A Fuzzy Two-Echelon Model to Optimize Energy Consumption in an Urban Logistics Network with Electric Vehicles

Round 1

Reviewer 1 Report

The paper titled “A fuzzy two-echelon model to optimize energy consumption in an urban logistics network with electric vehicles” is reviewed and here are some suggestions to improve the paper standards.

1.      The abstract must be revised and should focus on the novelty of the paper.

2.      The literature review in section-2 should be revised.

3.      Appreciate the author efforts in the critical review presented in Table-1 and should be more constructive.

4.      In line-67, authors had used the sentence “two meta-heuristic algorithms, namely grey wolf optimizer (GWO) and tabu search (TS), are used to solve the models”. Authors must discuss the other reported optimization algorithms in the similar works and must present the reasons of selecting the GWO and tabu search.

5.      The quality of figure-1 is needed to be improved.

6.      Once check the equation numbers and make sure each parameter must be defined in the text.

7.      Its better to put the mathematical modelling of GWO and tabu search techniques.

8.      Results section is satisfactory and it would be good, if the authors could discuss in the numerical aspects.

Author Response

Responses to Reviewer1's Comments

“A fuzzy two-echelon model to optimize energy consumption in an urban logistics network with electric vehicles”

which was submitted for possible publication in the

Sustainability

(Ref. Manuscript ID: sustainability-1936024)

Thank you for your careful review of our manuscript. Many thanks for your valuable suggestions for improving the quality of our manuscript. Before responding to your comments, we are so sorry for the errors that occurred regarding typographical errors Below, we explain how we dealt with your comments. After applying your comments, some shapes and constraints to the model have been added. Therefore, the number related to constraints, equations, tables, and figures has been updated in the modified manuscript.

 

Responses to Comments

 

Comment 1:

The abstract must be revised and should focus on the novelty of the paper.

 

Response: Thanks for your concern and supportive comment. The abstract was revised by applying your point of view according to the text below.

 

“With the increase in pollutants, the need to use electric vehicles (EVs) in various urban logistics activities is focused more on each year. Currently, the high efficiency of transport companies in recognizing the effects of uncertain factors in daily logistics operations. Thus, this research proposes a novel fuzzy two-echelon vehicle routing problem involving heterogeneous fleet EVs and internal combustion vehicles (ICVs). The first echelon is recyclable wastes collected from waste pickup points and transported to the primary centers by EVs. The second echelon is transporting recyclable wastes to recyclable centers by ICVs. In the proposed models, fuzzy numbers are used to express the rate and energy consumption depending on the amount of load, vehicle speed, and recyclable waste. In addition, a penalty cost of the time windows is considered in both echelons. The models are solved by CPLEX and two meta-heuristic algorithms, gray wolf optimizer (GWO) and tabu search (TS), based on different instance sizes. The results show the efficiency of the proposed algorithms.”

 

Comment 2:

The literature review in section 2 should be revised.

 

Response: We take this opportunity to thank you for your constructive comments. The literature review was revised as follows.

“The field of literature review related to fuzzy two-echelon electric vehicle routing problem with mixed fleet and time window(F2E-EVRP-MF-TW) can be seen in Fig. 1.

 

 

Figure 1. The literature review related to the F2E-EVRP-MF-TW

 

The EVRPs issues are based on vehicle routing problems (VRPs) issues, and the salient role of research in this area cannot be overlooked, (e.g., Laporte (2000), Ramezani et al. (2013), Behnke and Kirschstein (2017), Dabaghian et al. (2020), Ganji et al. (2020), Wang et al. (2019), Tao et al. (2021)). Worley et al. (2012) in a paper presented to a conference, proposed the integration of charging station location with the routing decision problem (ELRP), then Schiffer and Walther (2017) addressed the issue of location routing with time windows and partial charging. But there are fundamental differences between them, including the limited driving range, battery capacity limitation, limited charging, and the swapping station number, and gradual technology development in electric flight vehicles (EFVs) the complexity of EVRP.

 

2.1. EVRP /ELRP with and without TW

Since the early 21 century, researchers have considered the EFVs routing problems, which are often used in goods distributing operations. The overall purpose of these issues was to deliver goods to customers. However, the popularity of electric vehicles in densely populated cities, such as quietness and non-emission of pollution, led to their use in other municipal services, such as garbage/waste transportation. For papers dealing with EV routing problems, the reader can refer to Shao et al. (2018) and Kancharla and Ramadurai (2020).

