Evolution of Green Vehicle Routing Problem: A Bibliometric and Visualized Review

Abstract

The Green Vehicle Routing Problem (GVRP) has garnered considerable attention as a prominent subject within the field of green logistics. Scholars, organizations, and legislators have dedicated substantial efforts to comprehensively investigate and implement solutions for this problem. To thoroughly understand the research status in this field, this paper provides a bibliometric review of all-round GVRPs between 2000 and 2021 based on 1230 publications filtered from the Web of Science Core Collection with the help of CiteSpace V5.8.R3 and VOSviewer 1.6.13. The results of bibliometric features analyses indicate that GVRP has entered into a stage of prosperity in the past decade, and over 2500 researchers from 72 countries and regions have contributed to the development of this field. Furthermore, combining the keywords and co-citation analyses, we obtain nine subfields of GVRP, elaborate their study content evolution history, and accordingly apply the research potential evaluation model to envisage its future directions. The findings show that fuel consumption and electric vehicles are major research hotspots with the most optimistic prospects, and cold chain logistics, which has both high maturity and high recent attention, is the current mainstream of GVRP. The findings may provide guidance for future research in this field.

1. Introduction

In contemporary discourse, there has been a notable emphasis placed by scholars and environmentalists on the environmental and social impacts caused throughout the transportation network, including carbon emissions, noise and air pollution, congestion, and even traffic accidents [1]. These transportation-related negative externalities not only have a harmful effect on the environment, but also implicitly decrease the economic benefits [2] (e.g., delayed delivery losses and rising fuel costs caused by traffic congestion, policy suppression, and increasing pollution control costs caused by environmental damage). Despite improvements in ‘green technology’, such as using next-generation electronic vehicles [2] and improving internal combustion engine technology and using clean energy [3], the optimization of logistics and transportation at the operational decision level remains crucial in mitigating negative externalities. Therefore, the green vehicle routing problem (GVRP) considering environmental protection and sustainable development has rapidly developed into a prominent research field among numerous variants of VRP.

Compared with traditional VRP, which aims at optimizing vehicle scheduling at a minimum cost subject to side constraints, GVRP pays more attention to energy saving, emission reduction, and waste value-added creation [2]. Considering these extensive objectives have led to more complicated optimization problems and inspired more variants applicable to various real-world application scenarios. In order to obtain a full understanding of the current research landscape in this particular field and establish the significance of our work, we have compiled a summary of previous review papers pertaining to GVRP. This summary is presented in

Table 1. Summary of reviews on GVRP.

Publication	Year	Scope	Methodology	Time Span	Scale
Juan et al. [4]	2016	EVRP	Content Analysis	1984–2016	114
Margaritis et al. [5]	2016	EVRP	Content Analysis	1964–2015	37
Pelletier et al. [6]	2016	EVRP	Content Analysis	2001–2015	137
Erdelić et al. [7]	2019	EVRP	Content Analysis	1953–2019	175
Ghorbani et al. [3]	2020	EVRP	Content analysis	2011–2020	125
Asghari and Al-e-hashem [8]	2021	EVRP	Systematic Analysis	2000–2020	313
Sbihi et al. [9]	2007	VRPRL	Content Analysis	1958–2006	84
Beliën et al. [10]	2014	VRPRL	Systematic Analysis	1974–2010	78
Govindan et al. [11]	2015	VRPRL	Systematic Analysis	2007–2013	382
Govindan et al. [12]	2017	VRPRL	Systematic Analysis	2001–2014	83
Lu et al. [13]	2017	VRPRL	Systematic Analysis	1974–2014	78
Demir et al. [1]	2014	GVRP	Systematic Analysis	2006–2013	58
Lin et al. [2]	2014	GVRP	Systematic Analysis	1959–2013	280
Bektaş et al. [14]	2019	GVRP	Content Analysis	1982–2018	153
Moghdani et al. [15]	2021	GVRP	Systematic Analysis	2006–2019	309
Dündar et al. [16]	2021	GVRP	Content analysis	1975–2019	158
Gil et al. [17]	2022	GVRP	Content analysis	2010–2021	89
Sabet and Farooq [18]	2022	GVRP	Systematic Analysis	1990–2021	450
Our Study		GVRP	Bibliometric Analysis	2000–2021	1230

Note: EVRP: electric vehicle routing problem; VRPRL: vehicle routing problem in reverse logistics; GVRP: green vehicle routing problem.

, which provides information on the publication year, research topic, review methodology, time span, and the number of articles reviewed (Scale) for each paper. In recent decades, electric vehicles (EVs) have emerged as a potentially effective alternative for urban freight transportation, garnering interest from public authorities and companies seeking to reduce environmental pollution and operational costs. Accordingly, the electric vehicle routing problem (EVRP) has become an emerging variant of GVRP. Ghorbani et al. [3], Juan et al. [4], Margaritis et al. [5], Pelletier et al. [6], Erdelić [7], and Asghari and Al-e-hashem [8] focused their eyes on the EVRPs, reviewing the technical and environmental challenges and characteristics of different types of EVs, respectively.

To improve end-of-life value and reduce the environmental impacts of the products’ final disposal, reverse logistics (RL) and closed-loop supply chain and waste management have garnered significant attention from the public and scientific community. Within the realm of GVRP, VRP in reverse logistics (VRPRL) has gained considerable popularity. Sbihi and Eglese [9] introduced the area of green logistics and described some problems including RL, VRP, and scheduling. Kannan et al. [11] and Kannan and Hamed [12] reviewed, categorized and evaluated papers in RL and closed-loop supply chain. Belien et al. [10] and Lu et al. [13] reviewed the literature on waste collection problems from different perspectives.

In addition, with the theme of green logistics or green transportation, Lin et al. [2] categorized GVRP into Green-VRP, Pollution Routing Problem (PRP), and VRPRL. Demir et al. [1] and Bektaş et al. [14] provided a review of recent research on green freight transportation. Moghdani et al. [15] proposed an extensive structure that includes GVRP variants, objective functions, uncertainty, and a solution method to analyze GVRP. Dündar et al. [16] provided an overview of sustainable practices in urban VRPs. Gil et al. [17] directed their attention towards heuristic and hybrid approaches to solve GVRPs considering emissions. With the purpose of addressing issues related to charging, pick-up, delivery, and energy consumption, Sabet and Farooq [18] carried out a comprehensive review on the variations and specializations of GVRP.

It is evident that the majority of these studies have focused mainly on a specific part of GVRP, examining a specific variant, a singular category of problems, or a particular facet of GVRP, with little or no coverage of the entirety of GVRP. In addition, it is worth noting that the predominant methodology employed in reviews are content analysis, which involves studying the details and implications of the content, and systematic analysis, which entails the synthesis of a limited body of scholarly literature using both quantitative and qualitative approaches, without the utilization of bibliometric software [19]. When the research scope is narrow or the volume of the literature is manageable for manual review, it is appropriate to employ these approaches for summarizing and synthesizing the findings of the existing literature. However, in the field of GVRP, which has a vast array of topics and involves thousands of articles, it is difficult to examine the status of the existing research in its entirety, or provide the state of the intellectual structure, and/or identify new directions [20]. Hence, after analyzing the subfields and being inspired by the classification methods of the existing literature exemplified by Lin et al. [2], this paper conducts a bibliometric analysis that is capable of dealing with a larger number of papers to observe the GVRP field from an overview perspective.

The contribution of this study is listed as follows: Firstly, this paper studies a wider scope of GVRP from multiple perspectives, which is more comprehensive than other studies that just paid attention to certain aspects of environmental issues. The number of papers reviewed is over twice that of the largest among published reviews. Secondly, this review utilizes in-depth analysis with the help of bibliometric methods and visualized software, including a discussion on the development stage of the field, an analysis of countries, authors, and journals that have made significant contributions, a keyword-based thematic evolution analysis, and an exploration of research hotspots based on literature co-citation networks. Last but not least, this paper discusses the future trends in a quantitative way, which serves as a valuable complement to the subjective conclusions that are constrained by the authors’ knowledge, providing a comprehensive interpretation of GVRP.

