analysis of scientific collaboration patterns in the co-authorship network of...

Simulation Modelling Practice and Theory xxx (2014) xxx–xxx

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Simulation Modelling Practice and Theory

journal homepage: www.elsevier .com/ locate/s impat

Analysis of scientific collaboration patterns in the co-authorshipnetwork of Simulation–Optimization of supply chains

http://dx.doi.org/10.1016/j.simpat.2014.02.0071569-190X/� 2014 Elsevier B.V. All rights reserved.

⇑ Corresponding author. Address: Faculty of Engineering, Av. Universidad 3000, Ciudad Universitaria, C.P. 04510, Mexico. Tel.: +52 555841956E-mail address: [email protected] (A. Huerta-Barrientos).

Please cite this article in press as: A. Huerta-Barrientos et al., Analysis of scientific collaboration patterns in the co-authorship netSimulation–Optimization of supply chains, Simulat. Modell. Pract. Theory (2014), http://dx.doi.org/10.1016/j.simpat.2014.02.007

Aida Huerta-Barrientos ⇑, Mayra Elizondo-Cortés, Idalia Flores de la MotaDepartment of Operations Research, National Autonomous Mexico University, Ciudad Universitaria, 04510 Mexico, DF, Mexico

a r t i c l e i n f o

Article history:Available online xxxx

Keywords:Simulation OptimizationNetwork analysisScientific collaborationSupply chain

a b s t r a c t

In the 1970s, a co-authorship network in the field of Simulation Optimization of supplychains was established, supported by local associations. Then, the development of this net-work was favored by the foundation of new co-authorships and the consolidation ofalready existing. The purpose of this study is to analyze the structure, collaboration pat-terns and the time-evolution of the co-authorship network of Simulation Optimization ofsupply chains. Data are based upon 202 peer-reviewed contributions published from1970 to August 2012 in relevant journals indexed in the ISI/Web of Science database andInternational Conferences. The analysis is conducted using exploratory social networkanalysis technique. Results indicate that the development of knowledge in SimulationOptimization of supply chains has been carried out mainly by 353 authors from 35 coun-tries. Also, there have been proposed over forty Simulation Optimization methods by dif-ferent authors however the most usual is response surface methodology, followed bygradient based search method and genetic algorithms. In addition, applications of Simula-tion Optimization methods and techniques are found mainly in areas as health care, man-agement, transport, airline, telecommunications, aerospace, and financial. Althoughresearch in Simulation Optimization of supply chains has received much attention by thesimulation community, its application in key industries continues to be still small, limitingits support in decision-making.

� 2014 Elsevier B.V. All rights reserved.

1. Introduction

Simulation Optimization is a structured approach that is useful to determine optimal settings for input parameters asso-ciated with a simulation model. In this case, the optimality is measured by a (steady-state or transient) function of outputvariables [1]. As suggested by Fu [2], the general optimization problem consists of finding a setting of controllable param-eters that minimizes a given objective function, i.e.

min JðhÞh 2 H

ð1Þ

where h e H represents the vector of input variables, J(h) is the objective function, and H is the constraint set, which may beeither explicitly or implicitly defined. The assumption in the Simulation Optimization setting is that J(h) is not availabledirectly, but must be estimated via simulation [2].

5.

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The key difficulty in Simulation Optimization involves a trade-off between allocating computational resources for search-ing h e H versus conducting additional simulation replications for better estimating the performance of current promisingsolutions [3]. Since the 1970s several Simulation Optimization techniques have been proposed for finding optimal settingsfor input parameters of a simulation model. Some of these methods have been very sophisticated while others have beennaïve just generating several input values at random and running the simulation model at each of these input values. Noneof Simulation Optimization techniques is sure to work for all problems, but each one has characteristics which make it usefulfor certain types of problems [4]. Extensive reviews and surveys about Simulation Optimization methods and techniqueshave been carried out by different authors and can be found in [5–14,3,15,16]. However, at present little attention in theliterature has been paid to the co-authorship network of Simulation Optimization and its time-evolution and very littlehas been written about main applications of Simulation Optimization techniques in industry.

