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26
ОБЩИЙ И СТРАТЕГИЧЕСКИЙ МЕНЕДЖМЕНТ
UDC: 005.31; 519.8 JEL: C44; C61; L14; O32
LEADER IDENTIFICATION IN A RESEARCH COLLABORATIVE NETWORK
S. Kazemi
St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
For citation: Kazemi S. 2021. Leader identification in a research collaborative network. Vestnik of Saint PetersburgUniversity. Management 20 (1): 58-85. https://doi.org/10.21638/11701/spbu08.2021.103
There is considerable empirical evidence on the advantages of interorganizational research collaborative networks across societies and research institutes such as research and development (R&D) centers and universities. Identifying a leader in this contexts is important both theoretically for doing leadership studies, and practically for effective governmental funding allocation and private investments. Inconsistent definitions and non-homogeneous attributes with unidimensional measurement approaches such as subjective measuring of power or considering a central company as the leader made the previous efforts inefficient for identifying leaders in an interorganizational setting. This research aims to identify a leading organization among a set of homogenous R&D centers in a research collaborative network context through implementing the main leader's attributes in different dimensions. The article presents a multidimensional common weight model based on the data envelopment analysis (DEA) approach in a parallel system with several operational dimensions each of which consumes a set of inputs (budget, lecturers, and students) to produce a set of outputs (scientific meetings and conferences, national and international papers). Centrality and visibility are two main leaders' attributes combined with efficiency influence the contributions and outcomes of each collaborative network partner. It is demonstrated how the proposed model performs its high-efficiency score in the most influential R&D center named the "leader" among 47 R&D centers in medical universities in Iran. The comparative analysis of managerial results showed that reputation has a greater impact on leader identification than centrality. The results based on mathematical calculations showed a robust discriminating power for efficiency measurement of the proposed model.
Keywords: research collaborative network, leader, data envelopment analysis, common weights, non-discretionary variables, efficiency, network centrality, reputation.
INTRODUCTION
The COVID-19 pandemic has demonstrated the importance of cross-border research collaborative networks to create a safe and effective COVID-19 vaccine [Lee,
This research has been conducted with financial support from St. Petersburg State University (Project No. 60419633).
© St. Petersburg State University, 2021
Haupt, 2020]. While there are different definitions of the collaborative network in the literature [Thomson, Perry, 2006], the two main elements of working together and sharing knowledge directed many scholars to define it as a network consisting of a variety of entities (organizations and people) that are largely autonomous, geographically distributed, heterogeneous in terms of their operating environment, culture, social capital, and goals, but work together toward common and compatible goals [Tsimiklis, Makatsoris,
2019]. Organizations are interested in collaboration to share research and development (R&D) costs and risks, accelerate new products or processes introduction, or gain new markets and skills accessibility [Powell, Koput, Smith-Doerr, 1996] by exploitation of external resources, capabilities, and competencies [Muller-Seitz, Sydow, 2012]. This research addresses an example of collaborative networks which is named "research collaboration network" particularly among a set of R&D centers in universities that work together for doing joint research (e.g., [Chen et al., 2020]).
In these research collaborative networks identifying the leader is important because R&D centers are interested in direct collaboration with the leader and imitating its strategies and behaviors to enhance their visibility, legitimacy, and survival chance [Have-man, 1993]. Leader selection is regarding the collaborative partner selection as a research direction among interested scholars in this realm (e.g., [Kalesnikaite, Neshkova,
2020]) based on the persistent belief that leaders are sources of knowledge and expertise [Haveman, 1993], right decision-makers, and successful in accessing higher levels of resources [Mehra et al., 2006] that can influence the collective actions, behaviors, and performance [Mehra et al., 2006; Mokhtar et al., 2019b]. Finding a leader among collaborative R&D centers in universities is also important for governmental funding allocation and for achieving a high reputation within the research community. The leader's reputation can attract highly qualified foreign students and indirectly lead to society's welfare through attracting foreign R&D centers to collaborate and invest. In addition, organizations are more interested in collaboration with leading R&D centers in universities for doing industry-university research for improving national innovative capabilities [Zhang et al., 2016; Chen et al., 2020].