The remainder of this paper is structured as follows. Section 2 introduces the data source collection and processing processes as well as some methods used for subsequent analysis. The bibliometric features of GVRP, including publication profile, nation, author, and journal distribution, are clarified from the macro level in Section 3. Section 4 explores the research hotspots and knowledge base of GVRP in terms of keywords evaluation and reference co-citation analysis. Section 5 employs the research potential evaluation (RPE) model introduced by Zhou et al. [21] to predict the future research directions of GVRP field. Finally, conclusions are drawn in Section 6.

2. Materials and Methods

The data was first generated by a basic retrieval within the Web of Science (WoS) Core Collection database, and 2343 articles whose keywords contain ‘green vehicle routing’, ‘pollution vehicle routing’, ‘reverse logistics vehicle routing’, ‘electric vehicle routing’, ‘greenhouse gas vehicle routing’, ‘carbon emission vehicle routing’, ‘alternative fuel vehicle routing’, or ‘waste collection vehicle routing’ ranging from January 2000 to December 2021 were obtained. Then, by reading and analyzing the title, keywords and abstract of these articles, removing repeated and irrelevant articles, 1230 of them that are actually relevant to GVRP were extracted. Afterwards, they were imported into CiteSpace for subsequent visualization, and a series of analyses based on the outcomes of these knowledge graphs and key information summarized by a literature review of the 1230 articles were conducted.

2.1. National Comprehensive Strength

Studying national comprehensive strength helps recognize the current research level and then cooperate with other leading countries. For this purpose, Yin et al. [22] proposed a method for measuring comprehensive strength. This method first selects eight indicators: total publication number (TP), total citations (TC), total hot (Top 20) publications (TH) and their citations (THC), total most cited (Top 100) publications (TMC) and their citations (TMCC), productive authors (PA) and institutions (PI). Then, it calculates the standard scores for each country according to Equations (1) and (2):

$$N{S}_{pq}=\frac{X_{pq}-\overline{X_q}}{\sqrt[2]{\frac{{\sum }_p{(X_{pq}-\overline{X_q})}^2}{M}}},$$

(1)

$$TN{S}_p=\sum _{q}N{S}_{pq},$$

(2)

where $N{S}_{pq}$ is the standard score of country p on indicator q; $X_{pq}$ is the indicator q score of country p, the specific calculation method is referred to Yin et al. [22]; $\overline{X_q}$ is the mean score of indicator q; M is the number of countries; $TN{S}_p$ is the total score of country p, in other words, the national comprehensive strength.

2.2. Keywords Merging Operations

The author keywords (provided by the authors of articles) and the keywords plus (provided by the WoS database) serve as the base of keywords analysis. We have merged multiple keywords representing the same concept (singular or plural form, with or without “–”, abbreviation, synonym, etc.; for instance, ‘Vehicle routing problem’, ‘vehicle-routing problem’, ‘vehicle routing problems’, VRP, and VRPs are presented as ‘vehicle routing’) and obtain 3299 keywords, among which 237 keywords appeared more than 5 times.

2.3. Research Potential Evaluation Model

Zhou et al. [21] mentioned that previous studies identifying research fronts were highly unstable for their dependence on publication data, and proposed an RPE model for evaluating the research potential by two indicators. First is maturity, which is defined as

$$Maturity=\frac{numberofhighlycitedpapers}{totalnumberofpapers},$$

(3)

where highly cited papers are those have citations over $N=0.749\times \sqrt{N_{max}}$, in which $N_{max}$ is the most cited article’s citations. Regardless of other factors, the subfield with lower maturity is considered to be of higher research potential. Another indicator, recent attention (RA), is formulated as

$$RecentAttention=\frac{TC}{TP\times D}\times \frac{1}{R},$$

(4)

where $TC$ and $TP$ are the total citations and the total publications, D is the duration, i.e., the time span over which publications have appeared, and R is the recency, quantified by the half-life of publication. RA describes the degree to which scholars are focused on the subfield.

The RPE model takes maturity and RA as two dimensions, forms a two-dimensional matrix, and classifies various subfields into four quadrants. Topics in “Diamond in the Rough” (low maturity and high RA) have attracted great attention recently with limited achievements. Thus, they are regarded as high-potential issues. “Hard Core” (high maturity and high RA) is regarded as the mainstream with great attention, maintaining a good development momentum. “Possibility” (low maturity and low RA) includes some new but unpopular subfields and long-standing and large-scale ones with less attention recently. As RA changes, the subfields may shift between the “Possibility” and “Diamond in the Rough” quadrants. Topics in Chicken Ribs (high maturity and low RA) have inspired lots of research and lack popularity as well, so it is difficult to make significant progress in this area. According to these characteristics, we can rank the research potential of four quadrants as “Diamond in the Rough” > “Hard Core” > “Possibility” > “Chicken Ribs”.

3. Features of Publication Outputs

3.1. Publication Profile

Literature is one of the main forms of scientific and technological achievements. The number of publications is an important indicator reflecting the overall development and research progress of a research field. From the annual and cumulative number of publications from 2000 to 2021 shown in Figure 1, we can see that the number of publications in the GVRP field has been increasing year-by-year and accelerating since 2013. It exceeded 100 articles per year for the first time in 2017 and maintained rapid growth in the following years, indicating that the field has gradually become an increasingly popular research field. Researchers in science and bibliometrics have developed many literature growth models through the statistical analysis of a large amount of literature data. Among them, exponential and logistic growth models are the most widely recognized and highly praised models in practice [23]. In order to scientifically and accurately explore the law of literature growth in GVRP, the cumulative publication number is also illustrated in Figure 1. Accordingly, a tendency curve is drawn, taking the publication year and cumulative publication number as the x- and y-axis, respectively, from which we can see an exponential growth trend. To verify this conclusion, the software SPSS26 is used to carry out the fitting of exponential and logical curves based on a total of 1230 pieces of literature in twenty-one years. The result and correlated information are shown in Figure 1. When making either exponential fitting or logistic fitting, the square of R is 0.974, coming near to 1, indicating a strong correlation between the year sequence and the literature accumulation, which means a good fit in the curve. And the value of significance is 0.00, indicating validity in the population regression model.

Li and Yao [24] stated that the literature growth model is summarized from practice through statistical analysis and can only function within a certain period, since one would be replaced by other growth models as the stage changes. Therefore, they proposed four stages of the literature growth process and pointed out that for different research fields, the time taken for the accumulative literature number to go through the four stages could be different, but these four growth trends are bound to occur. The four stages are:

(1)

Infancy stage: a stage when a small amount of literature started to appear in this field at an unstable growth rate.

(2)

Development stage: a period of rapid development when the number of publications grows at an exponential speed.

(3)

Relatively mature stage: the growth of related scientific literature is gradually slowing down, entering a stable growth stage.

(4)

Aging stage: a well-developed phase with the growth of the literature approaching a state of “saturation”.

We can see from Figure 1 that the relevant scientific literature in GVRP is now in a state of exponential growth. Moreover, in terms of annual publication, the difference is significant between the following two periods. A total of 85 papers were published in the first 13 years from 2000 to 2012, accounting for only 6.9% of the total, and there was no significant increase in the number of papers during this period. Meanwhile, the last 8 years have seen 1145 articles published so far, and the annual number is exponentially increasing. Thus, according to the fitting result by SPSS and the characteristics of the four stages summarized by Li and Yao [24], the period from 2000 to 2012 can be taken as the infancy stage, while that from 2013 to 2021 is the development stage for the field of GVRP.

