# Operations Research/Management Science Research in Europe: A Bibliometric Overview

Authors: Canser Bilir; Cengiz Güngör; Özgür Kökalan
Journal: Advances in Operations Research
 (2020)

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## Abstract

This paper provides a bibliometric analysis of the articles in the field of operations research or management science (OR/MS) published in the years 1980–2018 by European researchers. The analysis’s objective is to identify and examine the current state of OR/MS studies in Europe, which publishes about 38% of the papers published worldwide. The analysis was based on the data from the Web of Science (WoS) databases. We found a total of 65,352 papers in 148 different journals in the OR/MS field. The results provide a general picture of the studies, which are classified according to the most influential authors, institutions, papers, and journals. The study revealed that the ratio of OR/MS studies having at least one European author has steadily increased over the decades from 28.27% in the 1980 s to 41.29% in the 2010 s. The analysis also provides citation statistics of the European OR/MS articles. The study concluded that the impact of European publications is less than the impact of U.S. publications. The bibliometric analysis of the studies showed that only a small portion of the countries/regions, institutions, and even authors published a substantial portion of the papers, as indicated by the Pareto rule. The research trends have been identified through an analysis of keyword usage over the years. In keyword analysis, which subcategories are studied together is also identified. In the paper, collaboration among countries and institutions is also identified and depicted by using VOS viewer.


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## Body

## 1. Introduction and Literature Review

Operations research and management science (OR/MS) studies are considered an essential part of economic life because organizations are continually looking for the most efficient and productive ways of running their businesses. Therefore, the number of OR/MS studies has increased substantially over the last four decades [1]. Even though the initial OR/MS studies were mainly limited to specific regional areas such as the United States and the United Kingdom, the practice of operations research and management science has seen an enormous increase all over the world, including other developed countries, developing countries, and even underdeveloped countries.Bibliometric analysis, motivated by the development of Internet and online databases, is receiving increasing attention from the scientific community, and the number of bibliometric studies is increasing [2]. Several studies provided bibliometric analysis in many research areas, including OR/MS [1], project management [3], management [4], economics [5], supply chain management [6], and pricing research [7]. However, the number of papers presenting bibliometric analysis in OR/MS has been limited. Merigo and Yang [1] presented a bibliometric overview of research published in operations research and management science in recent decades. The paper’s main objective was to identify some of the most relevant research in this field and some of the newest trends according to the information found in the Web of Science (WoS) Database [1]. Laengle et al. [8] presented a bibliometric analysis in OR/MS to identify the most productive and influential universities between 1991 and 2015. The authors also collected the data from WoS database; however, the analysis is limited to universities and the location of those universities. Chang and Hsieh [9] evaluated the distribution of papers published by Asian authors in OR/MS journals from 1968 to 2006. The authors also compared the impact of OR/MS research in Asia with that of the research in United States and the world. The study also highlighted research trends by analyzing keywords [9]. Bilir et al. [10] provided a bibliometric analysis of the articles in the field of OR/MS published between the years 1980–2017 by researchers from Turkey. The main objective of the analysis was to identify and examine the current state of OR/MS studies in Turkey. The authors also identified the current research trends through a keywords analysis. However, the study was limited to one country [10]. Laengle et al. [11] presented a general overview of the European Journal of Operations Research over its lifetime using bibliometric indicators. They discussed the performance of the journal compared to other journals in the field and identified key contributing countries/institutions/authors as well as trends in research topics. Even though that study provided valuable information about OR/MS studies, it was limited to papers published in the European Journal of Operations Research.Our review revealed that there is no bibliometric study of OR/MS research in Europe even though there is one for the overall world and another study for Asia. To bridge that gap in the literature, in this paper, we aimed to provide a general overview of European OR/MS research over the last decades using bibliometric methods and compare the results of OR/MS research in Europe with that of the world and other regions. We used the WoS as the database for collecting information. Another objective is to identify the research trends in the field in Europe to understand the drivers of the development of European OR/MS studies and to compare the impact of OR/MS research in Europe with that of the United States and the world. Section2 describes the bibliometric methodology we applied in the analysis. Section 3 contains the results of our analysis. Section 4 summarizes findings and provides suggestion for future research.


## 2. Methodology

To conduct the bibliometric study, we reviewed and analyzed articles available in the WoS databases, which comprise the Science Citation Index Expanded (SCI-Expanded), the Social Sciences Citation Index (SSCI), the Arts and Humanities Citation Index (A&HCI), the Science Citation Index (SCI), and the Emerging Science Citation Index (ESCI). The WoS database, which is owned by Thomson and Reuters, includes studies from a wide range of research areas (252 subject categories), one of which is OR/MS. In the first step, we selected the articles in that category. We then excluded publications from 2019 because that year is not yet complete. As articles from 1975–79 were very limited, we also excluded those years. The list thus included 299,822 publications, including articles, proceedings paper, reviews, and notes. To focus on the most influential of the publications, we selected only articles. Thus, we reduced the number of publications to 172,535, published in 160 different journals. Because we included only articles in the WoS database, we did not exclude any journal from our analysis.To further refine the selection, countries in Europe are selected to have a list of articles in which at least one author is from a European country, where a list of 65,352 articles is generated from 50 different countries, published in 148 different journals. In analyzing collaborating countries and keywords, we also used VOSviewer [12] (a scientific software tool for constructing and visualizing bibliometric networks).


## 3. Results

We present our research results in the following subsections: number of papers throughout the selected years in Europe compared with the world, leading journals, and most productive authors; citation statistics and most-cited articles; and most productive institutions, collaboration analysis, and keyword analysis.


### 3.1. Number of Papers

The number of papers published in a specific area is an important indicator in scientific research. To analyze the number of OR/MS papers in Europe, we present the number of papers published in the world and in Europe (Figure1). The length of each bar represents the total number of papers published in the OR/MS category in the WoS database. The dark-colored bar represents the number of papers published in Europe, whereas the light-colored bar represents the number of papers published in the world. There is an upward trend in the number of papers in the OR/MS category starting from the 1980 s whose slope increases further after 2003. The number of studies with at least one European author is 65,352 (37.88%). However, the ratio of European studies to studies worldwide has increased steadily over the decades, from 28.27% in the 1980 s, to 32.76% in the 1990 s, to 39.68% in the 2000 s, and to 41.29% in the 2010 s.Figure 1
Number of papers in the OR/MS category (1980–2018).Figure2 presents the number of OR/MS papers from the top 25 most productive countries/regions in the world. The results show that one-third of the papers (56,602) have at least one author from the United States. Although the United States dominates OR/MS studies, the ratio of studies from the United States has been decreasing slightly over the decades. China follows the United States with 21,683 studies (12.57%), followed in turn by the United Kingdom (6.84%), Canada (6.40%), France (5.03%), and Taiwan (4.93%). Thirteen of the top 25 most publishing countries/regions in OR/MS are European (Figure 2).Figure 2
Number of OR/MS papers from the 25 most prolific countries/regions (1980–2018).We also analyzed the number of papers from the top eight publishing countries in Europe and the development of the number of papers throughout the years in those countries (Figure3) to identify how the number of papers from European countries changes between 1980–2018. Results showed that England is still the leading country in terms of the number of papers published each year; however, the number of papers published from French, German, and Italian researchers are close to the number published by English researchers in recent years. Another conclusion which may be drawn from the is that the number of papers published by researchers from Spain and Turkey was close to the number of papers published by the top publishing countries around 2010; however, the number of papers showed a rapid decline in recent years.Figure 3
The number of papers from the eight top publishing countries/regions in Europe (1980–2018).