However, despite the growing attention and studies devoted to the leader in an in-terorganizational setting, the term is characterized by relatively inconsistent definitions with non-homogeneous attributes and measurements which lead to a rather incoherent picture of leader for identification [Muller-Seitz, Sydow, 2012; Mokhtar et al., 2019b]. Previous studies also do not explicitly focus on identifying leaders in networks and have targeted dyads in a buyer-supplier relationship and a focal company as a leader (e.g., [Mokhtar et al., 2019a; Shin, Park, 2021]). Further, leadership studies in an in-terorganizational context have paid little attention to the heterarchical networks, i.e., consisting of more or less independent partners without a formally legitimated leading position such as collaborative networks. In other words, the focus of this marginal and diverse body of works has been on the leadership styles of behavior (see [Mokhtar et al., 2019b]), and less attention has been paid to unanimously and comprehensively characterize the leaders and their attributes in interorganizational setting like research
collaborative networks. Therefore, this study aims to answer the following two research questions.
Research question 1. What central attributes of leaders in an interorganizational context can be implemented to identify leaders in research collaborative networks?
Research question 2. How we can identify a leader in a research collaborative network among a set of R&D centers?
To address these two questions, this study contributes to the body of knowledge on this topic in two ways. Firstly, we articulate the main leaders' attributes by the review of the previous works and focusing on the leader as an organization at the network level of analysis. To this aim, this research focuses on the most recent relevant studies (e.g., [Mokhtar et al., 2019b; Zenkevich, Kazemi, 2020]) and defines a research collaborative network leader as an organization that based on its influence on other collaborative partners demonstrates a higher level of efficiency. Secondly, we address a call for research by S. Kazemi with coauthors [Kazemi et al., 2021] to identify a leading organization in a multidimensional way by developing a multidimensional common weight model (MDCW) based on the data envelopment analysis approach for identifying the leader in a more holistic way among a set of collaborative R&D centers in medical universities.
The remainder of this paper is organized as follows. The second section introduces the most important attributes of a leading organization. The third section presents the development of the model. The problem description, data collection, and model application are presented in the fourth section. Finally, the paper concludes by providing some directions for future research.
LITERATURE REVIEW
Research collaborative network. The importance of interorganizational collaborations has motivated particularly innovative organizations to form collaborative networks where they can exchange information, ideas, and other critical resources with each other (e.g., [Zhang et al., 2016]). Collaborations among these innovative organizations or research institutes facilitate the integration of internal and external knowledge and enable them to be more productive and efficient in producing innovative outcomes [Chen et al., 2020].
Research institutes such as R&D centers in universities as the critical actors in research collaborative networks are important for the economic development and competitiveness by promoting cutting-edge research in science and technology through acquisition, implementation, creation, and transfer of knowledge among collaborative partners [Zhang et al., 2016]. These actors which are usually independent organizations in a different operating environment with unique resources, capabilities, and competencies form research collaborative networks to take advantage of each other for achieving competitive advantages and higher performance [Tsimiklis, Makatsoris, 2019; Chen et al., 2020]. They can share investment costs and risks and access to complementary resources toward a higher innovative performance [Guan, Zhang, Yan, 2015].
However, there is a paradoxical situation in which interorganizational collaborations while having so many advantages for the research institutes such as R&D centers [Zhang et al., 2020], the majority of these collaborations fail to meet the expectations [Ospina, Saz-Carranza, 2010]. In this regard, the role of leaders can be highlighted based on the persistent belief that leaders can enhance collective performance [Mehra et al., 2006]. In these contexts, a leading organization has been viewed from three perspectives:
1) evaluating leaders among operationally heterogeneous organizations (e.g., [Shu et al., 2019]);
2) evaluating leaders among operationally homogenous organizations (e.g., [Li et al., 2018]);
3) evaluating leaders among a set of operationally homogenous and heterogenous organizations (a network form) (e.g., [Hao, Feng, Ye, 2017]).
This study with considering a research collaborative network consisting of a set of R&D centers in universities with homogenous operations addresses the identification of the leader in the second form, among a set of operationally homogenous decision-making units (DMUs) based on the major attributes of the leader in the literature and corresponding theoretical basis. Also, a fundamental assumption of DEA models in measuring the efficiency of DMUs is based on their homogenous operations, which limits our choice to consider the identifying leader among a set of homogenous DMUs.