3.2. Nation Distribution

Table 2. The top 10 productive countries on GVRP, 2000–2021.

Rank	Country	BY	TP	TP-R (%)	H-Index	TC	AC
1	China	2007	360	29.27	40	5841	16.23
2	USA	2004	182	14.80	37	4900	26.92
3	Canada	2006	93	7.56	30	4100	44.09
4	Iran	2013	93	7.56	22	1671	17.97
5	England	2007	78	6.34	27	3633	46.58
6	Italy	2002	71	5.77	27	2271	30.28
7	Turkey	2008	70	5.69	24	1547	22.10
8	Germany	2001	55	4.47	22	2287	41.58
9	France	2003	53	4.31	21	1656	31.25
10	Spain	2011	53	4.31	19	1287	24.28

Note: BY: Begin Year; TP: Total Publications; TP-R: Total Publication Proportion; TC: Total Citations; AC: Average Citations.

illustrates the information about the top ten productive countries or regions, including the beginning year they researched in this field (BY), TP, and corresponding proportion (TP-R), H-index, TC and average citations (AC). It shows that the total number of publications in these ten countries is 1108, accounting for 90.1% of the total. In particular, China has the most publications, with 360 articles accounting for 29.27% of the total, followed by the USA, with a TC of 182. The number of articles in the other eight countries ranges from 50 to 100. The study of GVRP in China began in 2007, slightly later than in five developed countries (the USA, Canada, Italy, Germany, and France), whereas the number of publications far exceeds all the other nine. This can be attributed to the expeditious development of this developing country and the increasing emphasis on environmental issues during its development period. It is also worth noting that Iran, which entered this field in 2013, currently ranks fourth in publication in 2021, with a strong trend of catching up from behind.

AC is one of the important indicators for measuring the influence and quality of an article [25]. A higher AC indicates that the results of the article are more valuable, and that the impact it has on academia and society is greater. China and the USA take the lead in publication quantity, whereas Canada, England, and Germany are superior in terms of publication quality. With only 93, 78, and 55 publications, their TCs reached 4100, 3633, and 2287, respectively, resulting in much higher AC than the other countries, with 44.09, 46.58, and 41.58, respectively.

By using Equations (1) and (2), we can calculate the average score of the comprehensive academic level of the top 10 publication countries. After collating and analyzing the relevant literature data, we draw a coordinate graph containing a percentage stacked area chart, a line chart, and a table in Figure 2. The horizontal and vertical axes, respectively, represent countries and scores on indicators; each color represents an indicator, and its height represents the score of each country on each indicator, the line represents the total score.

From Figure 2, we can see that China ranks first in terms of comprehensive academic level with a TNS of 25.05, since the scores on TP, TC, PA, and PI are much higher than those of the other countries. Canada ranks second only to China with a score of 22.46 due to its high scores on TH, THC, and TMCC. The USA performs well on TC, TMC, and PI, and thus ranks third with a score of 22.03. Similar to Canada, England has high scores on TH, THC, TMC, and TMCC, and its TNS is only 0.47 less than that of the USA. The result further confirms the conclusion of Table 2 that China and the USA are superior in publication quantity, and Canada and England have an advantage in terms of publication quality.

3.3. Productive Authors Analysis

Every field has some scholars who are pioneers.

Table 3. The top 10 productive authors on GVRP, 2000–2021.

Rank	Author	Country	BY	TP	H-Index	TC	AC
1	Gilbert Laporte	Canada	2006	29	19	2456	84.69
2	Angel A. Juan	Spain	2014	18	12	441	24.50
3	Tolga Bektaş	England	2011	13	10	1957	150.54
4	Javier Faulin	Spain	2011	13	10	509	39.15
5	Emrah Demir	England	2011	11	9	1031	93.73
6	Erfan Babaee Tirkolaee	Iran	2018	9	9	314	34.89
7	Richard F. Hartl	Austria	2008	8	7	501	62.63
8	Bulent Catay	Turkey	2010	9	6	341	37.89
9	Reza Tavakkoli-Moghaddam	Iran	2013	9	5	152	16.89
10	Ola Jabali	Canada	2012	7	7	601	85.86

shows the top ten productive authors in terms of TP and TC. Among them, Gilbert Laporte, who works at the University of Montreal, Canada, made the greatest contribution, with 29 publications cited a total of 2456 times, 19 H-index, and half of the articles cited more than 50 times. Another author coming from the University of Montreal is Ola Jabali, who is ranked tenth in Table 3. Among his seven articles, six were collaborations with Gilbert, and the remaining one was published on Production and Operations Management which received nearly 200 citations. Thus, although the number of publications is relatively small, the TC and AC of Jabali reached 601 and 85.86, ranking fourth and third, respectively.

The second and fourth most productive authors are both Spanish. Angel A. Juan has been involved in this field since 2014 and ranks second in terms of publication number with 18 articles published over a period of 8 years. Among the 13 papers published by Javier Faulin, 7 were co-authored with Juan, and the relatively high TC was mainly due to the high citations of the article published on International Journal of Production Economics in 2011.

An interesting fact is that as the most influential author in this area, Gilbert Laporte not only collaborated with Ola from the same school, but also cooperated with the third-ranked British scholar, Tolga Bektaş, on over half of Bektaş’s papers, with a total of over 1000 citations. Similarly, the fifth most productive author, Emrah Demir, is also British and a collaborator of Gilbert Laporte and Tolga Bektaş. Therefore, Bektaş and Demir are the authors with the highest ACs of 150.54 and 93.73. The high citations of these three authors’ articles also precisely explain the excellent performance of Canada and the United Kingdom in terms of publication quality in Section 3.2.

It is worth noting that the Iranian author Erfan Babaee Tirkolaee, who ranked sixth, has only been engaged in research in the field of GVRP since 2018, publishing nine articles and receiving 314 citations in just 4 years. A review of his papers reveals that he mainly focused on VRPs related to waste collection, one of the hotspots currently.

3.4. Journal Distribution

Journal distribution is also one of the most important bibliometric features. A total of 278 journals contributed to GVRP between 2000 and 2021.

Table 4. The top 10 productive journals on GVRP, 2000–2021.

Rank	Journal	TP	TC	AC	BY	BC	IF	JCR
1	Journal of Cleaner Production	52	1072	20.62	2014	0.03	11.07	Q1
2	Sustainability	50	311	6.22	2014	0.03	3.89	Q2
3	Transportation Research Part D	45	1342	29.82	2009	0.04	7.04	Q1
4	European Journal of Operational Research	41	2559	62.41	2000	0.12	6.36	Q1
5	Computers & Operations Research	40	1500	37.50	2006	0.16	5.16	Q1
6	Computers & Industrial Engineering	37	866	23.41	2010	0.08	7.18	Q1
7	Transportation Research Part B	33	2139	64.81	2011	0.07	7.63	Q1
8	Waste Management	32	1293	40.41	2008	0.03	8.82	Q1
9	Transportation Research Part E	31	1482	47.81	2012	0.10	10.05	Q1
10	Expert Systems with Applications	29	1318	45.45	2006	0.03	8.67	Q1

Note: BC: betweenness centrality.

lists the top 10 productive journals, along with various indicators implying their influence and quality, including TP, TC, AC, BY, betweenness centrality (BC), impact factor (IF), and partition from Journal Citation Reports (JCR) in 2021. We can see that 9 of the top 10 journals are from region Q1 and only 1 is from Q2. Among them, Journal of Cleaner Production has the highest impact factor of 11.07. Meanwhile, as a transdisciplinary journal focusing on environmental and sustainability research, it started publishing GVRP-related papers at the latest (2014) but has a maximum publication number of 52 and a fourth citation of 1072. As one of the best-known journals in the management science discipline, European Journal of Operational Research was the earliest (2000) to publish GVRP-related articles, and a more detailed analysis (although not illustrated in the table) shows that before 2010, it had published 7 papers with relatively high citations, accounting for 15.21% of the total number of articles during that period. Hence, the TC of this journal is the highest, reaching 2559.