One of the challenges of electric vehicles is the limitation of their range of motion, which requires recharging the battery after a limited distance. Although in urban areas, from the initial movement of vehicles to their return, the need to charge the battery is less, but cannot be considered charging/swapping battery stations on the route. Therefore, some studies on the routing issues of electric vehicles about charging/swapping battery stations (e.g., Montoya et al. (2017), Zhang et al. (2019), Froger et al. (2019), Koç et al. (2019), Lu et al. (2020)), and some routing-locating charging or swapping stations (e.g., Yang and Sun (2015), Hof et al. (2017)). The EV location-routing problem with time windows was first introduced by Schneider et al. (2014) and then by other researchers (Desaulniers et al. (2016), Schiffer and Walther (2017)). Keskin and Çatay (2016) investigated the EVRPTW instead proposed in Schneider et al. (2014) paper for a location-routing problem with time windows and partial charges. Regarding the use of different types of chargers and also battery replacement, can refer to these papers (e.g., Desaulniers et al. (2016), Basso et al. (2019), Zhang et al. (2020), Keskin et al. (2021)).

 

2.2. A mixed fleet of ICEVs and EVs

  The issue of routing electric vehicles with a mixed fleet, with and without a time window, is another issue that can be addressed by researchers (Van Duin et al. (2013), Lebeau et al. (2015), Goeke and Schneider (2015), Hiermann et al. (2016, 2019), Chen et al. (2021)).

 

2.3. Related review on the EVRP with energy consumption

The other challenges of EVs are the limited capacity of the battery. Thus, the routing problem needs to exact methods for controlling the quantity of energy consumed on the roads. In many referred papers, the battery is supposed to be emptied linearly in terms of distance. Barth et al. (2005) represented the amount of consumed energy required to move any certain arc based on the characteristic of vehicle and arc. This model considers speed, acceleration, mass, elevation, frontal area, rolling friction, and air drag in energy consumption. Also, Yi and Bauer (2017) demonstrate how environmental factors such as wind speed, climate, road conditions, and temperature can significantly change the attainable limitation of EVs. Xiao et al. (2019) proposed the EVs routing with time windows without considering charge station locating. They presented the energy consumption rate based on speed and load along the route under the linear planning model. They make linear the non-linear relation between speed and travel time with internal and external estimation, then solve the model by exact method for small instance and by heuristic method for hundred customers. Some papers consider EV routing and energy consumption (Pelletier et al. (2019), Lin et al. (2016), Vahedi-Nouri et al. (2022)).

 

2.4. Related review on the EVRP under uncertainty

Most research is studied in a certain environment but involving the uncertain factors of the problem makes it closer to the real environment. Urban and interurban logistics operation planning includes two uncertain factors. The first one is related to the vehicle. The other is related to external factors, such as claimant conditions, traffic, road conditions, charge or swap battery stations, and customer uncertainty demand. The studies mentioned above relate to certain conditions, and there are many limited studies that regard uncertain factors. Uncertain factors often influence the results. Therefore, Keskin and Çatay (2016) and Nejad et al. (2017) suggested considering these uncertain factors in future studies.

As it was said, some of the recent EVRP studies are presented in an uncertain condition; however, it is difficult to measure the probability distribution of uncertain factors and approach them in a real operation. Fontana (2013) is one of the frontiers, suggesting the uncertainty in EVs energy consumption. This author modeled the problem with a robust optimization framework. Zhang et al. (2020) expressed that the data for the factors (e.g., the instability of human behavior and estimation of probability distribution relating to energy consumption and travel time) are limited and more complex. Thus, in this paper, fuzzy numbers are used in some parameters. It can be referred to some papers under uncertainty in the proposed model (e.g., Zhang et al. (2021), Ghobadi et al. (2021)).

 

2.5. Related review on the 2E-EVRP

Multi-echelon network of electric vehicles has been a new topic in some articles (e.g., Breunig et al. (2019), Basso et al. (2019), Jie et al. (2019), Cao et al. (2021), Wang and Zhou). Fig. 2 depicts an example of a two-echelon distribution network problem for electric vehicles (Jie et al., 2019).

Based on this survey, it shows that a limited number of papers with a focus on 2E-VRP involving EVs, where the work on the mixed fleet and for two-echelons and under uncertainty are rare.