Peer-reviewed contributions are considered an important source of information that let us to identify the development ofknowledge in a specific field, and pinpoint how research is organized and structured [17]. In this direction, specific researchquestions addressed by this study are: how do authors of peer-reviewed articles in the field of Simulation Optimization ofsupply chains collaborate? How is structured the co-authorship network of Simulation Optimization of supply chain? WhichSimulation Optimization methods have been proposed by researchers? And last but not least, which industries have beensupported by Simulation Optimization methods? In line with this, the aim of this study is to analyze the structure, collab-oration patterns and the time-evolution of the co-authorship network of Simulation Optimization of supply chains. In orderto achieve this aim 202 peer-reviewed articles were selected using the purposive sampling method, which is defined in Sec-tion 2. Based on the information about authors, we developed the co-authorship network and analyze its structural proper-ties and time-evolution using exploratory social network analysis technique. This technique has the advantage of determineat global level structural features of a network, detecting its patterns. Then Simulation Optimization methods were classifiedbased on their application areas. This classification is of relevance because provides guidance for industrials, academics andpractitioners in optimization method selection. After that, industries that have been supported by Simulation Optimizationmethods in making decisions processes were listed. Although theoretical Simulation Optimization methods are numerous,key industrial areas of application are still small. We highlight this gap and recommend how to increase the application ofSimulation Optimization methods in real-world problems solutions.

The remainder of this paper is organized as follows. In Section 2, the data collection method is presented. The exploratorysocial network analysis technique is described in Section 3. The co-authorship network of Simulation Optimization of supplychains is characterized in Section 4. The structure and time-evolution of the co-authorship network of Simulation Optimi-zation of supply chains is analyzed in Section 5. Main conclusions and future research are drawn in Section 6.

2. The data collection

We collected 202 peer-reviewed contributions in Simulation Optimization of supply chains from relevant journals in-dexed in the ISI/Web of Science database and International Conferences. These contributions were selected based on purpo-sive sampling method. This method is also referred to as qualitative sampling that involves certain units or cases based on aspecific purpose rather than randomly [18]. Three broad categories of purposive sampling techniques are well known: sam-pling to achieve a representativeness or comparability, sampling special or unique cases, and sequential sampling [18]. Inthis study, peer-reviewed contributions were sampled based on the first category of the purposive sampling techniquesto achieve a representativeness of the application of Simulation Optimization in supply chain field. The criterion to filtera contribution was the inclusion of the phrase ‘‘simulation optimization’’ in its title but with its application in supply chainfield. The period of publication taken in account was from 1970s to August 2012. As the first contribution was published inthe 1970s, additional queries regarding five periods were placed in data as follows: Period I, 1970–1979; Period II,1980–1989; Period III, 1990–1999; Period IV, 2000–2009; and Period V, 2010–2012. As it is noted from Table 1, for each per-iod peer-reviewed contributions were quantified as well as International Journals and Conferences, authors and their coun-tries. The tendency in the number of peer-reviewed contributions published over five periods already mentioned, suggeststhe attracting increasing interest from the simulation community in Simulation Optimization field since the last decades.

The distribution of peer-reviewed contributions based on the number of co-authors is summarized in Table 2.Two-authored contributions represent the biggest proportion with 41% of the total. In contrast to this, the single-authoredcontributions represent only 15%.

Table 1Dissemination of peer-reviewed contributions of Simulation Optimization of supply chains.

Period I II III IV VYears 1970–1979 1980–1989 1990–1999 2000–2009 2010–2012

Authors 10 20 32 232 100Peer-reviewed contributions 5 15 20 118 44Int. Journals/Conference 1 2 1 23 17Countries 1 2 2 29 18

Please cite this article in press as: A. Huerta-Barrientos et al., Analysis of scientific collaboration patterns in the co-authorship network ofSimulation–Optimization of supply chains, Simulat. Modell. Pract. Theory (2014), http://dx.doi.org/10.1016/j.simpat.2014.02.007


Table 2The distribution of peer-reviewed contributions of Simulation Optimization of supply chains bynumber of authors.