Three journals under Transportation Research were selected as the top ten high-yield journals, including Transportation Research Part D, Transportation Research Part B, and Transportation Research Part E, which are ranked third, seventh, and ninth, respectively. Among them, Transportation Research Part D, which focuses on the impact of transportation on the environment and policy responses to these impacts, was the first to participate in research in the GVRP field, with the highest TP of 45 among the three. Transportation Research Part B is committed to providing methodologies and mathematical analyses to optimize the design and optimization of logistics systems, and is the most directly related journal to the GVRP field. As a result, it ranks second with 2139 TC and first with 64.81 AC. As a supplement to the other five parts, Transportation Research Part E has also published 31 articles, ranking fourth with 1482 citations and third AC of 47.81. These three journals make Transportation Research the most cohesive and comprehensive reference for current research in transportation science.

BC refers to the mediating effect of nodes in the transmission of information between other nodes, an indicator helps understand the influence and position of the authors, disciplines or institutions in the field. It ranges from 0 to 1, and it is generally considered that a value greater than 0.1 is a meaningful central medium. A high BC indicates that the nodes are more important in the process of information transmission, and the nodes are closer connected. From this perspective, Computers & Operational research ranks first with a BC of 0.16. This journal publishes research in many scientific fields including transportation and logistics, and does not only focus on optimization methods, but also covers the application fields of these sciences, thus having a wide range of topics and playing an important intermediary role in the GVRP field which has numerous branches.

Overall, in terms of TP, TC, JCR ranks, and publish years covered, the journals in Table 4 perform well and are representative, indicating the strong research capability and quality of authoritative and influential journals.

4. Research Hotspots and Knowledge Base

In this section, keywords analysis and reference co-citation analysis with the help of Citespace and VOSviewer are given to explore research hotspots and demonstrate some fundamental knowledge in major evolved research interests.

4.1. Evaluation of Keywords and Research Hotspots

Keywords can reflect the main ideas and methodology of a study, highly occurring keywords, to some extent, can symbolize the research hotspots of the field, which helps us review the evolution process and predict future trends of this field [26]. Additionally, keywords can be provided as important evidence for naming clusters of reference co-citation network, in which notable publications receiving more citations lay the knowledge base for corresponding research branches and for GVRP as a whole. To this end, we make an evaluation of keywords by analyzing the most occurring keywords and the co-occurrence network in density visualization.

4.1.1. Analysis of Most Occurring Keywords

Table 5. The top 20 high-frequency keywords on GVRP during 2000–2021.

Rank	Keyword	Occ.	APY	Rank	Keyword	Occ.	APY
1	vehicle routing	396	2016.57	11	emissions	98	2017.80
2	algorithm	287	2016.79	12	transportation	92	2016.77
3	optimization	244	2017.53	13	genetic algorithm	91	2017.64
4	model	213	2017.44	14	management	84	2016.98
5	time windows	177	2017.13	15	tabu search	82	2015.83
6	electric vehicle	159	2018.19	16	logistics	81	2017.18
7	routing problem	140	2017.44	17	reverse logistics	80	2014.00
8	system	111	2017.33	18	delivery problem	69	2017.43
9	heuristic	107	2015.22	19	design	66	2017.51
10	fuel consumption	103	2017.08	20	green logistics	62	2016.68

Note: Occ.: Occurence.

provides a list of the top 20 high-frequency keywords in descending order of their occurrences, together with the average publication years (APYs) calculated by averaging the years in which each keyword appears. It is not surprising that vehicle routing is at the top of the list since it covers the whole scope of our study. Many of the keywords reflect the properties and characteristics of VRP, such as optimization, logistics, management, routing problem, system, delivery problem, and transportation since vehicle routing is a systematic problem always involving delivery and transportation that should be optimized from the perspective of logistics as well as management. Algorithm, optimization, and model are the mainstream research methodology while studying VRP and heuristic and meta-heuristic algorithms are mostly employed to solve GVRPs with the highest ranking in algorithms, among which the genetic algorithm (GA) and tabu search (TS) algorithm are gaining more popularity. Time window which ranks 5 is a crucial constraint in models. There are five keywords closely related to GVRP, including EVs, fuel consumption, emissions, RL, and green logistics, which rank 6, 10, 11, 17, and 20, respectively.

The APY can be used to measure whether a keyword or research hotspot has recently been proposed [27]. Therefore, it makes sense that the APYs of RL, heuristic algorithms, and TS algorithm are before 2016, whereas EVs, emissions, and fuel consumption are keywords that appeared around 2017 and 2018.

4.1.2. Keywords Analysis in Two Stages

According to the bibliometric features analyses in Section 3, we divide the development of GVRP in 2000–2021 into two stages, namely the infancy stage (2000–2012) and the development stage (2013–2021). Statistics show that there are 285 keywords, with 20 appearing more than dive times, in the infancy stage, and 3171 keywords, with 228 appearing over five times, in the development stage. Considering that the frequency of the keywords in the infancy stage is relatively low, the data is not illustrated in the table, and we only list the top 20 high-frequency keywords in the development stage. Actually, by comparing Table 5 and

Table 6. Keywords with most occurrence in the development stage on GVRP.

Rank	Keyword	Occurence	Rank	Keyword	Occurence
1	vehicle routing	358	11	genetic algorithm	87
2	algorithm	263	12	heuristic	86
3	optimization	234	13	transportation	84
4	model	206	14	management	80
5	time windows	165	15	logistics	78
6	electric vehicle	159	16	tabu search	72
7	routing problem	135	17	delivery problem	63
8	system	104	18	design	61
9	emissions	96	19	vehicle	60
10	fuel consumption	96	20	search algorithm	59

, it can be seen that the vast majority of high-frequency keywords in the infancy stage are the same in Table 5 (15 words), among which the top few with frequencies exceeding 20 are ‘vehicle routing’ (38), ‘algorithm’ (24), ‘reverse logistics’ (24), and heuristic (21), indicating that early research in this field focused more on RL and algorithms. While the remaining five are ‘waste collection’ (8), ’waste management’ (6), ’meta-heuristic’ (6), ’traveling salesman problem’ (6), and ’product recovery’ (5), respectively. On the other hand, it also shows that the frequencies of ‘emissions’, ‘electric vehicle’, and ‘genetic algorithm’ during the development stage are almost the same as the whole period, indicating that they gradually gained attention during the development stage, which is consistent with their relatively later APYs. Moreover, compared with the whole period, ‘reverse logistics’ does not appear in Table 6, which confirms that it is the early focus, with an APY equal to 2014.

4.1.3. Density Visualization of the Keywords Co-Occurrence Network

The density visualization of the keywords co-occurrence network using VOSviewer can display the information more intuitively and completely. Although the keywords plus feature provided by the WoS database can help scholars search for relevant literature more comprehensively, it may also provide some inappropriate, broad, or meaningless information, which may affect the effectiveness of the keywords co-occurrence analysis. Therefore, in order to obtain more accurate results, the density visualization was conducted by using the author keywords that were more relevant to the content of the articles. We selected 28 keywords with a frequency exceeding 15 to depict Figure 3, where the font size represents the keyword’s frequency, and each color block represents a cluster, in which the co-occurrence strength of keywords is relatively high and the kernel keywords have the darkest colors/highest density. It can be seen that the keywords with the highest frequency are respectively ‘vehicle routing’ (320), ‘electric vehicle’ (147), ‘heuristic’ (67), ‘reverse logistics’ (63) and ‘optimization’ (60). In addition, 28 keywords were divided into 4 clusters, with the kernel keywords being ‘vehicle routing’, ‘heuristic’, ‘reverse logistics’ and ‘carbon emission’ (keywords colored in purple).