### 3.2. Leading Journals

Our detailed analysis of the 65,352 publications revealed that the researchers have published articles mostly in theEuropean Journal of Operational Research (7,973 articles). The number of publications in this journal constitutes 12.2% of all the publications made in this field in Europe. Expert Systems with Applications (3,870; 5.9%), the International Journal of Production Research (2,906, 4.5%), the International Journal of Production Economics (2,782, 4.3%), and the Journal of the Operational Research Society (2,581; 3.9 %) were among the first five journals in which researchers published articles at the highest rates; 30.85% of the total publications appeared in those five journals.However, Merigó and Yang’s [1] analysis identified the three top journals for OR/MS publication as Management Science, Operations Research, and the European Journal of Operations Research. That study showed that researchers from European countries mainly preferred journals of European origin (especially the Netherlands, Germany, and the United Kingdom), more so than did researchers worldwide.The journal with the highest h-index among those preferred by academicians was the European Journal of Operational Research (h-index: 211); the one with the lowest index value was the International Journal of Technology Management (h-index: 48). Our study has also revealed that 16 of the 25 most publishing journals are among the best 25% (Quartile 1) of the journals in the field. Table1 shows the countries/regions in which the articles were published, the numbers of articles, and the proportion of these articles to all articles, their h-index information, the classification made by WoS, and the JRC 2016 Impact Factor values of the 25 journals in which European researchers mostly published.Table 1
Most publishing 25 journals in OR/MS in Europe (1980–2018).
RankJournal nameCountry/Region# of articles% of totalH-indexQuartileJCR 2016 impact factor1European Journal of Operational ResearchNetherlands7,97312.2%211Q13.4282Expert Systems with ApplicationsUnited States3,8705.9%145Q13.7683International Journal of Production ResearchUnited Kingdom2,9064.5%107Q12.6234International Journal of Production EconomicsNetherlands2,7824.3%141Q14.4075Journal of the Operational Research SocietyUnited Kingdom2,5813.9%87Q31.2256Reliability Engineering System SafetyNetherlands2,2583.5%112Q11.6667Journal of Optimization Theory and ApplicationsUnited States2,1313.3%74Q31.2348Systems & Control LettersNetherlands2,0693.1%117Q12.6569Annals of Operations ResearchNetherlands2,0113.1%86Q21.86410Computers & Operations ResearchUnited Kingdom2,0083.1%124Q12.96211Safety ScienceNetherlands1,6812.6%81Q22.83512International Journal of System ScienceUnited Kingdom1,5882.4%59Q22.18513Mathematical ProgrammingGermany1,3922.1%99Q12.49014Operations Research LettersNetherlands1,1231.7%63Q40.64315Management ScienceUnited States1,0931.7%209Q12.82216Journal of Global OptimizationNetherlands1,0751.6%70Q21.40717OMEGA-International Journal of Management ScienceUnited Kingdom1,0241.6%108Q14.31118International Journal of Technology ManagementUnited Kingdom1,0201.6%48Q20.41019TechnovationUnited Kingdom9641.5%102Q12.01020Production Planning & ControlUnited Kingdom9301.4%61Q12.33021Transportation Research Part B: MethodologicalUnited Kingdom8101.2%107Q13.11022Mathematics of Operations ResearchUnited States7531.2%67Q11.27023Decision Support SystemsNetherlands7421.1%115Q13.56524International Journal of Computer Integrated ManufacturingUnited Kingdom7311.1%44Q21.99525IEEE NetworksUnited States7151.1%106Q11.500


### 3.3. Most Productive Authors

We ranked the most productive/influential authors both by number of papers and by number of citations. The author publishing the most papers in the OR/MS category in Europe was Enrico Zio from Politecnico Milano, having published 154 papers. The second-ranked author was Luk N. Van Wassenhove from INSEAD Business School, France, with 122 papers. Wassenhove had two different author name accounts with spelling differences in the WoS database that must be merged. Terje Aven from Stavenger University, Norway, attained the third rank with 116 papers. Table2 presents most productive authors with their affiliation and number of published papers and ranks them by the total number of citations their papers have received. The most-cited author was Van Wassenhove with 9,684 citations. Van Wassenhove also has the highest H-index value (49), which shows that h number of papers have at least h number of citations. The second-ranked authors by number of citations were Rainer Storn and K. J. Price both from Siemens, Germany, even though they only had one paper in OR/MS.Table 2
Most productive authors in OR/MS in Europe (1980–2018).
Sorted by number of papersSort by total citationsRankAuthorsPapersInstitutionsRankAuthorPapersCitationsCitation per paperInstitutionH-index1Zio, Enrico154Politecnico Milano1Van Wassenhove, Luk N.1229,68179.35Insead Business School492Van Wassenhove, Luk N.122Insead Business School2Storn, Rainer19,0579057Siemens, Germany13Aven, Terje116Stavanger University3Price, K.19,0579057Siemens, Germany14Puerto, Justo111University of Seville4Beasley, John E.725,88281.69Brunel University355Speranza, M. Grazia108University of Brescia5Toth, Paolo984,63647.31University of Bologna396Dolgui, Alexandre101Centre National De La Recherche Scientifique6Potts, Chris N.804,24853.10University of Southampton337Dekker, Rommert99Erasmus University Rotterdam7Zio, Enrico1543,90425.35Politecnico Milano348Toth, Paolo98University of Bologna8Dekker, Rommert993,70337.40Erasmus University Rotterdam328Woeginger, Gerhard J.98Rwth Aachen University9Pisinger, David673,59953.72University of Copenhagen2910Hartl, Richard F.87University of Vienna10Fischetti, Mateo803,58641.66University of Padua3411Fischetti, Mateo86University of Padua11Cool, Karel23,4841742Insead Business School212Chu, Chengbin85Universite Paris Saclay12Dierickx, Ingemar23,4841742Insead Business School213Bruneel, Herwig83Ghent University13Slowinski, Roman583,02952.22Poznan University of Technology2914Carrizosa, Emilio82Lancaster University14Kelly, FP112,953268.45University of Cambridge815Potts, Chris N.80University of Southampton15Yang, Jian-Bo662,89243.82University of Manchaster2815Escudero, Laureano F.80Universidad Rey Juan Carlos16Disney, Stephen M.562,85450.96Cardiff University2717Dallery, Yves79Universite Paris Saclay17Wolsey, Laurence A.752,82937.72Catholic University of Louvain3018Marti, Rafael78University of Vallencia18Kahraman, Cengiz362,75676.56Istanbul Technical University2719Boysen, Nils77Friedrich Schiller Univ Jena19Aven, Terje1162,75123.72Stavanger University3120Kovalyov, Mikhail Y.76University of Siegen20Speranza, M. Grazia1082,64024.44University of Brescia27