Description Peer-reviewed contributions % Peer-reviewed contributions

Two-authored 82 41Three-authored 52 26Four-authored 37 18Single-authored 31 15

Table 3Journals and international conferences accounting for at least one peer-reviewed contribution in Simulation Optimization of supply chains from 1970 to 2012.

Journal/conference Peer-reviewed contributions

Winter Simulation Conference 154Simulation Modelling Practice and Theory 5Int. J. Production Economics 4Computers and Chemical Engineering 3Computers and Operations Research 3European Journal of Operational Research 3Computers and Industrial Engineering 2IIE Transactions 2ACM Transactions on Modeling and Computer Simulation 1Applied Soft Computing 1Automatica 1Engineering Applications of Artificial Intelligence 1Engineering Optimization 1European Simulation Symposium 1Expert Systems with Applications 1Handbooks in Operations Research and Management Science 1Industrial and Engineering Chemistry Research 1INFORMS Journal on Computing 1INFORMS Simulation Society Research Workshop 1International conference on Intelligent Systems Modelling and Simulation 1International conference on Service Systems and Service Management 1International Journal of Computer Integrated Manufacturing 1International Journal of Industrial Engineering: Theory Applications and Practice 1International Journal of Production Economics 1International Journal of Production Research 1Irish Journal of Management 1Journal of Mining Science 1Mathematics and Computers in simulation 1Naval Research Logistics 1OR Spectrum 1Simulation Practice and Theory 1Technological and Economic Development of Economy 1The Arabian Journal for Science and Engineering 1

A. Huerta-Barrientos et al. / Simulation Modelling Practice and Theory xxx (2014) xxx–xxx 3

Table 3 indicates 33 journals and international conferences that include at least one peer-reviewed contribution sampledfor this study. The top contributor is International Conference Winter Simulation Conference followed by International JournalSimulation Modelling Practice and Theory. Involved international journals and conferences, suggest a multidisciplinary interestin the application of Simulation Optimization methods in supply chain field, as they belong to different industrial areas suchas Production, Operations Research, Chemical Engineering, Industrial Engineering, Computer Engineering, Economy, Man-agement, and Logistics.

3. The exploratory social network analysis technique

Social networks can be analyzed using different techniques. Important results have been obtained using the exploratorysocial network analysis technique. Through this technique, it is possible to analyze the time-evolution of a network. Also it ispossible to detect and interpret patterns of social ties.

In general, the exploratory social network analysis technique consists of four parts [19]:

1. The definition of a network;2. The network manipulation;3. The determination of structural features;4. The visual inspection.



Fig. 1. The pattern of the co-authorship network of Simulation Optimization of supply chains from 1970 to 2012.

Fig. 2. The pattern of the co-authorship network of Simulation Optimization of supply chains independently of the year from 1970 to 2012.


The definition of a set of vertices and a set of lines where each line connects two vertices is included in the definition of anetwork. A vertex is considered the smallest unit in a network, while a line is a tie between two vertices. In social networkanalysis, a vertex represents an actor, and a line represents any social relation. The network manipulation is a very powerfultool that lets us to modify a network according with our requirements.

Considering an entire network, by social network analysis technique, its structural features can be determined at globallevel. And considering a sub network or a single vertex extracted from the entire network, its structural features can bedetermined at individual level. Additionally, the visual inspection of a network by means of the social network analysis tech-nique facilitates the intuitive understanding of its features, helping us to trace and represent patterns of ties [19]. It is impor-tant to stress that visual inspection of a network can be carried out using the Kamada–Kawai free algorithm, well supportedby Pajek software. This algorithm is useful for drawing undirected and weighted graphs. The basic idea of this algorithm con-sists on regarding the desirable ‘‘geometric’’ (Euclidian) distance between two vertices in the drawing as the ‘‘graph theo-retic’’ distance between them in the corresponding graph and introducing a virtual dynamic system in which every twovertices are connected by a ‘‘spring’’ of such desirable length. So, the optimal layout of vertices indicates us the state in whichthe total spring energy of the system is minimal [20].