There are nine keywords in the red cluster with ‘vehicle routing’ as the core. Related articles focused more on energy consumption reduction by using alternative fuel vehicles or EVs. Mixed-integer linear programming is usually used for modeling, and meta-heuristic algorithms, especially ant colony algorithm, are designed to solve these VRPs. In the cluster marked in yellow, ‘heuristic’ is the kernel keyword. It often co-occured with some broad concepts such as optimization, transportation, and logistics, and some related articles focused on its application in the field of waste management. ‘Reverse logistics’ is a hot research topic, and related research has paid more attention to sustainability and location while routing. Therefore, multi-objective optimization is often the main focus, and genetic algorithm was a commonly used solution method. ‘Carbon emission’ is the core concern of articles on green logistics/GVRP and waste collection, and closely related to fuel consumption. Some scholars have also focused on the impact of heterogeneous fleets and time windows. Such articles often use simulated annealing or TS algorithms for solutions.

4.2. Reference Co-Citation Analysis

Scholars generally use citations to quote the research results of predecessors in their works and attach them in the form of references. A and B form a co-citation relationship when they appear together in the reference of another article, C. The process of exploring the co-citation relationship between articles is called co-citation analysis, which can assist in tracing both the origins of the research field and its subsequent evolution. Those frequently co-cited papers can be reasonably considered as the knowledge base of the field and common points from these references can be extracted to illustrate research domains. In this section, CiteSpace has been used to conduct a reference co-citation analysis and to discuss papers in some typical clusters after co-citation clustering. At last, crucial knowledge bases of GVRP are explored from the perspectives of TC, citation burst (sudden increase in number of citations) of the literature, and BC, respectively, to exhibit a multi-dimensional understanding of the whole field.

4.2.1. Reference Co-Citation Clustering

With the purpose of unfolding the panorama of the general situation and the evolution history in each subfield of GVRP, we utilize the CiteSpace clustering function to construct a reference co-citation network, explore common topics of similar literature fields, and categorize the papers with a common knowledge base into several clusters. We selected the top 50 references with the most citations in each year for cluster-viewing and utilized the log-likelihood ratio algorithm to name the resulting clusters. Then, we screened out nine clusters whose size is less or equal to 10 and sequenced them in descending order of their sizes in the co-citation network derived from Citespace, as shown in Figure 4.

There are two indicators that can measure the validity of the network. One is “Modularity Q”, ranging from 0 to 1, an indicator for measuring the network’s modularity. Generally, a clustering network with “Modularity Q” larger than 0.3 is considered to be significant and reliable. The other is “Weighted Mean Silhouette”, which measures the network’s homogeneity, i.e., the extent to which the clusters share specified and similar themes. It ranges from −1 to 1 and is generally acceptable if it is higher than 0.5. Our network has a “Modularity Q” of 0.8874 and a “Weighted Mean Silhouette” of 0.9636, and thus completely meets the standard. Each node represents a reference and is colored yellow if it was significantly active at one point in history. The size and rings of each node represent the reference’s citation times and citation history. The edge between two nodes symbolizes the two papers’ co-citation relationship with the thickness in proportion to the co-citation times. The highly cited references in each cluster are marked with the first author’s name and publication year. The nine clusters are: #0 Fuel Consumption, #1 Electric Vehicle, #2 Service areas, #3 Reverse Logistics, #4 Adaptive Large Neighborhood Search (ALNS) Algorithm, #5 Waste Collection, #6 Two-Echelon Location-Routing Problem (2E-LRP), #7 User equilibrium, and #8 Cold chain logistics.

Figure 5 displays the relationships among the clusters in terms of timeline in a more simplistic structure. Some marked time-related features need our attention. Clusters #0 and #1 both include many papers having citation bursts last to the present, and their sizes are considerable, indicating that fuel consumption and EVs are hot research topics and may still be active in the future. Cluster #8 is an emerging branch in recent years, which originated from around 2014 and has been gaining the popularity since then. By contrast, Clusters #2, #4, and #6 have a relatively short duration and end early in this field. Cluster #3 is the earliest to start and has a relatively long span. And its highly relevant domain, Cluster #5, has the longest history from 2002 to 2018. More bibliometric features of each cluster will be detailed later.

4.2.2. Discussion on Typical Clusters

Table 7. Co-citation clusters of the literature.

Cluster ID	Size	Silhouette	APY	Label
0	51	0.895	2012	fuel consumption
1	40	0.928	2015	electric vehicle
2	31	0.861	2009	service areas
3	28	0.983	2007	reverse logistics
4	26	0.998	2011	adaptive large neighborhood search algorithm
5	21	0.965	2008	waste collection
6	19	0.987	2007	two-echelon location-routing problem
7	14	0.977	2012	user equilibrium
8	14	0.944	2016	cold chain logistics

lists the detailed information about the 9 main clusters, including their size, silhouette, average publication year, and label. Since Cluster # 2 is a relatively broad concept with a small silhouette value, we leave out it and take the other eight clusters as typical ones, discussing and summarizing their research contents and evolutionary progress in detail combining their bibliometric features.

• #0 fuel consumption

Fuel consumption is the cluster with the largest number of members and time span from 2006 to 2017. It can be directly seen from Figure 4 that most of the cited references with high citations are in this cluster. Figure 5 shows that the development of this subfield could be roughly divided into three stages. In the first stage (2006–2009), there are only three cited references, with citations between 7 and 14. In the second stage (2010–2014), there are a total of 28 cited papers, among which the top 15 mostly cited articles are ranked top 15 in the whole cluster as well, providing a solid foundation for this subfield. In the third stage (from 2015 to 2017), there are 14 cited references with a mean citation time of 17. Compared with the previous stage, the number of documents and citations in this stage has decreased significantly, but is obviously higher than in the first stage.

From a content perspective, in Cluster #0, fuel consumption is not always assumed to be a linear function of driving distance like in [28]. Demir et al. studied the factors affecting fuel consumption [1,37], and divided them into vehicle, environment, traffic, driver, and operations factors, including speed, road gradient, congestion, driver, transmission, number of stops, and so on [29,38,39,40]. The majority of the models concerning fuel consumption focused on the first three factors, but did not capture issues related to drivers that are relatively difficult to measure. There is a close connection between fuel consumption and CO₂ emissions, and thus a large number of papers have incorporated some factors into their emission models to better plan an ’environmental-friendly’ routing [41,42]. Modeling CO₂ emissions in time-dependent VRPs has been mostly discussed [30,42,43,44], where emissions could be reduced by adjusting driving speed, and thus when estimating emissions, speed is considered to be a more crucial factor than driving distance. Since different vehicle types have different CO₂ emission characteristics, studies on CO₂ minimization using a heterogeneous vehicle fleet have been conducted [45,46,47]. Among all, Kopfer et al. [47] presented a major finding that using heterogeneous fleets could tremendously reduce CO₂ emissions. Congestion impacts on vehicle emissions are highly significant though difficult to predict, which leads many researchers to focus on them, such as [48,49]. Additionally, Xiao et al. [31] proposed a model incorporating fuel consumption rate into capacitated VRP, and verified that it could reduce fuel consumption by an average of 5% compared with the conventional model. PRPs involve broader and more comprehensive objective functions besides travel distance or time minimization; they are seeking for a tradeoff between emissions/fuel consumption and overall cost. Scholars are interested in the extensions of PRPs, such as time-dependent PRP [29,50], PRP with time windows, and PRP considering a heterogeneous vehicle fleet [51]. Although PRPs are significantly more difficult to find the optimal solution, they have the potential to save overall costs. Researchers have devoted themselves to developing algorithms for this class of problem within the framework of ALNS [30,32,50], variable neighborhood search, GA, artificial bee colony algorithm [52], and other specifically designed approaches. Tradeoffs between performance indexes, such as capacity utilization, fuel, emissions and other costs, have been analyzed by some scholars as well [41,51]. Among authors in this cluster, Tolga Bektaş and Gilbert Laporte, of foundational significance to the field as mentioned in Section 5, have 5 papers in this cluster, i.e., [1,30,32,37,41], with 4 of them co-authored with Emrah Demir.

