Local Search Heuristic for the Two-Echelon Capacitated Vehicle Routing Problem in Educational Decision Support Systems

Thank you very much for taking the time to review this manuscript and suggestions regarding our article. Your thorough analysis has significantly contributed to the improvement of our work. Please find the detailed responses below and the corresponding revisions/corrections highlighted/in track changes in the re-submitted files.

Point-by-point response to Comments and Suggestions for Authors

Comments 1: The concept of “Last Mile” is mentioned in the introduction but not fully discussed. Please define and explain this concept for non-expert readers.

Response 1: Thank you for pointing this out. To better explain this to the readers, in the introduction, second paragraph, line 29, we changed the term “last mile” to “the final delivery stage, often referred to as the last mile.”

Comments 2: The explanation of the conceptual model of the 2E-CVRP should not be included in the literature review section. Please reorganize this section accordingly.

Response 2: Thank you for your comments. To introduce the concept of the 2E-CVRP, we explored its mechanics a bit more in the Introduction, paragraph 2, lines 30 to 36.

Comments 3: In Section 2, you state: “These approaches successfully tackle problems involving up to 5 satellites and 50 customers for the first group, and 15 satellites with 300 customers for the second group, with an average computational time of one hour.” However, you refer to a 2009 study for the branch-and-cut algorithm. Are you certain this is the most recent application of branch-and-cut for solving the 2E-CVRP? Please confirm or update the reference.

Response 3: Thank you for your comments. There are some other more contemporary works, such as Liu et al. (2018) [https://doi.org/10.1016/j.ejor.2017.10.017], which we included in the body of the text. However, these studies remain limited to 5 satellites and 50 clients; that is, they have evolved significantly in technique, but are not sufficient to solve larger problems. Additionally, some of them do not indicate computational time, which we know from the NP-hard nature of the problem is very lengthy.

Comments 4: The sentence: “Another category of strategies encompasses local search heuristics, constructive heuristics, and genetic algorithms. However, similar to exact algorithms, many of them tend to be very time consuming for Decision Support Systems (DSSs)” requires references from the literature to support these claims.

Response 4: Thank you for your comments.

The main heuristics reviewed in this work are focused, assertively, on solving the 2E-CVRP with the aim of getting as close to the optimal solution as possible, without considering the time needed to achieve that end. However, in our work, we are operating within the context of decision support systems, where the decision-maker or student, in our case, must evaluate various scenarios. Therefore, the solution provided by the heuristic must be very fast while ensuring that the solution quality is competitive with other heuristics. Thus, as presented in paragraph 3 of the introduction, lines 45 to 47, heuristics that take longer than the established time limit to solve real-scale problems are unviable for a DSS.

To provide better clarification on this, we modified the cited paragraph (4th paragraph in the Literature Review, lines 82 to 85) to: “Other categories of strategies, discussed below, include local search heuristics, constructive heuristics, and genetic algorithms. However, similar to exact algorithms, it is noted that many of them tend to take a long time to reach their final results, sometimes extending to hours, making them unfeasible for use in Decision Support Systems (DSSs).”

Comments 5: The phrase “involves research where a chromosome serves as a solution to the problema” is unclear and awkwardly phrased. Please revise it for clarity.

Response 5: Thank you for your comments.

In genetic algorithms, chromosomes can be modeled in various ways, and the paragraph aims to explain the main approaches for doing so. For better clarity, we have revised it (5th paragraph of the Literature Review, lines 86 to 92) to: “The use of Genetic Algorithms (GAs) in the context of 2E-CVRP involves research that models the chromosome in various ways. The main approach is to use chromosomes that represent a complete solution to the problem [15], with each gene representing a route from the First (FE) or Second (SE) echelon. Another approach considers a complete solution as an individual composed of several chromosomes [16], where each chromosome symbolizes a route, and its genes correspond to the nodes of the problem. An extra chromosome is introduced to establish connections between the chromosomes of the FE and SE.”

Comments 6: Line 88: The sentence “These works [which works? avoid the use of demonstratives to take for granted what you are referring to in scientific texts], along with [16] and [17] [add surnames of the authors. Numbers between brackets are not nouns. Correct this error throughout the text]” needs to be revised for proper scientific writing. Avoid using demonstrative pronouns without clarification, and always provide the names of the authors when citing.

Response 6: Thank you for your comments.

We have revised the text of the paragraph (6th in the Literature Review, 93 to 95) to: “In addition, various constructive heuristics are used to build the initial population of a GA[17, 18], and the process of selecting individuals for reproduction includes techniques such as Random Selection, Tournaments, Roulette, and Best Fitness.”

Comments 7: Please review the English in this phrase: “the where for satellites with a cumulative demand greater than the capacity of the first-echelon vehicles (FE)” (line 177).

Response 7: Thank you for your comments.