A summary of EVRP under uncertainty and two-echelon electric vehicle are given in Table (1). In addition, the literature review is given in detail in Appendix (A).”

 

The following reference was added.

“Wang, D., & Zhou, H. (2021). A Two-Echelon Electric Vehicle Routing Problem with Time Windows and Battery Swapping Stations. Applied Sciences, 11(22), 10779.

 

Worley, O., Klabjan, D., & Sweda, T. M. (2012, March). Simultaneous vehicle routing and charging station siting for commercial electric vehicles. In 2012 IEEE International Electric Vehicle Conference (pp. 1-3). IEEE.”

Comment 3:

Appreciate the author’s efforts in the critical review presented in Table 1 which should be more constructive.

 

Response:

Table 1. Review of some studies related to F2E-EVRP-MF-TW and the feature of this paper.

Explanation	Solution method	Objective function	Reference
			EVRP-MF (electric and conventional vehicles)
Conventional, hybrid, or electric vehicles, E (electric)-urban freight	LS	Min TOC	Van Duin et al. (2013)
	CWS + tree branching	Min TOC	Lebeau et al. (2015)
Multi-objective, TW	ALNS	Min VN, EC, BSSC	Goeke and Schneider (2015)
	Branch-and-price algorithm and ALNS	Min TOC, VN	Hiermann et al. (2016)
Time windows, conventional, A plug-in hybrid, and electric vehicles	Metaheuristic consists of a genetic algorithm, LS/LNS	Min TOC	Hiermann et al. (2019)
			EVRP uncertainty
Electric car, Robust	LR	UE	Fontana (2013)
Robust optimization		Max AI	Zhang et al. (2021)
Multi-depot electric vehicle routing problem with fuzzy time windows, pickup/delivery constraints	VNS, SA	Min TOC	Ghobadi et al. (2021)
			2E-EVRP/2S-EVRP
The based on the method in Baldacci et al. (2013), BSSs	LNS	Min TOC	Breunig et al. (2019)
Electric buses in public transportation/ 2sEVRP with topography and speed profile, improve energy consumption. Only uses EVs in the second echelon distribution stage	BL	Min TOC	Basso et al. (2019)
EVs in both echelons	CG+ALNS	Min TOC, BSSC	Jie et al. (2019)
Heterogeneous fleet	HG+LNS	Min TOC	Cao et al. (2021)
TW	VNS	Min TOC	Wang and Zhou (2021)
Mix fleet, fuzzy numbers are used to express the rate and energy consumption depending on the amount of load, vehicle speed, and recyclable waste	GWO, TS	Min TOC	This Paper

Note: TOC: total cost (vehicle fixed/ time/ distance/ labor/ driver wage costs);VN: Vehicle number; TW: time windows; AI: the annual income; UE: uncertainty in EVs energy consumption; LR: Lagrange relaxation; LNS: large neighborhood search; ALNS: Adaptive large neighborhood search; VNS: Variable neighborhood search; SA: Simulated annealing; CWS: savings method of Clarke and Wright; BSSs: battery swapping stations BSSC: battery swapping costs at the battery swapping stations; HG+LNS: hybrid genetic algorithm with LNS algorithm; BL: Bellman-Ford algorithm (linear programming solver); GWO: grey wolf optimizer; TS: tabu search;

 

Appendix(A)

Table A.1. Overview of the EVRP variants and the feature of this paper.