### 3.4. Citation Statistics and Most-Cited Articles

By the end of 2018, OR/MS papers in the WoS database with at least one author from a European country had received 1,176,426 citations. We calculated the average number of citations per paper as 18.05. The average number of citations per paper for the articles published by U.S. researchers was 25.12. In comparing the two figures, someone might conclude that European publications had less impact than U.S. publications. Table3 presents the average number of citations per paper for the top 15 publishing countries.Table 3
Top publishing countries/regions in Europe-citation statistics (1980–2018).
Country/RegionNumber of papersTotal number of citationsCitation per paperEngland11,801224,41519.02France8,670152,38017.58Germany7,404130,02817.56Italy6,758116,35417.22Spain6,14798,77116.07Netherlands5,813110,47319.00Turkey3,64576,70121.04Belgium2,83670,46024.84Greece2,03636,73718.04Sweden1,86532,88417.63Poland1,77126,10114.74Portugal1,76831,53217.83Austria1,54426,11316.91Switzerland1,48132,20021.74Norway1,47227,61018.76Finland1,46228,39319.42We also classified the OR/MS articles in the WoS database by the number of citations received. Thus, the articles that have received most attention by the scientific community have been identified (Table4). Table 4 presents a list of the 20 most-cited articles from between 1980 and 2018 in OR/MS field in Europe. For each article, the table provides the name of the journal in which the article was published, the article’s ranking, the total number of citations, the paper’s title, the author(s)’ name(s), the publication year, and the average number of citations per year.Table 4
Most-cited articles in OR/MS in Europe (1980–2018).
RankTitleAuthorsJournalPublication yearTotal citationsAverage per year1Differential evolution-A simple and efficient heuristic for global optimization over continuous spacesStorn, R; Price, KJournal of Global Optimization19979,057411.682Asset Stock Accumulation and Sustainability of Competitive AdvantageDierickx, I; Cool, KManagement Science19893,215107.173Rate control for communication networks: shadow prices, proportional fairness and stabilityKelly, FP; Maulloo, AK; Tan, DKHJournal of the Operational Research Society19982,689128.054A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithmKaraboga, Dervis; Basturk, BahriyeJournal of Global Optimization20072,313192.755Thermodynamical Approach to the Traveling Salesman Problem–An Efficient Simulation AlgorithmCerny, VJournal of Optimization Theory and Applications19851,56045.886A Procedure for Ranking Efficient Units in Data Envelopment AnalysisAndersen, P; Petersen, NCManagement Science19931,36552,507Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSISOpricovic, S; Tzeng, GHEuropean Journal of Operational Research20041,22681.738Adapted Solution of a Backward Stochastic Differential EquationPardoux, E; Peng, SGSystem & Control Letters19901,09237.669Benchmarks for Basic Scheduling ProblemsTaillard, EEuropean Journal of Operational Research19931,05340.5010Arcs of integration: an international study of supply chain strategiesFrohlich, MT; Westbrook, RJournal of Operations Management200196253.4411OR-Library – Distributing Test Problems by Electronic MailBeasley, JEJournal of the Operational Research Society199095733.0012In search of complementarity in innovation strategy: Internal R&D and external knowledge acquisitionCassiman, B; Veugelers, RManagement Science200692571.1513An effective implementation of the Lin-Kernighan traveling salesman heuristicHelsgaun, KEuropean Journal of Operational Research200092548.6814Smooth minimization of non-smooth functionsNesterov, YMathematical Programming200588363.0715Exploratory innovation, exploitative innovation, and performance: Effects of organizational antecedents and environmental moderatorsJansen, Justin J. P.; Van den Bosch, Frans A. J.; Volberda, Henk W.Management Science200688067.6916AD Model Builder: using automatic differentiation for statistical inference of highly parameterized complex nonlinear modelsFournier, David A.; Skaug, Hans J.; Ancheta, Johnoel; Ianelli, James; Magnusson, Arni; Maunder, Mark N.; Nielsen, Anders; Sibert, JohnOptimization Methods & Software2012878125.4317How to Select and How to Rank Projects–The Promethee MethodBrans, JP; Vincke, P; Mareschal, BEuropean Journal of Operational Research198685025.7618A new discrete-time robust stability conditionsde Oliveira, MC; Bernussou, J; Geromel, JCSystem & Control Letters199984742.3519Linearization by Output Injection and Non-linear ObserversKrener, AJ; Isidori, ASystem & Control Letters198383023.0620Robust Optimization of Large Scale SystemsMulvey, JM; Vanderbei, RJ; Zeinos, SAOperations Research199582634.42The most-cited article is on a heuristic method for global optimization problems by R. Storn and K. Price in Journal of Global Optimization in 1997. The article received 9,057 citations so far. Then a study on asset stock accumulation comes with 3,215 citations by I. Dierickx and K. Cool in Management Science in 1989. Third rank is attained by a paper on communication networks by F. P. Kelly, Ak Maulloo, and D. K. H. Tan in theJournal of the Operational Research Society in 1998 with 2,689 citations. As seen in the table, four of the most-cited 20 papers appeared in Management Science and in the European Journal of Operations Research respectively.


### 3.5. Most Productive Institutions

Twenty institutions in Europe produced more than 500 papers during the years analyzed. The most productive institution in Europe in this field is the Centre National De La Recherche Scientifique, France with 2,492 papers (3.8% of the total). Other institutions with more than 1,000 papers are the Universite Paris Saclay Comue, France and Eindhoven University of Technology, Netherlands. Table5 lists the top 20 institutions, their number of papers, and the percentage of the total. The results show that around one-fourth of the papers are published by only 20 institutions, 15 of which are located in only three countries: the United Kingdom, Netherlands, and France.Table 5
Most productive institutions OR/MS in Europe (1980–2018).
InstitutionsCountry/RegionNumber of papers% of totalCentre National De La recherche scientifiqueFrance2,4923.8Universite paris saclay comueFrance1,1561.8Eindhoven University of technologyNetherlands1,1251.7University of londonUnited Kingdom8881.4Erasmus University rotterdamNetherlands8841.4INRIAFrance8211.3Ku leuvenBelgium7211.1Delft University of technologyNetherlands7171.1Polytechnic University of milanItaly7071.1University of manchasterUnited Kingdom7021.1University of southamptonUnited Kingdom6911.1Imperial college londonUnited Kingdom6601.0University of sevillaSpain6491.0University of BolognaItaly6411.0Universidade De lisboaPortugal6100.9Tilburg UniversityNetherlands6080.9Universite paris saclayFrance6040.9University of warwickUnited Kingdom5900.9University of twenteNetherlands5770.8Lancaster UniversityUnited Kingdom5570.8