4. The co-authorship network of Simulation Optimization of supply chains

The co-authorship network of Simulation Optimization of supply chains is represented by authors of peer-reviewed con-tributions and their interrelations. An author is represented by a vertex, while the interrelations between authors are rep-resented by edges in the co-authorship network.



Fig. 3. The giant component of the co-authorship network of Simulation Optimization of supply chains.

Table 4Authors who integrate the giant component of the co-authorship network of Simulation Optimization of supply chains.

Author Index a

Luo Y. 352Cho H. 348Jacobson S. 334Hyden P. 333Keng N. 267Shi L. 248Carson J. 247Chen Ch. 246Healy K. 245Eren Ultanir A. 233Bektas T. 232Ilenda V. 231Hall J. 212Better M. 202Yücesan E. 182Yoo T. 179Swisher J. 160Prudius A. 138Laguna M. 102Kleinman N. 91Kelly J. 86Jarugumili S. 82Hutchison D. 79Hill S. 76Fu M. 59Dengiz B. 48Bowden R. 27Boesel J. 26April J. 15Andradóttir S. 12

a The index used to identify authors in the co-authorship network of Simulation Optimization of supply chains.





4.1. Trends in the co-authorship network of Simulation Optimization of supply chains

The primary constraint on the pattern of the co-authorship network is the number of authors on a contribution. Inthis direction, the first co-authorship network was defined to detect the total pattern of co-authorships between authorsin the timeline from 1970 to 2012, described in Section 2. In this case, each author in 1 year is represented by one vertex.It is important to note that for each contribution the co-authorships were established between first and second author,between first and third author, and between first and fourth author, respectively. Using the Kamada–Kawai free algorithm,the visualization of the co-authorship network of Simulation Optimization of supply chains is showed in Fig. 1.

In other case, considering that one vertex represents one and just one author, independently of time on which its contri-bution was published, the co-authorship network was developed, see Fig. 2. That means that an author is represented by onevertex, independently if the same author has others co-authorships in the timeline considered.

To really interpret patterns of co-authorship of Simulation Optimization of supply chains, it was necessary to determinethree of the main structural features of the co-authorship network: the giant component, the centralization and structuralholes. On one hand, the giant component represents a subnet formed by the largest share of vertices (authors) interconnectedwithin a network. The importance of the giant component lies on the possibility to reach a large number of other authors ofthe same collaboration network starting by one author of the giant component and moving along its connections. The

Table 5The top ten centers of the co-authorship network of Simulation Optimization of supply chains correlated with theirweighted values and index.

Author Weighted values Index a

Fu M. 40 59Biles W. 34 24Eskandari H. 14 56Yücesan E. 13 182Ding H. 13 51Hay L. 12 72Azadivar F. 8 19Chen Y. 8 37Othman S. 8 129Dengiz B. 7 48

a The index used to identify authors in the co-authorship network.

Fig. 4. Centers of the co-authorship network of Simulation Optimization of supply chains.




appearance of the giant component with 30 authors is verified by black vertices of the co-authorship network presented inFig. 3. The giant component embraced 8.78% of vertices in the network. It means that it was possible to reach a large numberof other authors starting by one of vertices that conforms the giant component and moving along its connections. As the ver-tices in the co-authorship network were enumerated by its index, we listed in Table 4 the authors included in the giant com-ponent based on their index.

On another hand, the centrality is one of the main concepts used in network analysis and refers to positions of individualvertices within a network. As is pointed out in [21], the centrality, concept proposed by Freeman, supports the measurementof centralization and can be calculated in terms of the degree to which a vertex falls on the shortest path between othersvertices and therefore has a potential for controlling communication in a network. The importance of centrality lies onthe idea that information may easily reach central vertices (authors) in a communication network. It is important to notethat authors can benefit from serving as intermediaries between others authors who are not directly connected in a network.