Explanation	Solution method	Objective function	Reference
			EVRP
Fixed charging time	Hybrid genetic algorithm	Min total costs: travel, charging, penalty, and fixed vehicle costs	Shao et al. (2018)
EVRP with non-linear charging and load-dependent discharging	ALNS	Min total time (travel times + charging times)	Kancharla and Ramadurai (2020)
			EVRP-TW
Homogenous EV fleet	VNS/TS	Min the total distance traveled	Schneider et al. (2014)
Four E-VRPTW variants recharge the battery	Branch-price and cut GENCOL +CPLEX	Min vehicle number and total routing costs	Desaulniers et al. (2016)
Time windows and partial recharging policy	ALNS	Min total distance traveled	Keskin and Çatay (2016)
		Min energy cost +vehicle acquisition cost+ driver wage	Keskin et al. (2021)
			ELRP/ ELRP -TW
Locations of battery-swapping stations and EVRP	Combines tabu search algorithm and modified Clarke–Wright saving algorithm and SIGALNS	Min total routing and construction costs	Yang and Sun (2015)
BSS-EV-LRP	AVNS+LS	Min total routing and construction costs	Hof et al. (2017)
EVRP with a non-linear recharging	ILS (VND)+ heuristic concentration	Min total travel and recharging time	Montoya et al. (2017)
ELRP with time windows and partial recharging	ALNS/LS	Min total distance, number of vehicles and charge stations used	Schiffer and Walther (2017)
Locations of BSSs, EVRP, and stochastic demands	Hybrid heuristic is composed of a binary PSO algorithm and VNS heuristic	Min cost number and location of battery-swapping stations (BSSs)	Zhang et al. (2019)
EVRP-NL	Heuristic for FRVCP	Min total travel, service, charging and waiting time	Froger et al. (2019)
Locations of BSS, EVRP, multiple depots, and investment in charging stations	Multi-start ALNS heuristic	Min the sum of the fixed opening cost of charge stations and the driver’s cost	Koç et al. (2019)
Time-dependent electric vehicle routing, routing electric vehicles to serve a set of customers and determining the speed	VNS	Min energy cost, drivers’ wages, fixed cost	Lu et al. (2020)
ELRP, BSS LRP for mixed fleet electric vehicles	branch-and-price algorithm with an adaptive selection	Min BBSs variable cost and shipping cost	Chen et al. (2021)
			EVRP with energy consumption
Public vehicles-first model the impact of good on energy consumption	Exact, MATLAB	Min travel time cost, energy cost, and number of EVs dispatched	Lin et al. (2016)
	Meta-heuristic Ant	Energy consumption reducing	Zhang et al. (2018)
Speed and load on energy consumption are investigated. TW	CPLEX	Min fixed cost for EVs and drivers, /energy consumption, and the variable cost related to traveling time (or traveled distance)	Xiao et al. (2019)
EVRP with energy consumption uncertainty, Robust framework	Cutting-plane algorithm and two-phase heuristic based on LNS	Min the total fixed cost and maintenance cost proportional to traveling distance and worst-case energy cost	Pelletier et al. (2019)
Bi-objective, collaborative EVRP	Meta-heuristic	Min total cost and energy consumption	Vahedi-Nouri et al. (2022)

Note: Reference: referenced paper; TW: time windows; AI: the annual income; LNS: large neighborhood search; ALNS: Adaptive large neighborhood search; VNS: Variable neighborhood search; SA: Simulated annealing; CWS: savings method of Clarke and Wright; BSSs: battery swapping stations BSSC: battery swapping costs at the battery swapping stations; HG+LNS: hybrid genetic algorithm with LNS algorithm; BL: Bellman-Ford algorithm (linear programming solver); TS: tabu search;

 

Comment 4:

In line 67, the authors used the sentence “two meta-heuristic algorithms, namely grey wolf optimizer (GWO) and tabu search (TS), are used to solve the models”. Authors must discuss the other reported optimization algorithms in similar works and must present the reasons for selecting the GWO and tabu search.

 

Response: Thank you for your comment. The introduction was revised by applying your point of view according to the text below.

 

“Generally, algorithms such as large neighborhood search (LNS), adaptive large neighborhood search (ALNS), and hybrid genetic with LNS have been used to solve 2E-EVRP models. The reason for using the optimization method of GWO, in addition to not having a specific requirement for the objective function and the exact characteristics of the optimization problem, is that it is easy to implement and has few parameters to adjust (Hatta et al., 2019). The Ts algorithm is a global optimization technique, while search memory is an important component (Alotaibi, 2022). On the other hand, Glover pointed out the ability of the TS algorithm for network design issues. Also, the use of the fuzzy approach and meta-heuristic algorithms for complex problems is expanding in articles (Movassaghi and Avakh Darestani (2021), Maghzi et al. (2022)). According to the studies done so far, this is the first time that GWO and TS algorithms are used to F2E-EVRP-MF-TW. Meanwhile, the two-echelon network is compared in deterministic and fuzzy forms.”

 

The following references were added to the manuscript.

“Hatta, N. M., Zain, A. M., Sallehuddin, R., Shayfull, Z., & Yusoff, Y. (2019). Recent studies on optimisation method of Grey Wolf Optimiser (GWO): a review (2014–2017). Artificial Intelligence Review, 52(4), 2651-2683.