• #1 Electric Vehicle

Starting from 2008, Cluster #1 is the second largest, with 40 papers and a total citation of 1238, unarguably occupying a pivotal position among several subfields of GVRP. This phenomenon can be simply explained by the fact that EVs were invented for a ‘green’ purpose.

With rising fuel prices and increasingly strict emission regulations, EVs are more and more favored by logistics enterprises than internal combustion engine vehicles. Pelletier et al. [6] outlined the technological and marketing background of EVs, offering insights for many transportation researchers. Many scholars have also studied economic and technological aspects, such as the competitiveness of commercial EVs [53,54] and battery degradation and behavior in transportation problems [55]. Though EVs have high energy utilization and low maintenance cost, they have not yet been widely used in logistics distribution, mainly because of the limited vehicle driving range, long recharging time and limited refueling infrastructure. Many scholars have proposed various solutions to mitigate these difficulties by alternative fuel-powered vehicle fleets [56], planning detours to the recharging stations [57], and focusing on the strategic decisions of designing cost-effective battery-swapping infrastructure networks [58]. Though faced with many limitations at present, researchers have made great contributions to tapping the potential of EVs and related optimization issues, including the EVRP aiming at finding an optimal plan for visiting a given set of customers, and the EVRP considering vehicle capacity and time windows constraints [59]. Many papers have studied different recharging schemes including implementing full-recharge policy [33], partial recharge strategies [34,59,60], battery swap [61,62], recharging at customers’ locations, partial recharges with normal, fast, and super-fast recharges [63] and other diverse recharging policies [64]. Papers investigating the partial charge drew a common conclusion that partial recharge may substantially improve the routing decisions and is more practical than the full recharge. Moreover, in the existing models, the battery-charge level is mostly assumed as a linear function of the charging time. However, neglecting nonlinear charging may, in fact, result in infeasible or overly expensive solutions, which should be considered in models [57,65]. Scholars’ interest in fleet composition in green logistics has increased since 2010, such as a mixed fleet of traditional internal combustion vehicles and commercial EVs [33], a combinational fleet of traditional, plug-in hybrid, and EVs [66], a heterogeneous fleet of EVs and hybrid EVs with multiple limited driving ranges [67] and particularly different types of EVs in two echelons [68]. Gerhard et al. [35] modeled an EVRP with EVs of different capacity, battery sizes, and acquisition costs considering recharging times and locations, adding more complexity to the typical problem. Computational results suggested that in a large variety of price scenarios, using a mixed fleet carefully could significantly reduce operational costs compared to a homogeneous fleet. As the research on these problems becomes mature, more real-life factors are incorporated into models including a driver’s stopping tolerance [69], charging-while-driving technology [70], and EVs have more application scenarios, such as the Dial-a-Ride problem [71]. Researchers have paid much attention to locating facilities for the EV distribution network as well [61,72,73,74,75,76,77,78,79], which affects the vehicle routes significantly. Furthermore, various important formulations and solutions have been presented in this cluster. For instance, Koc and Karaoglan [80] put forward a new mathematical formulation including fewer variables and constraints with no augmentation, and proposed a simulated annealing-based solution method for optimally solving the GVRP. He et al. [81] formulated three mathematical models considering various flow dependencies of the energy consumption of battery EVs and recharging time. Algorithms developed for EVRPTW include a hybrid variable neighborhood search/TS algorithm [36], ALNS [33,60], simulated annealing [34], GA [66], and exact branch-price-and-cut algorithms [64]. Figure 5 displays that the citation history of Cluster #1 lasts to 2020, indicating that the EVRP is and will remain a research hotspot of GVRP. Meanwhile, the figure also conveys a message that the development of EVRP has slowed down in recent years.

• #3 Reverse Logistics

Cluster #3 has a long time span of 2001 to 2013 and total citation of 126. RL plays a crucial role in closed-loop supply chain which is a non-negligible subfield of GVRP. However, Figure 5 conveys that this domain was once a research hotspot in the infancy stage, but now the size of it is shrinking. In order to avoid the unnecessary waste of vehicle transport capacity and effectively reduce the distribution cost, logistics companies usually consider implementing product distribution and waste collection simultaneously, which has given rise to the VRP with simultaneous pickup and delivery (VRPSPD). Generally, the VRPSPD assumes that all the delivered and pickup goods must originate from and transported back to the depot, each customer can be visited only once, and the goods must be unloaded before loading [82]. Readers interested in mathematical formulations of the VRPSPD may refer to [83,84,85]. VRPSPD has many practical applications, such as grocery store chains [82,84], and RL [86]. Furthermore, Alshamrani et al. [86] solved a problem slightly different from VRPSPD where materials can be returned to the depot in the following period of delivery. The VRP with backhauls is similar to the VRPSPD, except that it prioritizes linehaul customers over backhaul ones while delivering and picking up goods [87,88]. When it is unnecessary to meet all the pickup demands, the problem is called the VRP with deliveries and selective pickups [89]. Developing effective problem-solving strategies is also crucial for the efficient operation of the transportation system. To solve large-scale VRPSPDs arising in practical operations, research attention for combinatorial optimization has turned to more robust and effective hybrid metaheuristics. Within the framework of particle swarm optimization algorithm [83,90], ant colony system algorithm [91,92], TS algorithm [93,94,95,96], and a parallel iterative local search (LS) [97], large number of hybrid metaheuristics have been developed. To approximately solve the VRPSPD with high computational efficiency, Bianchessi and Righini [98] developed constructive algorithms, LS and TS algorithms for comparison, and implemented the application of the TS paradigm in complex and variable neighborhood-based algorithms. Besides the most commonly used heuristics and metaheuristics, some exact algorithms were also developed to solve the VRPSPD. For instance, Dell’Amico et al. [99] put forward a branch-and-price algorithm and employed two strategies to solve the exact dynamic programming and state space relaxation. Subramanian et al. [100] suggested a branch-and-cut algorithm with lazy separation for the VRPSPD.

• #4 Adaptive Large Neighborhood Search Algorithm

The ALNS algorithm was first developed by Ropke and Pisinger [101] as an extension of the large neighborhood search (LNS) algorithm [102], and later employed for solving other VRP variants like two-echelon VRP [103]. Given the initial solution, the ALNS algorithm can use the removal and insertion algorithm to destroy and reconstruct, so as to improve the current feasible solution. Removal operators that are frequently used in algorithms include Shaw removal (also known as related removal), random removal and worst removal, while the well-known insertion operators are greedy insertion and regret insertion. Papers also specifically designed operators for specific problems. For instance, Coelho et al. [104] developed Empty One Period, Empty One Vehicle, Avoid Consecutive Visits for multi-vehicle inventory-routing. Satellite Removal, Satellite Opening, Satellite Swap, Route Removal, Greedy Insertion Forbidden, and Greedy Insertion Perturbation have been used for both 2E-VRP [105] and two-echelon capacitated location-routing problem [106], respectively. Additionally, introducing randomization in the operators can, to some extent, enhance the global search ability [105]. Using removal and insertion algorithms in the ALNS can be regarded as employing LS with neighborhoods. There are other universal algorithms and mechanisms that have good local searching ability as well as their hybridization, including simulated annealing algorithm [107,108,109,110,111], TS algorithm [112,113,114], LNS [115,116], variable neighborhood descent [117], variable neighborhood search [118], greedy randomized procedure [119], greedy randomized adaptive search procedure [117,118], path relinking [118], evolutionary LS [117], and others embedded with local heuristics [120,121,122]. Our clustering results suggest that papers employing ALNS highly cited references of these algorithms, which enabled us to construct a library of LS algorithms that can be used or further developed for future studies.