### 3.6. Collaboration Analysis

As part of the bibliometric analysis, we investigated the collaboration among authors and the collaboration among countries in the field of OR/MS studies in Europe. First, we analyzed how the average number of authors changed from 1980 through 2018. Then, we presented the most collaborated countries within Europe and non-European countries collaborating with European researchers.In the analyzed papers, the average number of authors per article was 2.52. Figure4 provides a graph showing the distribution of average number of authors per article over time. The average number of authors for the year 2018 was about 3.1, whereas in 1979, it was 1.45. The results show that collaboration among authors increased steadily over time. This implies that researchers in the field have been collaborating more and more through the years.Figure 4
Number of authors per article.Table6 provides detailed statistics relating to the number of authors per article. More than 34% of the articles were written by two authors, around 27% of the articles were written by three authors, and around 20% of the articles were single-author papers. The maximum number of authors per article was 22. Only 54 articles in the OR/MS field had 10 or more authors in Europe.Table 6
Total number of authors per article.
Number of authorsTotal number of articlesPercentage of the total (%)112,37720.3221,00534.4316,67127.347,62012.552,2653.767281.272280.48880.19420.1≥10540.1We also used data retrieved from the WoS database to show the number of different countries involved in collaborative research articles. In Table7, first the number of countries whose researchers collaborated on an article was calculated, with the percentage of each listed. That is, 62.65% of the articles had authors from only one country, 28.54% of the articles had authors from two different countries, 7.20% of the articles had authors from three different countries, and so on.Table 7
Number of different countries collaborating on a given article.
# of different Country(ies)/Region(s) (in an article)% of articles162.65228.5437.2041.345 or more0.27We also analyzed the data to calculate the number of articles between (or among) collaborating countries/regions (Table8) using the address field in the data retrieved to define collaborating countries/regions. The most collaboration occurred between British and Chinese authors with 482 articles. This is followed by Turkish and American authors with 450 articles. The United States was the most likely to collaborate with European countries in the field of OR/MS.Table 8
Top collaborating countries/regions.
Collaborating countries/Regions# of articlesUnited Kingdom, People’s Republic of China482Turkey, United States450France, United States417United Kingdom, United States396France, Italy385Germany, United States343Italy, United States292Netherlands, United States281France, Canada265Spain, United States234France, People’s Republic of China182United Kingdom, Germany162United Kingdom, People’s Republic of China, Hong Kong143We also examined collaborations between European and non-European authors. Table9 lists only non-European countries with more than 500 authors. The United States took first place with 6,227 articles (9.5%), followed by China (2,293 articles, 3.5%) and Canada (2,006 articles, 3.1%).Table 9
Number of articles written in collaboration with non-European countries.
Countries/RegionsNumber of articles% of articlesUnited States6,2279.5People’s Republic of China2,2933.5Canada2,0063.1Australia8601.3Brazil6731.0We also used collaboration data to depict the relationships between the countries of collaborating authors with VOSviewer, a bibliometric network visualization tool (VOSviewer Visualizing scientific landscapes) to create “Collaborated Countries/Regions Relationship Diagram,” as shown in Figure5. In Figures 5 and 6, the size of the circle for each country/region represents the number of collaborative studies, and the thickness of links represents the number of studies between collaborating countries. The figures show that the top publishing countries in Europe have a large number of collaborations with the United States and that the United Kingdom has a relatively higher ratio of collaboration with China. Another result evident from the figure is that some pairs of countries (such as the United Kingdom and France or Germany and France, etc.) have relatively higher numbers of collaborations. The figure also shows that European countries collaborated with non-European countries as well as they did with European countries.Figure 5
Collaboration relationships between countries/regions.Figure 6
Collaborations of British authors.VOSviewer also allowed us to highlight the strength of collaboration between one selected country and other countries by pointing to that selected country with the mouse. Figure6 shows countries collaborating with British researchers. The thickness of links indicates that British authors collaborated most often with Chinese (482 articles) and American (396 articles) authors.


### 3.7. Keyword Analysis

The WoS database includes two different types of keywords: “Author Keywords” and “Keywords Plus.” Some articles discuss which of them is better (e.g., [13]). While “Keyword Plus” yielded more keywords, “Author Keywords” better explained the content of the article because the author(s) selected them specifically. This research analyzed and included “Author Keywords” from 1990 through 2018 in the resulting tables.To do the keyword analysis, we first retrieved the author keywords from the WoS database and corrected spelling mistakes. Later, we changed some British spellings of words to American English, such as optimization and optimization. We deleted dashes or spaces that we thought unnecessary (e.g., “multiobjective” or “multiobjective” to “multiobjective”) and examined in detail keywords repeated more than five times. Then, we identified and merged keywords with the same or similar meanings, such as “MCDM” and “Multi Criteria Decision Making” or “AHP” and “Analytic Hierarchy Process.” In addition, we identified similar keywords with same the meaning, such as “Heuristic,” “Heuristic Algorithm,” “Heuristic Algorithms,” “Heuristic Method,” “Heuristic Methods,” “Heuristic Optimization,” “Heuristic Search,” and “Heuristics.” They were basically the same areas of study used by different articles, so we changed them all to Heuristics. In the analysis, we eliminated no keywords; we only examined them and changed, corrected, or merged them to maintain a common language among articles.Table10 depicts a list of the number of repetitions of the top 20 keywords, repeated 500 or more times between the years 1990 and 2018 (inclusive). The most repeated keyword is “Multiobjective Optimization” (1,900 times), followed by “Heuristics” (1,587 times) and “Scheduling” (1,577 times). The table also shows how the number of appearances of each keyword changed throughout the years analyzed.Table 10
Distribution of the most repeated keywords by year (between 1990 and 2018).
Keywords19901991199219931994199519961997199819992000200120022003200420052006200720082009201020112012201320142015201620172018Freq.Multiobjective optimization213151420282525304342354747604862878310697123115105981461191301351900Heuristics3191318263144335742362956555060618577817178838470908882651587Scheduling3161516282842214637384243335170578390797881848967937095821577Simulation07119102126262931322829314136375555746965695751775267711166Optimization1131513182620203022362835192825443344675361726640707379901141Supply chain management0000073337122435324930425960706374897866666084871103Genetic algorithms0001171411151917121819302732504572546573684266494257906Data envelopment analysis13225142013102016281214333325292156524162515868557491909Integer Programming26166815910291415222515301539383644445056324755695179877Decision support systems29121124131325281923242125222440332549362846443250555645834Combinatorial optimization044488817171014131516222840343847313946564057366045757Dynamic programming058121612152218162717132381724283642313331453944333945699Linear programming110261822161923162724201925222024272529242132222630422920659Optimal control1111058101116182016222023191625231826352541343329414650652Branch and Bound16778141913292122171117201919294428242527362920303330605Inventory037447181314241618816142633322628192728453430294035598Global optimization063151891118141620171514182119242640341928352325333634591Tabu Search03016716927161310171216251724393529304427242220189516Stochastic programming01421391414111613129141815312440262943232537343851557Metaheuristics00000020153587181826302541293149442741325924525We then generated mini column graphics based on numbers of keywords and on percentage of each keyword, calculated by dividing the number of keywords into the number of articles each year. Figure7 shows these mini column graphics. The mini graphics show that the frequency of “Multiobjective Optimization” increased in interest over the years studied. Although the frequency increased slightly percentagewise, it did not increase as much as did the keyword frequency. Almost no interest existed for “Supply Chain Management” before 2000 or for “Metaheuristics” before 2004. Considering the number of keywords by years in number, we can conclude that no substantial change in the number of articles with the keyword “Linear Programming” existed. However, the trend for the percentages of articles through the years with the keyword “Linear Programming” decreased.Figure 7
Mini column graphics of most repeated keywords.When we compare the most repeated keywords in our study and keywords in similar studies (e.g., [1, 9], we do not find much difference between the keywords in the studies in Europe and the studies worldwide or in Asia. That is, the European OR/MS studies have similar keywords and subresearch categories to those studies worldwide. The results also support the common belief that in academic life, some subjects become trendy, studied by researchers study heavily for a period of time (as in “Tabu Search” and “Metaheuristics”).Using the VOSviewer software, we investigated the original table of keywords analyzed and the 100 most repeated keywords for further consideration to visualize the keywords studied together. That visualization also helped us understand which subcategories of OR/MS are commonly studied together in Europe. We manipulated the above-mentioned data with VOSviewer to create “Keywords Relationship Diagram” in Figure8, which presents only categories that have been used 25 or more times.Figure 8
Keywords relationship diagram.In the diagram, the size of the circle for each keyword represents the number of articles using that keyword while the thickness of the links represents the number of articles that used the keywords in both sides of the link, similar to the network of collaborating countries/regions in Figure5.Drawing conclusions from Figure8 was somewhat complicated because it included 100 keywords. To make it easier to understand the relationships with mostly used keywords, we highlighted the most repeated keywords, as in Figures 9(a)–9(c).Figure 9
(a) Keywords relationship diagram of “Multiobjective Optimization,” (b) Keywords relationship diagram of “Heuristics,” (c) Keywords relationship diagram of “Scheduling.”
(a)(b)(c)Figure9(a). Keywords relationship diagram of “Multiobjective Optimization” depicts the relationships of the most repeated keyword, “Multiobjective optimization,” with the other keywords. The diagram clearly illustrates which methodologies are most commonly jointly used with “Multiobjective optimization” in the analyzed papers. The diagram indicates that “Multiobjective optimization” is mostly used together with “Decision support systems,” “Genetic algorithms,” and “Evolutionary algorithms.”Figure9(b). Keywords relationship diagram of “Heuristics” presents the same diagram for “Heuristics.” The diagram indicates that “Heuristics” is mostly used together with “Scheduling” and “Combinatorial optimization.”The same diagram is presented for “Scheduling” in Figure9(c). Keywords relationship diagram of “Scheduling.” This diagram also lists the scheduling studies with the number of appearances in the literature (production scheduling, production planning, maintenance scheduling, routing etc.) The diagram also shows that “Scheduling” is mostly used together with “Heuristics.”