Alotaibi, Y. (2022). A New Meta-Heuristics Data Clustering Algorithm Based on Tabu Search and Adaptive Search Memory. Symmetry, 14(3), 623.

Movassaghi, M., & Avakh Darestani, S. (2021). Multiple Cross-docks Scheduling with Multiple Doors using Fuzzy Approach and Metaheuristic Algorithms. Journal of the Operations Research Society of China, 1-51.

Maghzi, P., Mohammadi, M., Pasandideh, S. H. R., & Naderi, B. (2022). Operating room scheduling optimization based on a fuzzy uncertainty approach and metaheuristic algorithms. International Journal of Engineering, 35(2), 258-275.”

 

Comment 5:

The quality of figure-1 is needed to be improved.

Response: Thank you for your comment. Figure 1 was redesigned and added to the manuscript.

.

Comment 6:

Once check the equation numbers and make sure each parameter must be defined in the text.

 

Response: Thank you for your comment. The revision was done in equations number (4), (7), (4)a, and  (7)a.

 

Comment 7:

  Its better to put the mathematical modelling of GWO and tabu search techniques.

 

Response: Thank you for your comment. In Subsection 4.2.1 and   Subsection 4.2.2   were revised by applying your point of view according to the text below.

 

Subsection 4.2.1

“The steps of implementing the TS protocol’s pseudocode in this paper are summarized in Algorithm 1.

 

Algorithm 1

1. Generating the initial solution X0, the best solution X*, tabu list T. 2. Generating a set of neighborhood solutions (multiple neighborhoods). 3. Choosing the best neighborhood from the set of neighborhood solutions X' 4. Is X' on the tabu list? Yes 5. Is the aspiration criterion satisfied? Yes, go to 7. No, X' will be removed from the set of neighborhood solutions. Then go to step 3. 6. Is X' better than X*? Yes, go to 7. No, go to 8. 7. X' replaces X*. 8. Then X' replaces X. 9. Has the stopping criterion been reached? Yes, Go 10 No Update the tabu list. Back to step 2. 10. X* is selected.

 

The neighborhood search method of this algorithm is done as multiple neighborhoods. In each step of the algorithm iteration, if the network determined in the current step is more suitable than the previous network, this network is replaced. In the case that the number of iterations reaches the maximum number of times, the iterations will end to find a network with a certain size. Then, by increasing the number of routes in the network, the previous steps are iterated until the network reaches the maximum possible number of routes. The best network among all the networks obtained from the previous steps is determined as the solution to the route network design problem.”

Subsection 4.2.2

 

“The following equations are proposed to describe the encirclement behavior:

	(78)
	(79)
	(80)
	(81)
	(82)

 

In the above equations:

	The position vector of the gray wolf
	The position vectors of prey
	The distance between the wolf and the prey
,	Coefficient vectors
,	Random vectors in [0,1]
	Distance control parameter
	Current iteration
	Maximum iteration

 

The alpha, beta, delta, and omega gray wolves mainly search for prey. They search for prey separately, but they attack prey together. In a discrete search space, there is no idea about the optimal location (prey). To mathematically simulate the gray wolf's hunting behavior, it is assumed that in terms of alpha priority (the best solution among the current solutions); it has better information about the hunting place than beta and delta. Therefore, three solutions are saved. Other search agents (including w) are forced to update their position according to the position of the best search agent. The following mathematical equations describe these situations.

 

	(83)
	(84)
	(85)

 

In the above equation, , ,and  represents the distance between the current candidate wolves and the best three wolves.

During the exploration of prey, wolves move away from each other to explore different points of the solution space. For mathematical modeling of this process, A is used with a value greater than 1 to -1. In addition, to model the attack on the prey, the value of a is reduced. The following equations are proposed to describe attacking the prey:

 

	(86)
	(87)
	(88)
	(89)

The above equation, , ,and  are the position vectors of the wolves.

 

Comment 8:

Results section is satisfactory and it would be good, if the authors could discuss in the numerical aspects.

 

Response: Thank you for your comment. Section 5 was revised.

Author Response File: Author Response.pdf

Reviewer 2 Report

1.   The structure of the paper should be modified. In detail, the abbreviations and notations should be defined at the beginning of the main context.