• #5 Waste Collection

Waste collection is a type of rich VRP with high practical significance. There are various optimization problems in this subfield. For example, Crevier et al. [123] studied a special type of multi-depot VRP in which the depots can serve as intermediate replenishment stations on the route. A similar model was applied into the waste collection by Angelelli and Speranza [124]. Sbihi and Eglese [9] discussed the importance of waste management and collection in green logistics. As illustrated in Sbihi and Eglese [9], papers in waste collection can be basically divided into three categories. First is the models for hazardous-waste RL system, such as the cost-minimization model in Tung et al. [125]. Second, RL involving skips/roll-on roll-off containers commonly used for construction site waste [126], in which only one or two skips can be carried by a vehicle at once, and the number of customers can be visited before going to a disposal facility, is also limited. In the last category, there is the arc routing problem, in which collection is typically carried out along the streets [9]. The waste collection system always focuses on minimizing labor, operation, and transport costs, as well as emissions [127], with wide considerations of time windows [128,129,130], multiple disposal trips, and driver rest periods [128,129]. The optimization of collection services still depends on the understanding of local situations, so lots of studies have been proposed to solve the waste collection problem in localized scales. Geographic information systems technology, which provides locations of waste bins, road network topology, traffic conditions and population density, have been utilized to resolve waste collection system designs such as location, transportation, and installation [127,131,132].

Heuristic and meta heuristic algorithms are widely used by scholars to solve waste collection problems, including the nearest-neighbor algorithm [126], variable neighborhood search [128,130], Solomon’s insertion algorithm [129], guided variable neighborhood thresholding metaheuristic [133], particle swarm optimization [134], ant colony heuristics [135,136], backtracking search [137], list-based threshold accepting metaheuristic and variable neighborhood descent [138], and heuristics comprising route construction and route improvement [139].

Papers in this cluster focused more on solid waste collection [127,130,131,136], and some paid attention to oil waste requiring selective collection [138,140]. The distribution of studies on different waste types suggests that more concentration should be placed on special waste.

• #6 Two-Echelon Location-Routing Problem

The location-routing problem (LRP), arising in two-level transportation systems, is a major concern in supply chain network design. In such problems, goods are delivered to a major terminal and transported to the final customers through intermediate facilities. It addresses both facility location and vehicle routing problems to achieve overall optimization [141]. Due to its complexity compared to VRP, scholars usually need to construct multi-objective optimization models [141,142,143] and design algorithms to solve them, among which the most commonly used algorithm is TS [144,145,146]. As an approach of modeling and solving practical problems, it is studied in various scenarios including RL [144,147] and solid waste collection [145]. Nagy and Salhi [148] proposed a classification scheme of LRP, among which 2E-LRP is a very important variant. The difference between LRP and 2E-LRP is that routing in LRP occurs at the second echelon while that in 2E-LRP occurs at both levels. 2E-LRP is closely related to location problems and the supply chain management. As a consequence of integrating operations research with supply chain management, facility location problems have attracted widespread attention in the context of supply chain management [146,149]. Another relevant research, in a wider sense, is the design problem of supply chain networks which usually needs to determine a set of configuration parameters such as the number, capacity, location, and type of facilities [142,147,149,150]. We can observe that papers studying on 2E-LRP extensively cited references on these relevant research topics.

• #7 User Equilibrium

Logistics problems considering user equilibrium are usually based on the behavioral assumption that each driver travels on a route that minimizes travel time or cost from the origin to the destination (O-D pair) [151]. Congestion, location of refueling stations, and many other factors can affect travel choices, and drivers need to reach a balance between these factors and travel decisions. This user equilibrium condition can only be achieved when no driver can improve their travel time or cost by unilaterally changing their routes [81]. In the GVRP field, user equilibrium is mainly used to make decisions on locating refueling stations for alternative fuel vehicles [75,77,78,79] and/or charging station for EVs [70,74,76,81,152] and hybrid plug-in EVs [72], in order to address issues such as range anxiety, long charging time, or inconvenient battery swapping [153]. Therefore, it is often considered a location-allocation or location-routing problem.

• #8 Cold Chain Logistics

Papers on cold chain logistics consider various aspects of costs including the carbon emission costs, fixed costs, transportation costs, damage costs, refrigeration costs, fuel consumption costs, penalty costs, quality substitution cost, shortage costs, and so on. Among all, penalty costs incorporate customer satisfaction implicitly by adding costs when violating time window constraints [154,155,156]. Two papers on cold chain logistics particularly focused on the customer satisfaction. Hsiao et al. [157] fulfilled customer requirements for various foods with pre-appointed quality levels based on the estimated shelf life, which varies by food type and storage temperature, and continuously shortens during vehicle routing. Multi-item–multi-temperature vehicles were also involved in the distribution planning. Afterwards, Qin et al. [158] used the minimization of unit cost to achieve a fully satisfied customer as the objective. The results showed the trade-off between carbon emissions and customer satisfaction as the carbon price increased and that increasing the total cost by a small amount could greatly improve average customer satisfaction. Practical managerial implications for enterprises and government on reducing costs, protecting the environment, and improving customer satisfaction were provided as well.

From the above clustering analysis, we identified 9 clusters of GVRP and conducted further content analysis on six important topics. It can be seen that fuel consumption and EVs have been the focus of research by many scholars, and the latter’s popularity continued until 2020. RL has had a high level of popularity and attention. Although its popularity has declined since 2013, waste collection, as an important application field of GVRP and RL, has gradually developed into a topic with a certain level of popularity in the current context of severe ecological challenges. In addition, with the deepening development of the supply chain, the research focus in the GVRP field is expanding towards more complex LRPs. Finally, as the problems considered become more comprehensive and the models become more complex, algorithm solving is increasingly favored by scholars, among which ALNS is currently the algorithm with the most citations.

5. Research Potential Evaluation of GVRP

GVRP has been studied extensively and intensively, but the research potential of different subfields in GVRP deserves more attention. In this section, the RPE model is applied to evaluate the research potential for the nine typical clusters of GVRP obtained through CiteSpace in Section 4.2.2. We first count the TC and TP of all the articles in each cluster and calculated their ratio, TC/TP. Then, we calculate D, half-life, and R based on the earliest and latest publication year of articles in each cluster. Following that, the number of highly cited articles is derived according to Equation (3). Finally, the two indicators, maturity and RA, are figured out. The calculation results of the relevant indicators are elaborated in

Table 8. RPE indicators of clusters.

Cluster	AC	D	R	Half-Life	NH	Maturity	RA
#0	30.59	12	4	2012	28	0.55	0.64
#1	33.33	12	4	2015	26	0.65	0.69
#2	5.68	8	5	2009	15	0.48	0.06
#3	5.04	13	7	2007	20	0.71	0.06
#4	2.23	8	2	2011	26	1.00	0.14
#5	7.95	17	10	2008	12	0.57	0.05
#6	3.95	9	5	2007	12	0.63	0.09
#7	9.21	10	6	2012	14	1.00	0.15
#8	11.21	6	3	2016	14	1.00	0.62

Note: D: Duration; R: Recency; NH: Number of highly cited references; RA: Recent Attention.

.