## 3.1. Number of Papers

The number of papers published in a specific area is an important indicator in scientific research. To analyze the number of OR/MS papers in Europe, we present the number of papers published in the world and in Europe (Figure1). The length of each bar represents the total number of papers published in the OR/MS category in the WoS database. The dark-colored bar represents the number of papers published in Europe, whereas the light-colored bar represents the number of papers published in the world. There is an upward trend in the number of papers in the OR/MS category starting from the 1980 s whose slope increases further after 2003. The number of studies with at least one European author is 65,352 (37.88%). However, the ratio of European studies to studies worldwide has increased steadily over the decades, from 28.27% in the 1980 s, to 32.76% in the 1990 s, to 39.68% in the 2000 s, and to 41.29% in the 2010 s.Figure 1
Number of papers in the OR/MS category (1980–2018).Figure2 presents the number of OR/MS papers from the top 25 most productive countries/regions in the world. The results show that one-third of the papers (56,602) have at least one author from the United States. Although the United States dominates OR/MS studies, the ratio of studies from the United States has been decreasing slightly over the decades. China follows the United States with 21,683 studies (12.57%), followed in turn by the United Kingdom (6.84%), Canada (6.40%), France (5.03%), and Taiwan (4.93%). Thirteen of the top 25 most publishing countries/regions in OR/MS are European (Figure 2).Figure 2
Number of OR/MS papers from the 25 most prolific countries/regions (1980–2018).We also analyzed the number of papers from the top eight publishing countries in Europe and the development of the number of papers throughout the years in those countries (Figure3) to identify how the number of papers from European countries changes between 1980–2018. Results showed that England is still the leading country in terms of the number of papers published each year; however, the number of papers published from French, German, and Italian researchers are close to the number published by English researchers in recent years. Another conclusion which may be drawn from the is that the number of papers published by researchers from Spain and Turkey was close to the number of papers published by the top publishing countries around 2010; however, the number of papers showed a rapid decline in recent years.Figure 3
The number of papers from the eight top publishing countries/regions in Europe (1980–2018).


## 3.2. Leading Journals

Our detailed analysis of the 65,352 publications revealed that the researchers have published articles mostly in theEuropean Journal of Operational Research (7,973 articles). The number of publications in this journal constitutes 12.2% of all the publications made in this field in Europe. Expert Systems with Applications (3,870; 5.9%), the International Journal of Production Research (2,906, 4.5%), the International Journal of Production Economics (2,782, 4.3%), and the Journal of the Operational Research Society (2,581; 3.9 %) were among the first five journals in which researchers published articles at the highest rates; 30.85% of the total publications appeared in those five journals.However, Merigó and Yang’s [1] analysis identified the three top journals for OR/MS publication as Management Science, Operations Research, and the European Journal of Operations Research. That study showed that researchers from European countries mainly preferred journals of European origin (especially the Netherlands, Germany, and the United Kingdom), more so than did researchers worldwide.The journal with the highest h-index among those preferred by academicians was the European Journal of Operational Research (h-index: 211); the one with the lowest index value was the International Journal of Technology Management (h-index: 48). Our study has also revealed that 16 of the 25 most publishing journals are among the best 25% (Quartile 1) of the journals in the field. Table1 shows the countries/regions in which the articles were published, the numbers of articles, and the proportion of these articles to all articles, their h-index information, the classification made by WoS, and the JRC 2016 Impact Factor values of the 25 journals in which European researchers mostly published.Table 1
Most publishing 25 journals in OR/MS in Europe (1980–2018).
RankJournal nameCountry/Region# of articles% of totalH-indexQuartileJCR 2016 impact factor1European Journal of Operational ResearchNetherlands7,97312.2%211Q13.4282Expert Systems with ApplicationsUnited States3,8705.9%145Q13.7683International Journal of Production ResearchUnited Kingdom2,9064.5%107Q12.6234International Journal of Production EconomicsNetherlands2,7824.3%141Q14.4075Journal of the Operational Research SocietyUnited Kingdom2,5813.9%87Q31.2256Reliability Engineering System SafetyNetherlands2,2583.5%112Q11.6667Journal of Optimization Theory and ApplicationsUnited States2,1313.3%74Q31.2348Systems & Control LettersNetherlands2,0693.1%117Q12.6569Annals of Operations ResearchNetherlands2,0113.1%86Q21.86410Computers & Operations ResearchUnited Kingdom2,0083.1%124Q12.96211Safety ScienceNetherlands1,6812.6%81Q22.83512International Journal of System ScienceUnited Kingdom1,5882.4%59Q22.18513Mathematical ProgrammingGermany1,3922.1%99Q12.49014Operations Research LettersNetherlands1,1231.7%63Q40.64315Management ScienceUnited States1,0931.7%209Q12.82216Journal of Global OptimizationNetherlands1,0751.6%70Q21.40717OMEGA-International Journal of Management ScienceUnited Kingdom1,0241.6%108Q14.31118International Journal of Technology ManagementUnited Kingdom1,0201.6%48Q20.41019TechnovationUnited Kingdom9641.5%102Q12.01020Production Planning & ControlUnited Kingdom9301.4%61Q12.33021Transportation Research Part B: MethodologicalUnited Kingdom8101.2%107Q13.11022Mathematics of Operations ResearchUnited States7531.2%67Q11.27023Decision Support SystemsNetherlands7421.1%115Q13.56524International Journal of Computer Integrated ManufacturingUnited Kingdom7311.1%44Q21.99525IEEE NetworksUnited States7151.1%106Q11.500