Through such intermediation, some authors potentially can broke the information flow and synthesize ideas arising indifferent parts of a network. These principles form the underpinning for structural holes theory. This theory indicate us waysin which some vertices (authors) fill ‘‘holes’’ between groups or sub networks that are not otherwise interacting in a network[22]. Nowadays, two classic centralization measures are applied to characterize a network: closeness and between’s. First,closeness centralization is defined as the variation in the closeness centrality of vertices divided by the maximum variationin closeness centrality. Second, between’s centralization is defined as the variation in the between’s centrality of vertices di-vided by the maximum variation in between’s centrality. Using Pajek software, it was not possible to obtain measurementsof closeness centralization for the co-authorship network of Simulation Optimization of supply chains because this networkis not strongly connected. This fact means that there are not paths between all authors in the co-authorship network. In

Fig. 5. Structural holes of the co-authorship network of Simulation Optimization of supply chains.

Table 6Intermediary authors who are not directly connected in the co-authorship network of Simulation Optimization of supply chains.

Author Indexa

April J. 15Chang K. 36Fu M. 59Glover F. 61Hong L. 77Noack D. 127Syberfeldt A. 161Wan H. 174Yücesan E. 182Ng A. 195Rose O. 201Chen Ch. 246Nelson B. 262Tiwari M.K. 284

a The index used to identify authors in the co-authorship network of Simulation Optimization of supply chains.




contrast to this, the between’s centralization value was calculated equal to 0.00569. This means that few crucial authors inthe co-authorship network of Simulation Optimization of supply chains promote the information transmission through theentire co-authorship network established, i.e. Jacobson S., Fu M., and Andradóttir S. It is important to note that these crucialauthors were also elements of the giant component of the same network. Additionally, centers of the co-authorship networkin Simulation Optimization of supply chains were identified as vertices with the most weighted values based on the degree of

Fig. 6. The network of author’s countries.

Others25%

Mathematical programming

3%

Hooke-Jeeves pattern search method

3%Sample path method

4%Evolution strategy

4%Random search

algorithms4%Heuristics

4%Ranking & selection 4%

Scatter search5%

Tabu search5%

Stochastic approximation

6%

Simulated annealing6%

Genetic algorithm8%

Gradient based search methods

8%

Response surface methodology

11%

Optimization Techniques

Fig. 7. Optimization techniques most usual in peer-reviewed contributions of Simulation Optimization of supply chains.




vertices. Normally these weighted values are calculated using a weighted algorithm. Ten centers (authors) with the highestdegree of vertices in the co-authorship network of Simulation Optimization of supply chains are listed in Table 5 and showedgraphically in Fig. 4, represented by biggest black vertices.

Co-authorships that potentially can break the flow of information and synthesize ideas of the co-authorship network ofSimulation Optimization of supply chains are relationships represented by lines in grey color in Fig. 5. It is important to notethat authors, who represent vertices of these co-authorships (see Table 6), served as intermediaries between others authorswho are not directly connected in the co-authorship network.

4.2. The network of author’s countries

The network of author’s countries also was built. A vertex of this network represented an author’s country and edgesrepresented the collaboration between authors of different countries. On one hand, we observed the central role of authorsfrom USA in this network and their co-authorships with authors from Germany, China, Chile, Belgium, Turkey, Taiwan,France, Singapore, Mexico, Thailand, Korea, Netherlands, Iran and India, mainly. On another hand, authors from United ArabEmirates have collaborated in the field of Simulation Optimization of supply chains only with authors from Saudi Arabia. Thesame situation is observed for authors from Ireland who have collaborated just with authors from Austria as is illustrated inFig. 6.

4.3. Optimization techniques most usual in Simulation Optimization of supply chains

Other interesting part of this study is the analysis of optimization techniques used by authors of the co-authorship net-work of Simulation Optimization of supply chains. We counted over forty different optimization techniques. The most usualin peer-reviewed contributions was the response surface methodology followed by gradient based search methods, geneticalgorithms, simulated annealing, stochastic approximation, tabu search, scatter search, and others, as is presented in Fig. 7.