For better clarity and accuracy of the text, we made the following adjustment to paragraph 2 of the subsection: “Constructive Heuristic” in the section “Materials and Methods”, lines 182 to 185: We have revised the text from: “the where for satellites with a cumulative demand greater than the capacity of the first-echelon vehicles (FE), direct routes from the depot to the satellites are created.” to “In this procedure, after assigning the demands that will be finalized by each satellite, any that have a total demand greater than the capacity of the first-echelon vehicles (FE) will have direct routes with a fully loaded vehicle from the depot to the satellites.”

Comments 8: In line 194, you mention: “, in the format [s, c1, c2, c3, s, c4, c5, s, c6, c7, s].” However, these elements (c1, c2, c3, etc.) are not introduced earlier in the text, so the sentence lacks context for the reader. Please clarify.

Response 8: Thank you for your comments.

We revised this example using the full titles for better clarity: satellite, customer_1, customer_2, ..., in paragraph 1 of the subsection “Local Search Heuristic” in the section “Materials and Methods.”, lines 200 to 201.

Comments 9: Tables 1-3 report the average performance of your heuristic. However, if the distribution of the results is non-parametric, the average may not be a representative central metric. To provide a more accurate depiction of your heuristic's performance, consider adding a dispersion metric, such as the standard deviation for parametric data or the interquartile range for non-parametric data. For guidance on comparing random heuristics, you may refer to this work: http://dx.doi.org/10.3934/mbe.2021470.

Response 9: Thank you for your comments.

Since our instances and heuristic are deterministic, we chose to keep the results in the current format. However, we changed the text from "Avg." to "Heur." in the three tables to represent it correctly.

Comments 10: Finally, the data from the case study should be uploaded to an online repository to enhance transparency and reproducibility.

Response 10: Thank you for your comments.

Unfortunately, we do not have the company's permission to make the data public.

Thank you very much for taking the time to review this manuscript and suggestions regarding our article. Your thorough analysis has significantly contributed to the improvement of our work. Please find the detailed responses below and the corresponding revisions/corrections highlighted/in track changes in the re-submitted files.

Point-by-point response to Comments and Suggestions for Authors

Comments 1: « This study focuses on developing a heuristic for Decision Support Systems (DSS) in e-commerce logistics education, addressing the Two-Echelon Capacitated Vehicle Routing Problem 2 (2E-CVRP). « 

1.       So, the goal of the research and the paper is to develop a decision making tool, but for what ? Why « logistics education »  ? It is clear from the title and introduction that the problem is about optimal route planning and not education ;

Response 1: Thank you for pointing this out. The title of the work has been changed to "Local Search Heuristic for the Two-Echelon Capacitated Vehicle Routing Problem in Educational Decision Support Systems" and the objective of the work is to develop a heuristic that is fast and accurate for use in DSSs, rather than the development of the DSS itself. Additionally, for better clarification, paragraph 3 of the introduction has been adjusted.

Comments 2: « The rapid growth of e-commerce has heightened urban logistics challenges, requiring innovative solutions for efficient parcel delivery, particularly in major urban areas. « 

2.        Have the authors developed a route optimization tool that is tailored to the specifics of e-commerce? Moreover, due to the “development of e-commerce”, new problems arise that require no/new solutions, because the existing ones are no longer sufficient? So what do these new solutions offer? What did the previously used ones lack?

Response 2: Thank you for your comments.

The heuristic developed in this work is capable of solving 2E-CVRP problems, such as mail delivery, e-commerce, or any other type of delivery process in large urban centers that require multiple deliveries to many customers; that is, the vehicle needs to make several stops on its routes. Our work focuses specifically on e-commerce, as it is currently the most notable example of 2E-CVRP application. Despite this, we added this extra information to the first paragraph of the introduction, lines 19 to 21, for better clarity.

Comments 3: « The 2E-CVRP involves using Urban Transshipment Points (UTPs) to optimize deliveries. To tackle the complexity of the 2E-CVRP, Decision Support Systems (DSS) with fast and effective techniques can be employed for visual problem-solving. »

3.        Is visualization this particular innovation?

Response 3: Thank you for your comments.

The visualization process that the DSS enables greatly facilitates decision-making for a decision-maker, or in the case of our study, students in logistics, allowing for an immediate solution to a logistics network. However, for optimal functioning, the DSS requires fast algorithms, preferably instantaneous ones, while maintaining the quality of the solutions as much as possible. This is quite complex when dealing with challenging problems like routing. Therefore, the objective of this work is the development of this algorithm.

Comments 4:  Why was it necessary to use heuristics? Didn't previous methods use heuristics?

Response 4: Thank you for your comments.

Existing solutions to the problem, evaluated in this work, focus exclusively on solving the issue without significant concern for their computational time. However, given the learning context, this time is too long to be applied within a typical class period. Therefore, we propose a heuristic that is both fast and competitive compared to these previous models, given the proximity of its results to the best-known solutions in the literature.