## 3.3. Most Productive Authors

We ranked the most productive/influential authors both by number of papers and by number of citations. The author publishing the most papers in the OR/MS category in Europe was Enrico Zio from Politecnico Milano, having published 154 papers. The second-ranked author was Luk N. Van Wassenhove from INSEAD Business School, France, with 122 papers. Wassenhove had two different author name accounts with spelling differences in the WoS database that must be merged. Terje Aven from Stavenger University, Norway, attained the third rank with 116 papers. Table2 presents most productive authors with their affiliation and number of published papers and ranks them by the total number of citations their papers have received. The most-cited author was Van Wassenhove with 9,684 citations. Van Wassenhove also has the highest H-index value (49), which shows that h number of papers have at least h number of citations. The second-ranked authors by number of citations were Rainer Storn and K. J. Price both from Siemens, Germany, even though they only had one paper in OR/MS.Table 2
Most productive authors in OR/MS in Europe (1980–2018).
Sorted by number of papersSort by total citationsRankAuthorsPapersInstitutionsRankAuthorPapersCitationsCitation per paperInstitutionH-index1Zio, Enrico154Politecnico Milano1Van Wassenhove, Luk N.1229,68179.35Insead Business School492Van Wassenhove, Luk N.122Insead Business School2Storn, Rainer19,0579057Siemens, Germany13Aven, Terje116Stavanger University3Price, K.19,0579057Siemens, Germany14Puerto, Justo111University of Seville4Beasley, John E.725,88281.69Brunel University355Speranza, M. Grazia108University of Brescia5Toth, Paolo984,63647.31University of Bologna396Dolgui, Alexandre101Centre National De La Recherche Scientifique6Potts, Chris N.804,24853.10University of Southampton337Dekker, Rommert99Erasmus University Rotterdam7Zio, Enrico1543,90425.35Politecnico Milano348Toth, Paolo98University of Bologna8Dekker, Rommert993,70337.40Erasmus University Rotterdam328Woeginger, Gerhard J.98Rwth Aachen University9Pisinger, David673,59953.72University of Copenhagen2910Hartl, Richard F.87University of Vienna10Fischetti, Mateo803,58641.66University of Padua3411Fischetti, Mateo86University of Padua11Cool, Karel23,4841742Insead Business School212Chu, Chengbin85Universite Paris Saclay12Dierickx, Ingemar23,4841742Insead Business School213Bruneel, Herwig83Ghent University13Slowinski, Roman583,02952.22Poznan University of Technology2914Carrizosa, Emilio82Lancaster University14Kelly, FP112,953268.45University of Cambridge815Potts, Chris N.80University of Southampton15Yang, Jian-Bo662,89243.82University of Manchaster2815Escudero, Laureano F.80Universidad Rey Juan Carlos16Disney, Stephen M.562,85450.96Cardiff University2717Dallery, Yves79Universite Paris Saclay17Wolsey, Laurence A.752,82937.72Catholic University of Louvain3018Marti, Rafael78University of Vallencia18Kahraman, Cengiz362,75676.56Istanbul Technical University2719Boysen, Nils77Friedrich Schiller Univ Jena19Aven, Terje1162,75123.72Stavanger University3120Kovalyov, Mikhail Y.76University of Siegen20Speranza, M. Grazia1082,64024.44University of Brescia27


## 3.4. Citation Statistics and Most-Cited Articles

By the end of 2018, OR/MS papers in the WoS database with at least one author from a European country had received 1,176,426 citations. We calculated the average number of citations per paper as 18.05. The average number of citations per paper for the articles published by U.S. researchers was 25.12. In comparing the two figures, someone might conclude that European publications had less impact than U.S. publications. Table3 presents the average number of citations per paper for the top 15 publishing countries.Table 3
Top publishing countries/regions in Europe-citation statistics (1980–2018).
Country/RegionNumber of papersTotal number of citationsCitation per paperEngland11,801224,41519.02France8,670152,38017.58Germany7,404130,02817.56Italy6,758116,35417.22Spain6,14798,77116.07Netherlands5,813110,47319.00Turkey3,64576,70121.04Belgium2,83670,46024.84Greece2,03636,73718.04Sweden1,86532,88417.63Poland1,77126,10114.74Portugal1,76831,53217.83Austria1,54426,11316.91Switzerland1,48132,20021.74Norway1,47227,61018.76Finland1,46228,39319.42We also classified the OR/MS articles in the WoS database by the number of citations received. Thus, the articles that have received most attention by the scientific community have been identified (Table4). Table 4 presents a list of the 20 most-cited articles from between 1980 and 2018 in OR/MS field in Europe. For each article, the table provides the name of the journal in which the article was published, the article’s ranking, the total number of citations, the paper’s title, the author(s)’ name(s), the publication year, and the average number of citations per year.Table 4
Most-cited articles in OR/MS in Europe (1980–2018).
RankTitleAuthorsJournalPublication yearTotal citationsAverage per year1Differential evolution-A simple and efficient heuristic for global optimization over continuous spacesStorn, R; Price, KJournal of Global Optimization19979,057411.682Asset Stock Accumulation and Sustainability of Competitive AdvantageDierickx, I; Cool, KManagement Science19893,215107.173Rate control for communication networks: shadow prices, proportional fairness and stabilityKelly, FP; Maulloo, AK; Tan, DKHJournal of the Operational Research Society19982,689128.054A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithmKaraboga, Dervis; Basturk, BahriyeJournal of Global Optimization20072,313192.755Thermodynamical Approach to the Traveling Salesman Problem–An Efficient Simulation AlgorithmCerny, VJournal of Optimization Theory and Applications19851,56045.886A Procedure for Ranking Efficient Units in Data Envelopment AnalysisAndersen, P; Petersen, NCManagement Science19931,36552,507Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSISOpricovic, S; Tzeng, GHEuropean Journal of Operational Research20041,22681.738Adapted Solution of a Backward Stochastic Differential EquationPardoux, E; Peng, SGSystem & Control Letters19901,09237.669Benchmarks for Basic Scheduling ProblemsTaillard, EEuropean Journal of Operational Research19931,05340.5010Arcs of integration: an international study of supply chain strategiesFrohlich, MT; Westbrook, RJournal of Operations Management200196253.4411OR-Library – Distributing Test Problems by Electronic MailBeasley, JEJournal of the Operational Research Society199095733.0012In search of complementarity in innovation strategy: Internal R&D and external knowledge acquisitionCassiman, B; Veugelers, RManagement Science200692571.1513An effective implementation of the Lin-Kernighan traveling salesman heuristicHelsgaun, KEuropean Journal of Operational Research200092548.6814Smooth minimization of non-smooth functionsNesterov, YMathematical Programming200588363.0715Exploratory innovation, exploitative innovation, and performance: Effects of organizational antecedents and environmental moderatorsJansen, Justin J. P.; Van den Bosch, Frans A. J.; Volberda, Henk W.Management Science200688067.6916AD Model Builder: using automatic differentiation for statistical inference of highly parameterized complex nonlinear modelsFournier, David A.; Skaug, Hans J.; Ancheta, Johnoel; Ianelli, James; Magnusson, Arni; Maunder, Mark N.; Nielsen, Anders; Sibert, JohnOptimization Methods & Software2012878125.4317How to Select and How to Rank Projects–The Promethee MethodBrans, JP; Vincke, P; Mareschal, BEuropean Journal of Operational Research198685025.7618A new discrete-time robust stability conditionsde Oliveira, MC; Bernussou, J; Geromel, JCSystem & Control Letters199984742.3519Linearization by Output Injection and Non-linear ObserversKrener, AJ; Isidori, ASystem & Control Letters198383023.0620Robust Optimization of Large Scale SystemsMulvey, JM; Vanderbei, RJ; Zeinos, SAOperations Research199582634.42The most-cited article is on a heuristic method for global optimization problems by R. Storn and K. Price in Journal of Global Optimization in 1997. The article received 9,057 citations so far. Then a study on asset stock accumulation comes with 3,215 citations by I. Dierickx and K. Cool in Management Science in 1989. Third rank is attained by a paper on communication networks by F. P. Kelly, Ak Maulloo, and D. K. H. Tan in theJournal of the Operational Research Society in 1998 with 2,689 citations. As seen in the table, four of the most-cited 20 papers appeared in Management Science and in the European Journal of Operations Research respectively.


