusion.
Response 8: Since we could not find a clear explanation of how the ton-mile was calculated, we calculated the distance by conventional means using geospatial coordinates and outlined the outputs. The results were similar to our previous findings. They can be found in pages 13-14 lines 375-387.
Comment 9: There is a gap between the FAF data (2012-2017) and the experimental time (2023), and the impact of data timeliness on model validation needs to be discussed.
Response 9: Experiments were done in 2021, and the most recent data available at that time was in 2017.
Comment 10: The conclusion needs to supplement the limitations of the proximity factor model, such as whether it relies on the assumption of uniform distribution or its applicability in multimodal transportation.
Response 10: Added this on Page 15, line 428: In certain instances where distance between O-D pairs might play a huge role in determining the flow density (multi-modal applications, possibly), then the gravity model could be preferable over the proximity factor due to gravity model's reliance on distance.
Reviewer 3 Report
Comments and Suggestions for AuthorsThe paper gives an important contribution to the logistics modeling by providing a more powerful methodology for demand flow estimation. Its property of not requiring any historical data to work makes the proximity factor model very suitable for new network designs. Further statistics validations and discussion of model limitations, as well as comparisons with other methods, are needed to boost the impact of the study.
Suggestions for Improvement:
- Clarification of Conceptual Differences:
The limitations of the gravity model are discussed in the paper, yet more intuitive reasoning as to why the proximity factor is empirically favored could contribute enormously toward reaching an audience outside of the academia.
It would further enhance the reader's understanding if a visual comparison, such as a diagram, were presented to illustrate how proximity factor and the gravity model distribute demand differently. - A More Extensive Statistical Analysis:
In addition to the root mean square error (RMSE) that has been used for validation, use of other statistical metrics (MAPE, R² values) would only strengthen the argument of reliability of the proximity factor model.
While the correlation analysis of Figure 4 indicates poor correlation between the models, further statistical interpretation would enhance the meaning of this finding. - Consideration of Limitations for Proximity Factor:
A claim is made concerning the model's reliability, but there is no minor discussion of its weaknesses.
When would the gravity model be preferable?
How does the method hold up in scenarios with sparse datasets or where distance may not be the primary factor influencing demand flow? - Comparability with Other Alternative Models:
The research primarily contrasts the proximity factor with the one-parameter gravity model. Recent developments like the radiation model are mentioned but not examined in detail.
It would be useful to compare with other data-driven approaches, like machine learning-based demand estimation models. - Editing and Readability Improvements
Some sentences required clarifications. For example, there is a sentence given in the introduction, which states that:
"The design of logistics networks involves forecasting the demand flows between all pairs of points in the network, which is one of the most challenging factors."
It would be better rephrased as:
"It is a challenge of logistics network design to predict demand flows between points."
Some minor grammatical and awkward phrase usages could be refined for clarity.
Comments on the Quality of English LanguageSome minor grammatical and awkward phrase usages could be refined for clarity.
Author Response
Thank you very much for taking time to review the article.
Comment 1: Clarification of Conceptual Differences:
The limitations of the gravity model are discussed in the paper, yet more intuitive reasoning as to why the proximity factor is empirically favored could contribute enormously toward reaching an audience outside of the academia.
It would further enhance the reader's understanding if a visual comparison, such as a diagram, were presented to illustrate how proximity factor and the gravity model distribute demand differently.
Response 1: The following changes have been made on Page 2, Line 37:
This makes it possible to deal with distance values between pairs of points that are zero in the calculation while also not being sensitive to extremes in distance value. This independence from distance is the major innovation of the proximity factor model compared to the gravity model. While the proximity model has been used in several applications, including the design of a public logistics network and to estimate less-than-truckload (LTL) rates, it is not empirically tested and the quality of its results have not investigated.
Comment 2: A More Extensive Statistical Analysis:
In addition to the root mean square error (RMSE) that has been used for validation, use of other statistical metrics (MAPE, R² values) would only strengthen the argument of reliability of the proximity factor model.
While the correlation analysis of Figure 4 indicates poor correlation between the models, further statistical interpretation would enhance the meaning of this finding.
Response 2: R^2 is already mentioned in the paper. Wording was added to highlight the results: Our analysis concluded that the proximity factor was superior to the gravity model. R^2 values indicate that the proximity factor could explain 59.19% of the variation in data, whereas the gravity model is in the range of 0.93%.
Further analysis is added into the Appendix section.
Comment 3: Consideration of Limitations for Proximity Factor:
A claim is made concerning the model's reliability, but there is no minor discussion of its weaknesses.
When would the gravity model be preferable?
How does the method hold up in scenarios with sparse datasets or where distance may not be the primary factor influencing demand flow?
Response 3: Added this in Page 15 line 428: In certain instances where distance between O-D pairs might play a huge role in determining the flow density (multi-modal applications, possibly), then the gravity model could be preferable over the proximity factor due to gravity model's reliance on distance.
Comment 4: Comparability with Other Alternative Models:
The research primarily contrasts the proximity factor with the one-parameter gravity model. Recent developments like the radiation model are mentioned but not examined in detail.
It would be useful to compare with other data-driven approaches, like machine learning-based demand estimation models.
Response 4: We did an analysis of the radiation model at the beginning of our project. However, the results were not at the same level of accuracy as the gravity or the proximity factor model due to its bias towards shorter distances. Hence, we decided not to add it to the paper. We outlined this in the paper by adding these sentences on page 2, line 75:
However, the radiation model also lacks the accurate computation of human mobility at the city (or micro) scale. Our analysis of the radiation model further proved this to be true. The results were incomparable to either the gravity model or the proximity factor; hence, we opted not to include them in this paper. Other factors such as segregation and commercial/residential space distinction are primary drivers of population mobility in a city setting.
Comment 5: Editing and Readability Improvements
Some sentences required clarifications. For example, there is a sentence given in the introduction, which states that:
"The design of logistics networks involves forecasting the demand flows between all pairs of points in the network, which is one of the most challenging factors."
It would be better rephrased as:
"It is a challenge of logistics network design to predict demand flows between points."
Some minor grammatical and awkward phrase usages could be refined for clarity.
Response 5: Following sentence is added to the introduction: It is a challenge of logistics network design to predict demand flows between points.
Further revision of the language used in this paper is conducted per reviewer's request.
Round 2
Reviewer 2 Report
Comments and Suggestions for AuthorsThe authors have invested a substantial effort to address all issues from the previous review round, thus significantly improving the quality of their paper. Therefore, I suggest acceptance of the paper in its present form.
Reviewer 3 Report
Comments and Suggestions for AuthorsThe author has implemented all my recommendations
Comments on the Quality of English LanguageThe author has implemented all my recommendations