Comments 5: «  Therefore, the objective of this work is to develop a local-search heuristic to solve 2E-CVRP quickly and efficiently for implementation in DSS. The efficiency of the heuristic is assessed through benchmarks from the literature and applied to real-world problems from a Brazilian e-commerce retailer, contributing to advancements in the 2E-CVRP approach and promoting operational efficiency in e-commerce logistics education. « 

5.        So the usefulness of the model has been verified in practice? And again I wanted to ask - why is it developed for educational purposes?

Response 5: Thank you for your comments.

The heuristic was implemented using data from a real case; however, its main focus is for educational purposes in DSSs. This is because the DSS was designed, in another work, to train individuals to sharpen their intuition and improve their critical thinking skills. For this to be possible, a heuristic like this one is necessary—one that is fast and produces solutions very close to the optimal. We edited paragraph 3 of the introduction, lines 39 to 42, to clarify this further.

Comments 6: Another category of strategies encompasses local search heuristics, constructive heuris- tics, and genetic algorithms. However, similar to exact algorithms, many of them tend to be very time consuming for Decision Support Systems (DSSs)

6.        What makes these methods « are time consuming »?

Response 6: Thank you for your comments.

The solution time of the heuristic is very important for a DSS, as the decision-maker often evaluates many alternatives simultaneously and needs to assess their results quickly. The studied works aim assertively for solutions close to the optimal and use methods and strategies that require many iterations and checks to reach their answers. This guarantees a good response for a single scenario. In our work, while proximity to the optimal is important, speed is even more critical, as a DSS aims to study an even greater diversity of scenarios.

For better clarification of this, in addition to the adjustment in paragraph 3 of the introduction, we also edited the cited paragraph (4th paragraph of the Literature Review, lines 82 to 85) to:

“Other categories of strategies, discussed below, include local search heuristics, constructive heuristics, and genetic algorithms. However, similar to exact algorithms, it is noted that many of them tend to take a long time to reach their final results, sometimes extending to hours, making them unfeasible for use in Decision Support Systems (DSSs).”

Comments 7: After « 2. Literature Review” I again ask :

7.        What did these methods lack? Does it take too long to find the optimal solution? Why?

Response 7: Thank you for your comments.

The 2E-CVRP is an NP-Hard problem. As a result, exact methods have high processing times for realistically sized instances. The main heuristics applied in the literature require excessive iterations and checks, in addition to using more extensive search strategies. For example, in local search algorithms, the use of best improvement is prominent; that is, the algorithm evaluates all possible changes based on certain criteria, and the best result found is used for the next iteration, repeating this entire search until no new improvement is found. This is a good strategy, but it does not guarantee an optimal solution by the end of all iterations and makes each one more costly. In our work, we use the first improvement strategy, allowing iterations to occur more quickly while ensuring that the solution is sufficiently good for our purposes.

Comments 8: « The company studied in this work is a highly relevant e-commerce retailer in the industry, covering the entire Latin American region. The sample used in this study consists of data from one day of deliveries in the city of São Paulo, Brazil. 1.2 thousand shipments delivered throughout the city of São Paulo were analyzed, and specific regions were selected for the evaluation of the heuristic. In the problem, the objective is to minimize travel costs, which include costs per hour of travel and per kilometer traveled »

To assess the usefulness of this new method one would have to compare it with previous ones.

8.        Is the model developed for educational purposes only, or can it be used as a route planning tool for companies?

Response 8: Thank you for your comments.

This work focuses on DSS for educational purposes and aims to meet the requirements for that. Other heuristics, such as those presented by Jie et al. (2019) at https://doi.org/10.1016/j.ejor.2018.07.002, are considered among the best solutions in the literature and are well-suited for achieving a better approximation of the optimal. However, in both business and especially educational environments, there is a high demand for fast methods.

In our case study, we focus solely on evaluating the quality of the heuristic's solution compared to the solution from the mathematical optimization model of the problem.

Thank you very much for taking the time to review this manuscript and suggestions regarding our article. Your thorough analysis has significantly contributed to the improvement of our work.

Thank you very much for taking the time to review this manuscript and suggestions regarding our article. Your thorough analysis has significantly contributed to the improvement of our work. Please find the detailed responses below and the corresponding revisions/corrections highlighted/in track changes in the re-submitted files.

Point-by-point response to Comments and Suggestions for Authors

Comments 1: Thank you for the answers, now I understand the problem but I have only to questions: 1. Does it really in practice take so much time time to find an optimal solution? 2. Is this the first model for educational purposes?

Response 1: Thank you for pointing this out.

Yes, in interactive decision support systems, where multiple scenarios need to be evaluated, the time to resolve each one is essential, especially in an educational environment with its time constraints in the classroom. In this case, the preference is for instantaneous solutions. Thus, the proposed heuristic stands out for educational purposes, as it provides quick results that are close to the ideal, optimizing the use of the available time.