2.   How could (4) be derived? The explanations of the equations in the paper are always not clear.

3.   Why are there two models introduced in Section 3? Are the proposed solution methods applied to them all? Which one is focused on? Only the required contents are needed.

4.   In section 4, several algorithms are introduced, several of which are too brief since they contribute less to the paper. So why are they given? And why is the grey wolf optimizer method selected finally?

5.   The significance of the research should be explained in the Introduction part.

 

6.   English language must be polished.

Author Response

Responses to Reviewer2's Comments

“A fuzzy two-echelon model to optimize energy consumption in an urban logistics network with electric vehicles”

which was submitted for possible publication in the

Sustainability

(Ref. Manuscript ID: sustainability-1936024)

Thank you for your careful review of our manuscript and for providing valuable suggestions, which have improved the quality of the manuscript. Below we explain how we have addressed your comments.

 

Responses to Comments

 

Comment 1:

The structure of the paper should be modified. In detail, the abbreviations and notations should be defined at the beginning of the main context.

 

 

Response: Thanks for your concern and supportive comment. The entire text was reviewed.

 

Comment 2:

How could (4) be derived? The explanations of the equations in the paper are always not clear.

 

Response: Thanks for your concern and supportive comment. A review was made of the text.

" The objective function of the problem is of the minimize type and contains six parts. Parts 1 and 2 respectively the fixed cost to use EVs and the cost of transportation between two nodes. The third part of the objective function minimizes the extent of the unsatisfactory citizens of the city/wastebaskets (waste pickup points) of the penalty cost of time windows. The fourth part of the objective function minimizes the cost of energy consumption. The fifth part is the cost of constructing the charge station. Finally, the sixth part is the recharging costs in each charge station.”

In addition, explanations were added in Section 3.3.

“In fist-echelon network model discussed in Section 3.1, the objective function and Constraints (7) to (11), and (29) to (33) have uncertainty. Thus, the objective function and this constrains will be substitute with the following constraints. Then the fuzzy model is presented according to Constraints (67-77), and the rest will be unchanged. Therefore, Constraint (4) (the objective function of the first- echelon) is replaced by equation (67). In addition, Constraints (7) to (11) are replaced by Constraints (68) to (72), and finally, Constraints (73) to (77) are replaced by Constraints (29) to (33).

Also, consider that equations for computations formulas are applied in discussing the model fuzzy in the Appendix (B).”

 

Comment 3:

Why are there two models introduced in Section 3? Are the proposed solution methods applied to them all? Which one is focused on? Only the required contents are needed.

 

Response: Thanks for your concern and supportive comment. The revision in section 3 was done by adding the following text to clarify the issue.

“In this paper, the mathematical model of a two-echelon recyclable waste collection network for the problem of heterogeneous freight electric vehicle routing is considered by considering the time window for waste pickup from city citizens/garbage containers to collection centers and then transferring it to the main recycling center with traditional vehicles, so two models were proposed. Solving methods in the deterministic and fuzzy environments were applied for both models. This paper emphasizes that the factors affecting energy consumption in the real world are uncertain and should be considered in the total cost. Explanations were added to the introduction to clarify the issue.

In Subsections 3-1 and 3-2 respectively, the set, parameters, and variables for creating the proposed models of the first and second echelons are presented. Then, in Subsections 3-3, the changes needed by the models to consider the uncertainty of some parameters are stated."

 

Comment 4:

In section 4, several algorithms are introduced, several of which are too brief since they contribute less to the paper. So why are they given? And why is the grey wolf optimizer method selected finally?

 

Response: Thanks for your concern and supportive comment. We suggested solution methods according to different sizes of problems. To clarify the issue, some reasons for using solution methods were added in the introduction. In addition, measuring the performance of the algorithms according to the properties of the algorithm has shown this superiority in the proposed models.

“The reason for using the optimization method of GWO, in addition to not having a specific requirement for the objective function and the exact characteristics of the optimization problem, is that it is easy to implement and has few parameters to adjust (Hatta et al., 2019). The Ts algorithm is a global optimization technique, while search memory is an important component (Alotaibi, 2022). On the other hand, Glover pointed out the ability of the TS algorithm for network design issues. Also, the use of the fuzzy approach and meta-heuristic algorithms for complex problems is expanding in articles (Movassaghi and Avakh Darestani (2021), Maghzi et al. (2022)).”

 

Comment 5:

The significance of the research should be explained in the Introduction part.