Health care 15%

Management 15%

Transport 15%

Telecommunications 11%

Airline 9%

Aerospace 7%

Financial 7%

Chemical2%Fishery

2%

Military2%

Mining export2%

Newspaper2%

Energy 2%

Pharmaceutical 2%

Sport 2%

SD2%

Textil 2%

Other22%

Industries

Fig. 8. Industries supported by Simulation Optimization methods.

Table 7Supply chain and manufacturing activities supported by Simulation Optimizationmethods.

Supply chain Manufacturing

Design Production PlanningPlanning Production linePhysical distribution planning Process plant designManagement Flexible manufacturingScheduling Automated manufacturing systemResources allocation Lean manufacturingStorage and retrieval policies Robot manufacturing cellFlow Shop Buffer allocationLogistics SchedulingInventory Assembly line




4.4. Industries supported by the application of simulation optimization methods

A fundamental aspect of Simulation Optimization of supply chains is its application to support the solution of real-world problems. In this direction, industries that have been supported by Simulation Optimization methods and techniquesfrom 1970 to 2012 are showed in Fig. 8. Industries in which these methods have been more applied are: health care, man-agement, transport, telecommunications, airline, aerospace, and financial. Few applications in areas of energy, newspaper,mining export, military, fishery, chemical, textile, sustainable development, sport and pharmaceutical were found.Although Simulation Optimization methods are numerous, as we observed in Section 4.3, industrial areas of applicationare still small.

4.5. Supply chain areas supported by the application of Simulation Optimization methods and techniques

The application of Simulation Optimization methods in supply chain and manufacturing activities has been focalized justin certain activities, see Table 7. Although the technological potential of these techniques, they have not been applied exten-sively to support the decision-making.

Fig. 9. The co-authorship network of Simulation Optimization of supply chains in Period I (1970–1979).

Fig. 10. The co-authorship network of Simulation Optimization of supply chains in Period II (1980–1989).



Fig. 11. The co-authorship network of Simulation Optimization of supply chains in Period III (1990–1999).

Fig. 12. The co-authorship network of Simulation Optimization of supply chains in Period IV (2000–2009).





5. The structure and time-evolution of the co-authorship network of Simulation Optimization of supply chains

Since the 1970s, the structure of the co-authorship network of Simulation Optimization of supply chains started to bedeveloped based on several local associations, forming little communication groups between its members. In Period I, from1970 to 1979, five co-authorships were established, see Fig. 9. Optimization techniques mainly used by authors in this periodwere coordinate search, gradient based search, heuristics, Hooke–Jeeves pattern search, random search, and response surfacemethodology, in health care and transport industries.

In Period II, from 1980–1989, co-authorships were incremented to eight (see Fig. 10) and optimization techniques mainlyused were Nelder method, perturbation analysis, response surface methodology, simulated annealing, and stochasticapproximation supporting decision problems in the aerospace industry.

In Period III, from 1990 to 1999, co-authorships of Simulation Optimization of supply chains were incremented to 17 (seeFig. 11). Optimization techniques used in this period were mathematical programming, Nested partitions method, neuralnetworks, perturbation analysis, random search, ranking and selection, response surface methodology, sample path, scattersearch, simulated annealing, stochastic approximation and tabu search, to support the decision-making in airline and trans-port industries.

In Period IV, from 2000 to 2009, co-authorships of Simulation Optimization of supply chains were incremented to 195, seeFig. 12. In this period, authors used optimization techniques such as adaptive partitioning search, approximate dynamic pro-gramming, brute force method, coordinate search, evolution strategy, genetic algorithms, golden region search, gradientbased search, heuristics, Hooke–Jeeves pattern search, kriging methodology, mathematical programming, multiple compar-ison, Nested partitions, neural networks, particle swarm optimization, perturbation analysis, random search, ranking andselection, response surface methodology, retrospective approximation, sample average approximation, sample path, scattersearch, sequential selection, simulated annealing, stochastic approximation and tabu search. Industries of interest in apply-ing these techniques were aerospace, airline, telecommunications, management, financial, heath care, military, sustainabledevelopment, chemical, newspaper, energy, textile, and fishery.

Fig. 13. The co-authorship network of Simulation Optimization of supply chains in Period V (2010–2012).