From Table 8, we can see that the maturity of the nine clusters varies from 0.48 to 1. Therefore, we take the median values of 0.8 and 0.4 as the boundary point, divide maturity and RA into high and low intervals. Afterwards, taking maturity and RA as the horizontal and vertical axes, and (0.8, 0.4) as the origin, we construct the four-quadrant diagram Figure 6. The quadrant in blue is called “Diamond in the Rough” and contains two clusters (#0 and #1) with low maturity and high RA. Clusters #2, #5, and #6 have both low maturity and low RA, and are thus divided into the yellow quadrant “Possibility”. The quadrant in orange is called “Hard Core”, and there is only one cluster (#8) with both high maturity and high RA included. The remaining two clusters (#4 and #7) have high maturity and low RA and located in the red quadrant named “Chicken Ribs”. Figure 6 shows that the nine typical clusters are relatively uniform distributed in the quadrant diagram and clearly separated from each other, indicating that the RPE model has good recognition ability.

• Diamond in the Rough

Clusters #0 and #1 lies in the “Diamond in the Rough” quadrant are the most favorable research directions recently, which is consistent with the analysis of various research subfields in Section 2. Fuel consumption-related problems mainly aim to minimize the fuel consumption and carbon emissions, which also depends on the relevant research and development of fuel consumption and emission models in the transportation field to a certain extent. Just as in the field of GVRP, the high-maturity subfield promotes the development of other subfields, especially since there are some models and solution methods that can be cross-applied. So far, EVRPs mainly involve the VRPs of alternative fuel stations, charging stations and changing stations, as well as the problems of minimizing electric energy consumption of vehicles to reduce carbon emissions. In recent years, a large number of publications on EVRPs has emerged, and thus the half-life of these two clusters are very short, with an R value of only 4, which means that half of the latest published papers in the field of fuel consumption and EVRP were completed between 2013–2016 and 2016–2019, respectively.

• Hard Core

Cluster #8 is in the “Hardcore” quadrant, belonging to both high maturity and high frontier attention, indicating that this research area is the current focus of GVRP, and has reached a certain level of high-quality development. The literature in this subfield is highly valued, has a good development tendency, and the publication number is increasing steadily. Generally speaking, topics with higher maturity tend to have lower development potential, and may move from the “Hard Core” to the “Chicken Ribs” quadrant later. Nevertheless, cold chain logistics continued to attract attention and remained fast growth currently. Urbanization and changes in people’s lifestyles accelerate the growing needs for high-quality and fresh foods [159,160]. As stated in Accorsi et al. [161], 40% of foods require refrigeration during transportation, and 15% of global energy has provided fuel for cold chain infrastructure, promoting the rapid development of the cold chain logistics. As a special type of transportation logistics aiming at supplying fresh and cutting waste for perishable foods, cold chain logistics consumes more fuels and logistics costs and generates more carbon emissions than ordinary logistics [161,162,163]. Therefore, in the current era where environmental protection is increasingly valued, this topic is receiving more and more attention, and providing more and more support for practical applications, such as fruits-and-vegetables transportation [164,165]. As a result, it can be reasonably speculated that this subfield still has positive research potential and may even make some breakthroughs.

• Possibility

Clusters #2, #3, #5, and #6 are drawn in the “Possibility” quadrant. As can be seen from the RPE quadrant diagram, The subfield “service area” is least developed, since Cluster #2 obtains the lowest maturity though it has received some attention. The R values of Clusters #3 and #5 are 7 and 10, indicating that the literature on RL and waste collection are relatively old. One possible reason is that RL and closed-loop supply chain and waste collection and facility location are often jointly researched, and thus the occurence of them appearing individually as keywords decreased.

As the name “Possibility” implies, clusters in this quadrant may be of high diversity and uncertainty in their future, and may shift to one of the other three quadrants. For example, with the rapid social and economic development of many countries and the obvious urbanization process, sustainable/green supply chain design is of great help to the construction and development of urban logistics [166]. Under these circumstances, scholars may refocus their attention Cluster #6, which then might be transformed into the “Diamond in the Rough” quadrant.

• Chicken Ribs

Clusters #4 and #7 are in the “chicken rib” quadrant, belonging to the high-maturity and low-frontier attention. It can be seen that the ALNS algorithm is an early research hotspot, and has an R value of only 2, which means that half of the latest published papers in this subfield were completed between 2011–2012. For these subfields, it will be relatively difficult to make significant progress in the future.

In summarization, based on bibliometrics, RPE model analyzes and evaluates the research potential of the nine main subfields in GVRP. Among them, the prospects of Clusters #0 and #1 in the “Diamond in the Rough” quadrant are most optimistic, since they have low maturity and high RA. Subfield cold chain logistics in “Hard Core” has both high maturity and high RA, representing the current mainstream of research in the GVRP field. Over time, this topic will continue to be a research hotspot. With the attention increasing, Clusters #3, #5, and #6 may have the chance of shifting to the other quadrants, and be a hotspot in the GVRP field in the future.

6. Conclusions

This paper conducted a bibliometric-based survey of articles on GVRP in different scientific journals considering three aspects: GVRP, PRP, and VRPRL. Retrieved from the Web of Science database, 1230 papers published from 2000 to 2021 were reviewed and evaluated. In order to explore this research field qualitatively and visually, CiteSpace and VOSviewer have been employed to generate mapping knowledge domains, which helped carry out a bibliometric analysis from the macro and micro levels. From the macro level, this study conducted a systematic and comprehensive analysis of the literature growth trends, countries, authors, and journals, to provide researchers with an overview of the GVRP field, including the current development stage of the field, leading and rapidly developing countries in research, high-yield authors, and authoritative and high-quality journals. The GVRP field has gone through two stages. The number of publications fluctuated within ten per year during the infancy stage (2000–2012) while the developing stage (2013–2021) has witnessed a dramatic growth in both publications and citations of the published literature. When it comes to the performance of productive countries, China and the USA have published the largest number of articles, whereas the Canadian and British literature have the highest citations. From the perspective of high-yield authors, Gilbert Laporte is the most prolific and cited author with numerous collaborators, making the greatest contribution to GVRP. As for productive journals, the Journal of Cleaner Production, European Journal of Operational Research, and Transportation Research Part B became the most core and authoritative journals in the GVRP field due to their possession of the highest publication numbers, citations, and BC, respectively. From the micro level, this article provided readers with a further understanding of the development of various branches of GVRP through high-frequency keywords, keywords co-occurrence, reference co-citation, and detailed literature content analyses. High-frequency keywords can be categorized into two categories. One focuses on methodology, including modeling, optimization, heuristic and meta-heuristic algorithms, while the other focuses on themes such as RL, green logistics, fuel consumption, emissions, and EVs. The phased keywords analysis further indicated that RL, waste collection, and heuristic algorithm have received attention as early as the infancy stage, whereas emissions and EVs are products of their time and gradually became hot topics in the development stage. The keywords co-occurrence network density graph helped us achieve a further understanding of the relationships between these keywords. Reference co-citation analysis identified nine clusters, and content analysis showed that fuel consumption, EV, RL, ALNS, waste collection and 2E-LRP are the current research hotspots in the GVRP field.

Finally, the RPE model was employed to predict the future trends of GVRP research. Through further analysis, we pointed out that fuel consumption and EVRP have the most optimistic prospects in the near future, and that cold chain logistics has certain research potential and may even make some breakthroughs. In addition, with the development of the supply chain management, 2E-LRP may also become a “Diamond in the Rough”.

Generally speaking, by presenting a new and holistic scientometric analysis, this review contributes to clarifying the GVRP knowledge structure, which provides valuable guidance for scholars and researchers to find future directions. In the future, interested readers can explore multi-objective optimization problems starting from reducing fuel consumption, addressing new situations that may arise in electric vehicle routing and cold chain logistics, and integrating GVRP with other aspects of the supply chain to study more complex multiple-level supply chain network design problems such as location-routing, inventory-location-routing, and production-inventory-location-routing problems.