## 3.5. Most Productive Institutions

Twenty institutions in Europe produced more than 500 papers during the years analyzed. The most productive institution in Europe in this field is the Centre National De La Recherche Scientifique, France with 2,492 papers (3.8% of the total). Other institutions with more than 1,000 papers are the Universite Paris Saclay Comue, France and Eindhoven University of Technology, Netherlands. Table5 lists the top 20 institutions, their number of papers, and the percentage of the total. The results show that around one-fourth of the papers are published by only 20 institutions, 15 of which are located in only three countries: the United Kingdom, Netherlands, and France.Table 5
Most productive institutions OR/MS in Europe (1980–2018).
InstitutionsCountry/RegionNumber of papers% of totalCentre National De La recherche scientifiqueFrance2,4923.8Universite paris saclay comueFrance1,1561.8Eindhoven University of technologyNetherlands1,1251.7University of londonUnited Kingdom8881.4Erasmus University rotterdamNetherlands8841.4INRIAFrance8211.3Ku leuvenBelgium7211.1Delft University of technologyNetherlands7171.1Polytechnic University of milanItaly7071.1University of manchasterUnited Kingdom7021.1University of southamptonUnited Kingdom6911.1Imperial college londonUnited Kingdom6601.0University of sevillaSpain6491.0University of BolognaItaly6411.0Universidade De lisboaPortugal6100.9Tilburg UniversityNetherlands6080.9Universite paris saclayFrance6040.9University of warwickUnited Kingdom5900.9University of twenteNetherlands5770.8Lancaster UniversityUnited Kingdom5570.8


## 3.6. Collaboration Analysis

As part of the bibliometric analysis, we investigated the collaboration among authors and the collaboration among countries in the field of OR/MS studies in Europe. First, we analyzed how the average number of authors changed from 1980 through 2018. Then, we presented the most collaborated countries within Europe and non-European countries collaborating with European researchers.In the analyzed papers, the average number of authors per article was 2.52. Figure4 provides a graph showing the distribution of average number of authors per article over time. The average number of authors for the year 2018 was about 3.1, whereas in 1979, it was 1.45. The results show that collaboration among authors increased steadily over time. This implies that researchers in the field have been collaborating more and more through the years.Figure 4
Number of authors per article.Table6 provides detailed statistics relating to the number of authors per article. More than 34% of the articles were written by two authors, around 27% of the articles were written by three authors, and around 20% of the articles were single-author papers. The maximum number of authors per article was 22. Only 54 articles in the OR/MS field had 10 or more authors in Europe.Table 6
Total number of authors per article.
Number of authorsTotal number of articlesPercentage of the total (%)112,37720.3221,00534.4316,67127.347,62012.552,2653.767281.272280.48880.19420.1≥10540.1We also used data retrieved from the WoS database to show the number of different countries involved in collaborative research articles. In Table7, first the number of countries whose researchers collaborated on an article was calculated, with the percentage of each listed. That is, 62.65% of the articles had authors from only one country, 28.54% of the articles had authors from two different countries, 7.20% of the articles had authors from three different countries, and so on.Table 7
Number of different countries collaborating on a given article.
# of different Country(ies)/Region(s) (in an article)% of articles162.65228.5437.2041.345 or more0.27We also analyzed the data to calculate the number of articles between (or among) collaborating countries/regions (Table8) using the address field in the data retrieved to define collaborating countries/regions. The most collaboration occurred between British and Chinese authors with 482 articles. This is followed by Turkish and American authors with 450 articles. The United States was the most likely to collaborate with European countries in the field of OR/MS.Table 8
Top collaborating countries/regions.
Collaborating countries/Regions# of articlesUnited Kingdom, People’s Republic of China482Turkey, United States450France, United States417United Kingdom, United States396France, Italy385Germany, United States343Italy, United States292Netherlands, United States281France, Canada265Spain, United States234France, People’s Republic of China182United Kingdom, Germany162United Kingdom, People’s Republic of China, Hong Kong143We also examined collaborations between European and non-European authors. Table9 lists only non-European countries with more than 500 authors. The United States took first place with 6,227 articles (9.5%), followed by China (2,293 articles, 3.5%) and Canada (2,006 articles, 3.1%).Table 9
Number of articles written in collaboration with non-European countries.
Countries/RegionsNumber of articles% of articlesUnited States6,2279.5People’s Republic of China2,2933.5Canada2,0063.1Australia8601.3Brazil6731.0We also used collaboration data to depict the relationships between the countries of collaborating authors with VOSviewer, a bibliometric network visualization tool (VOSviewer Visualizing scientific landscapes) to create “Collaborated Countries/Regions Relationship Diagram,” as shown in Figure5. In Figures 5 and 6, the size of the circle for each country/region represents the number of collaborative studies, and the thickness of links represents the number of studies between collaborating countries. The figures show that the top publishing countries in Europe have a large number of collaborations with the United States and that the United Kingdom has a relatively higher ratio of collaboration with China. Another result evident from the figure is that some pairs of countries (such as the United Kingdom and France or Germany and France, etc.) have relatively higher numbers of collaborations. The figure also shows that European countries collaborated with non-European countries as well as they did with European countries.Figure 5
Collaboration relationships between countries/regions.Figure 6
Collaborations of British authors.VOSviewer also allowed us to highlight the strength of collaboration between one selected country and other countries by pointing to that selected country with the mouse. Figure6 shows countries collaborating with British researchers. The thickness of links indicates that British authors collaborated most often with Chinese (482 articles) and American (396 articles) authors.