Table 8Optimization methods used in Simulation Optimization of supply chains from 1970 to 2012.

Optimization method Period I Period II Period III Period IV Period V

Gradient based search methods X X X X XResponse surface methodology X X X X XHooke–Jeeves pattern search method X X X XHeuristics X X X XRandom search algorithms X X X XSimulated annealing X X X XStochastic approximation X X X XGenetic algorithm X X XMathematical programming X X XNested partitions method X X XNeural networks X X XPerturbation analysis X X XRanking and selection X X XSample path method X X XScatter search X X XTabu search X X XFrequency domain method X XNelder method X XEvolution strategy X XSimultaneous Perturbation Stochastic Approximation X XKriging methodology X XParticle swarm optimization X XSequential selection X XCoordinate search XGeoffrion and Graves method XDiscrete stochastic optimization XAdaptive Partitioning search XApproximate dynamic programming XBrute force method XCross-entropy method XEstimation of distribution algorithms XGolden region search XGreedy heuristics XIndifference-zone ranking XMixed integer programming XModel reference adaptive search XMultiple comparison XNon-monotonic search XRetrospective approximation XSample average approximation XBranch -and bound method, Linear programming XOptimal computing budget allocation X


Over time, the structure of the co-authorship network of Simulation Optimization of supply chains has been favoredmainly by the foundation of new co-authorships and the consolidation of already existing. It is important to stress that inPeriod V, from 2010 to 2011, a total of 71 co-authorships were established, see Fig. 13. Optimization techniques used byauthors in this period were genetic algorithms, gradient based search, heuristics, kriging methodology, mathematical pro-gramming, Nelder method, Nested partitions, neural networks, optimal computing budget allocation, particle swarm opti-mization, random search, ranking and selection, response surface methodology, sample path, scatter search, sequentialselection, simulated annealing, stochastic approximation, and tabu search to support the decision-making in aerospace, tele-communications, health care, port, transport, mining export, and pharmaceutical industries. Table 8 presents an overview ofoptimization techniques used in all five periods (Period I, Period I, Period III, Period IV and Period V). The optimization meth-od most usual is response surface methodology. It is important to outline that response surface methodology has beenapplied mainly in transport and health industries, in areas of inventory and manufacturing. Also this methodology has beencombined with other optimization techniques such as genetic algorithms and Taguchi.

6. Conclusions and future research

This study demonstrates that since the 1970s the knowledge dissemination of Simulation Optimization of supply chainhas involved a large number of authors from different countries, peer-reviewed contributions, international journals andconferences. We analyzed 202 peer-reviewed contributions in Simulation Optimization of supply chains from relevantjournals indexed in the ISI/Web of Science database and International Conferences. From the analysis, we observed thatabout 85% of peer-reviewed contributions were developed by more than one author. That means that the development of




knowledge in this field is mainly based on co-authorships. The co-authorship network of Simulation Optimization of supplychains was represented by authors of peer-reviewed contributions and their interrelations. The findings in the analysis of theco-authorship network indicate that it was possible to reach a large number of other authors in the network through 30authors moving along the edges of the subnet that form these authors. Also, few authors were crucial to the transmissionof information through the co-authorship network and some of these authors also had the function of centers in the networkas Fu M. and Yücesan E. Additionally, we observed that the optimization technique most usual in peer-reviewed contribu-tions analyzed was response surface methodology followed by gradient based search methods, genetic algorithms, simulatedannealing, stochastic approximation, tabu search and scatter search. Response surface methodology has not been used aloneinstead it has been combined with other optimization techniques, incrementing in this way the potential of optimization.Although Simulation Optimization methods are numerous, they have not been applied extensively to support the deci-sion-making in many areas of supply chain and manufacturing. As the structure of the collaboration network betweenauthors has been favored mainly by the foundation of new co-authorships and the consolidation of existing, it can be a goodstrategy to increment the number of applications of simulation optimization in more supply chain areas based on new co-authorships, collaborating. Future research is needed into co-authorship network analysis based on impact factors of jour-nals indexed in the ISI/Web of Science database.

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