 

Response: Thanks for your concern and supportive comment. The text was revised as follows.

“The above entry shows the importance of this research different countries' conditions must be considered to reduce pollution emissions. In this paper, we use the combination of ICVs and EVs based on prevailing conditions in developing countries. The objective function is to minimize the total cost of each echelon considering the type of vehicles used.  In the first-echelon network, the recyclable wastes of pickup points in the city, are collected with a heterogeneous EV fleet. In the second-echelon network, the conventional trucks transfer the recyclable wastes to the recycling centers out of cities. On the other hand, the studies on two-echelon networks for EVs routing problems are done, in a certain environment. Still, in the real world, unreal parameters play a prominent role in the efficiency of the network. To deal with uncertainty parameters, researchers often use the accidental optimization method. In this way, describing these parameters as random variables in practical applications is difficult because of not have enough historical data and analyzing them. Despite this, fuzzy variables can be used to deal with these uncertainty parameters (Liu, 2004).

Proposed models of the problem in this paper are solved small-sized problems using GAMS software and CPLEX solver. Then, by considering the classical VRP is NP-hard (Breunig,2016), its variant fuzzy two-echelon electric vehicle routing problem with mixed fleet and time window (F2E-EVRP-MF-TW) is undoubtedly an NP-hard problem class as well, two meta-heuristic algorithms, namely GWO and TS, are used to solve the models. Generally, algorithms such as large neighborhood search (LNS), adaptive large neighborhood search (ALNS), and hybrid genetic with LNS have been used to solve 2E-EVRP models. The reason for using the optimization method of GWO, in addition to not having a specific requirement for the objective function and the exact characteristics of the optimization problem, is that it is easy to implement and has few parameters to adjust (Hatta et al., 2019). The Ts algorithm is a global optimization technique, while search memory is an important component (Alotaibi, 2022). On the other hand, Glover pointed out the ability of the TS algorithm for network design issues. Also, the use of the fuzzy approach and meta-heuristic algorithms for complex problems is expanding in articles (Movassaghi and Avakh Darestani (2021), Maghzi et al. (2022)). According to the studies done so far, this is the first time that GWO and TS algorithms are used to F2E-EVRP-MF-TW. Meanwhile, the two-echelon network is compared in deterministic and fuzzy forms.

This paper is a valuable supplementary for studying the present EVRP on reverse logistics because this paper aims to support the use of EFVs in urban Logistics operations in particular. The main contributions of this work are as follows:”

 

In addition, the following section was moved to the introduction.

 

“

• To consider recyclable wastes, speed of vehicles, quantity of energy consumption of the vehicle, and energy consumption rate depending on the value load of vehicle in fuzzy form.
• In the first echelon, the time windows are considered to pick up the recyclable waste from citizens of the city/ wastebaskets (waste pickup points).
• In the second echelon, the time windows are considered to deliver the recyclable waste to the central station.
• To solve the models by both grey wolf optimizer and tabu search algorithms."

 

The following references were added to the manuscript.

“

Breunig, U., Schmid, V., Hartl, R. F., & Vidal, T. (2016). A large neighbourhood based heuristic for two-echelon routing problems. Computers & Operations Research, 76, 208-225.

 

Hatta, N. M., Zain, A. M., Sallehuddin, R., Shayfull, Z., & Yusoff, Y. (2019). Recent studies on optimisation method of Grey Wolf Optimiser (GWO): a review (2014–2017). Artificial Intelligence Review, 52(4), 2651-2683.

Alotaibi, Y. (2022). A New Meta-Heuristics Data Clustering Algorithm Based on Tabu Search and Adaptive Search Memory. Symmetry, 14(3), 623.

Movassaghi, M., & Avakh Darestani, S. (2021). Multiple Cross-docks Scheduling with Multiple Doors using Fuzzy Approach and Metaheuristic Algorithms. Journal of the Operations Research Society of China, 1-51.

Maghzi, P., Mohammadi, M., Pasandideh, S. H. R., & Naderi, B. (2022). Operating room scheduling optimization based on a fuzzy uncertainty approach and metaheuristic algorithms. International Journal of Engineering, 35(2), 258-275.”

 

Comment 6:

English language must be polished.

 

Response: Thanks for your concern and supportive comment. The manuscript was reviewed and revised in terms of word spelling and grammar, and the revisions have been applied.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

no more comments