## 3.7. Keyword Analysis

The WoS database includes two different types of keywords: “Author Keywords” and “Keywords Plus.” Some articles discuss which of them is better (e.g., [13]). While “Keyword Plus” yielded more keywords, “Author Keywords” better explained the content of the article because the author(s) selected them specifically. This research analyzed and included “Author Keywords” from 1990 through 2018 in the resulting tables.To do the keyword analysis, we first retrieved the author keywords from the WoS database and corrected spelling mistakes. Later, we changed some British spellings of words to American English, such as optimization and optimization. We deleted dashes or spaces that we thought unnecessary (e.g., “multiobjective” or “multiobjective” to “multiobjective”) and examined in detail keywords repeated more than five times. Then, we identified and merged keywords with the same or similar meanings, such as “MCDM” and “Multi Criteria Decision Making” or “AHP” and “Analytic Hierarchy Process.” In addition, we identified similar keywords with same the meaning, such as “Heuristic,” “Heuristic Algorithm,” “Heuristic Algorithms,” “Heuristic Method,” “Heuristic Methods,” “Heuristic Optimization,” “Heuristic Search,” and “Heuristics.” They were basically the same areas of study used by different articles, so we changed them all to Heuristics. In the analysis, we eliminated no keywords; we only examined them and changed, corrected, or merged them to maintain a common language among articles.Table10 depicts a list of the number of repetitions of the top 20 keywords, repeated 500 or more times between the years 1990 and 2018 (inclusive). The most repeated keyword is “Multiobjective Optimization” (1,900 times), followed by “Heuristics” (1,587 times) and “Scheduling” (1,577 times). The table also shows how the number of appearances of each keyword changed throughout the years analyzed.Table 10
Distribution of the most repeated keywords by year (between 1990 and 2018).
Keywords19901991199219931994199519961997199819992000200120022003200420052006200720082009201020112012201320142015201620172018Freq.Multiobjective optimization213151420282525304342354747604862878310697123115105981461191301351900Heuristics3191318263144335742362956555060618577817178838470908882651587Scheduling3161516282842214637384243335170578390797881848967937095821577Simulation07119102126262931322829314136375555746965695751775267711166Optimization1131513182620203022362835192825443344675361726640707379901141Supply chain management0000073337122435324930425960706374897866666084871103Genetic algorithms0001171411151917121819302732504572546573684266494257906Data envelopment analysis13225142013102016281214333325292156524162515868557491909Integer Programming26166815910291415222515301539383644445056324755695179877Decision support systems29121124131325281923242125222440332549362846443250555645834Combinatorial optimization044488817171014131516222840343847313946564057366045757Dynamic programming058121612152218162717132381724283642313331453944333945699Linear programming110261822161923162724201925222024272529242132222630422920659Optimal control1111058101116182016222023191625231826352541343329414650652Branch and Bound16778141913292122171117201919294428242527362920303330605Inventory037447181314241618816142633322628192728453430294035598Global optimization063151891118141620171514182119242640341928352325333634591Tabu Search03016716927161310171216251724393529304427242220189516Stochastic programming01421391414111613129141815312440262943232537343851557Metaheuristics00000020153587181826302541293149442741325924525We then generated mini column graphics based on numbers of keywords and on percentage of each keyword, calculated by dividing the number of keywords into the number of articles each year. Figure7 shows these mini column graphics. The mini graphics show that the frequency of “Multiobjective Optimization” increased in interest over the years studied. Although the frequency increased slightly percentagewise, it did not increase as much as did the keyword frequency. Almost no interest existed for “Supply Chain Management” before 2000 or for “Metaheuristics” before 2004. Considering the number of keywords by years in number, we can conclude that no substantial change in the number of articles with the keyword “Linear Programming” existed. However, the trend for the percentages of articles through the years with the keyword “Linear Programming” decreased.Figure 7
Mini column graphics of most repeated keywords.When we compare the most repeated keywords in our study and keywords in similar studies (e.g., [1, 9], we do not find much difference between the keywords in the studies in Europe and the studies worldwide or in Asia. That is, the European OR/MS studies have similar keywords and subresearch categories to those studies worldwide. The results also support the common belief that in academic life, some subjects become trendy, studied by researchers study heavily for a period of time (as in “Tabu Search” and “Metaheuristics”).Using the VOSviewer software, we investigated the original table of keywords analyzed and the 100 most repeated keywords for further consideration to visualize the keywords studied together. That visualization also helped us understand which subcategories of OR/MS are commonly studied together in Europe. We manipulated the above-mentioned data with VOSviewer to create “Keywords Relationship Diagram” in Figure8, which presents only categories that have been used 25 or more times.Figure 8
Keywords relationship diagram.In the diagram, the size of the circle for each keyword represents the number of articles using that keyword while the thickness of the links represents the number of articles that used the keywords in both sides of the link, similar to the network of collaborating countries/regions in Figure5.Drawing conclusions from Figure8 was somewhat complicated because it included 100 keywords. To make it easier to understand the relationships with mostly used keywords, we highlighted the most repeated keywords, as in Figures 9(a)–9(c).Figure 9
(a) Keywords relationship diagram of “Multiobjective Optimization,” (b) Keywords relationship diagram of “Heuristics,” (c) Keywords relationship diagram of “Scheduling.”
(a)(b)(c)Figure9(a). Keywords relationship diagram of “Multiobjective Optimization” depicts the relationships of the most repeated keyword, “Multiobjective optimization,” with the other keywords. The diagram clearly illustrates which methodologies are most commonly jointly used with “Multiobjective optimization” in the analyzed papers. The diagram indicates that “Multiobjective optimization” is mostly used together with “Decision support systems,” “Genetic algorithms,” and “Evolutionary algorithms.”Figure9(b). Keywords relationship diagram of “Heuristics” presents the same diagram for “Heuristics.” The diagram indicates that “Heuristics” is mostly used together with “Scheduling” and “Combinatorial optimization.”The same diagram is presented for “Scheduling” in Figure9(c). Keywords relationship diagram of “Scheduling.” This diagram also lists the scheduling studies with the number of appearances in the literature (production scheduling, production planning, maintenance scheduling, routing etc.) The diagram also shows that “Scheduling” is mostly used together with “Heuristics.”


## 4. Conclusion

This paper provides a systematic bibliometric review of OR/MS studies in Europe. Although some bibliometric analysis has been done on OR/MS studies worldwide, this study is the first paper to focus on Europe, which publishes about 38% of the papers published worldwide in the analyzed subject. In conclusion, along with the complete overview of the studies, we also present some major and interesting results. Our analysis revealed that the ratio of OR/MS studies having at least one European author has steadily increased over the decades from 28.27% in the 1980 s, to 32.76% in the 1990 s, 39.68% in the 2000 s, and 41.29% in the 2010 s. Thus, we expect the number of articles in the field of OR/MS in Europe and their impact will continue to increase for the foreseeable future. In addition, thirteen out of the top 25 most publishing countries are European.Approximately 65% of the analyzed articles were published in the top 25% of the journals in the field. The researchers mostly published articles in theEuropean Journal of Operational Research (7,973; 12.2%). Expert Systems with Applications (3,870; 5.9%), the International Journal of Production Research (2,906, 4.5%), the International Journal of Production Economics (2,782, 4.3%), and the Journal of the Operational Research Society (2,581; 3.9%) were among the top five journals in which researchers published at the highest rates; 30.85% of the total publications appeared in those five top journals. The analysis also revealed that the preferences of European researchers differ from the non-European researchers. Researchers from European countries mainly preferred to publish in journals of European origin.We calculated the average number of citations per paper as 18.05. Compared with the average number of U.S. citations in the same subject (25.12), we have concluded that the impact of European publications is less than the impact of U.S. publications. However, even in Europe, that ratio varied from author to author, from institution to institution, and, surprisingly, from country to country.Our bibliometric review revealed that substantial portions of the studies were written as joint efforts with academicians working in other countries, either within Europe or outside Europe. The increasing number of average authors per article implies that the researchers in the field have been collaborating more and more through years. In the analyzed papers, the most frequent collaboration occurred between British and Chinese authors (482 articles), followed by Turkish and American authors with 450 articles. European authors collaborated the most with American authors (6,227 articles), followed by European authors collaborating with Chinese authors (2,293 articles). The collaboration analysis results also showed that European researchers collaborated with non-European countries as much as with European countries in the field of OR/MS.Analysis on the most productive institutions revealed that 20 institutions produced more than 500 papers during the years under study. The results also show that one-fourth of the papers were published by only 20 institutions. Analysis of the papers showed that only a small portion of the countries, institutions, and even authors published a substantial portion of the papers in the field of OR/MS in Europe, as indicated by the Pareto rule.The keyword analysis indicated that the three keywords that frequently appeared in 2000–2018 were “Multiobjective optimization,” “Heuristics,” and “Scheduling.” When we compared the most repeated keywords in our studies with keywords in similar studies, the results did not show much difference between the keywords in the European studies and those from other parts of the world. The results also support that, in academic life, some trendy subjects are heavily studied for a short period of time.The bibliometric approach used in our study has one major limitation: it examined the OR/MS studies published only in OR/MS journals. Indeed, scholars do not necessarily publish their papers only in OR/MS journals indexed under the WoS. However, no practical way exists for identifying all OR/MS articles published in other journals or indexed by Scopus, ProQuest, or other indices.



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*Source: 1607637-2020-10-24.xml*