The leader in collaborative networks and its main attributes. Most of the leadership studies in interorganizational settings tried to address leaders as focal firms mostly in a dyadic buyer-supplier relationship (e.g., [Mokhtar et al., 2019a; Shin, Park, 2021]). In addition, leadership studies at the network level of the analysis demonstrate inconsistent definitions using non-homogenous attributes for defining and characterizing leaders. For example, a leader has been defined as "an organization capable of greater influence, readily identifiable by its behaviors, creator of the vision, and that establishes a relationship with other supply chain organizations" [Defee, Stank, Esper, 2010, p. 766], "formal and informal influence a hub firm exerts over partner firms" [Hao, Feng, Ye, 2017, p. 652], "a firm which influences and orchestrates the actions and behaviors of its own partners" [Mokhtar et al., 2019b, p. 257], etc. While there are different definitions of the leader, the majority of these definitions emphasize that the leader must stand out from followers through its higher capacity for influence [Shamir, 1999].
Also, following the neo-institutional theory and imitation isomorphism, every leading organization should demonstrate a higher level of success and performance to convince other organizations to follow its orders [Müller-Seitz, Sydow, 2012]. In other words, in a research collaborative network, it is expected that a leading company not only has a higher level of influence comparing other collaborative partners but also can demonstrate higher efficiency in using lower levels of inputs and producing higher levels of outputs. Therefore, a research collaborative network leader is defined as an organization that based on its influence on other collaborative partners demonstrates a higher
level of efficiency [Li et al., 2018; Mokhtar et al., 2019b; Zenkevich, Kazemi, 2020; Kazemi et al., 2021].
In this definition, influence is a central factor and is defined as the ability of a company to induce a change in the decision and behavior of another company [Reber, Berger, 2006]. The manner in which the influence is exerted can be different by which we are able to differentiate between different types of leaders and followers in interorganizational contexts. For example, a market leader influences through its reputation and visibility which are derived from possessing a higher market share in a particular market segment [Hora, Klassen, 2013], and a network leader which we name a non-market leader that exerts influence through several mechanisms stemming from its reputation [Shu et al., 2019] and positional advantages or centrality [Fernandez, Gould, 1994]. This research focuses on the non-market leader in research collaborative networks and tries to articulate these two main attributes by which leaders exert higher influence on other collaborative partners.
Reputation: A source of leaders' influence. Companies with higher reputations serve as a target of imitation and reference point for other companies and rivals to obtain the desired performance level [Hora, Klassen, 2013]. Many studies (e.g., [Mehra et al., 2006]) argue that reputation is one of the main attributes of a leader to be observable and distinguishable from followers. For example, in [Shu et al., 2019] authors indicated that companies with better reputations and popularity among consumers are more likely to become leaders. Although corporate reputation has been defined and measured differently in the literature (see [Lange, Lee, Dai, 2011]), different empirical works have revealed the association between corporate reputation and for example better efficiency and performance (e.g., [MacLeod, 2007]). Corporate reputation also affects the accessibility of resources and outcomes. In other words, past studies have demonstrated that the reputation of organizations affects their attractiveness to other organizations which finally results in higher access to resource providers (e.g., [Vanacker, Forbes, 2016]).
In [Lange, Lee, Dai, 2011] authors explain that a company's reputation stems from different sources, such as visibility and higher success levels in achieving goals and performance. The influential role of corporate visibility on corporate reputation has been investigated by several empirical works which in turn can provide the company with the capacity to influence other companies and eventually modify their decisions [Fernandez, Gould, 1994]. On the one hand, organizations are more likely to imitate and follow a more visible company as they consider this company with successful performance and superior information [Haveman, 1993]. On the other hand, the level of a company's success and performance as a signal of quality and competence is related to a leading company's prestige and reputation [Fernandez, Gould, 1994].
Therefore, following these arguments, the organization's reputation not only is a source of influence for leaders but also affects the efficiency of organizations through influencing on flows of resources. In a research collaborative network among R&D centers in universities, the most obvious indicator of reputation is the rank of the uni-
versity in the world. This research will consider this indicator as a proxy for measuring reputation.
Centrality: A source of leaders' influence. In the research collaboration context, co-authorship is the most visible and accessible indicator of collaborative network analysis [Milojevic, 2010]. In this context, the network theory is a dominant perspective and argues that the position of actors within the network affects the economic actions of actors, resource accessibilities, and their performance [Freeman, 1979; Zaheer, Gozubuyuk, Milanov, 2010]. The main idea is that the pattern of relationships among actors is unique, provides the opportunity for sharing resources, affects the behavior and performance of actors, and potentially confers competitive advantage [Zaheer, Gozubuyuk, Milanov, 2010].
Many scholars (e.g., [He et al., 2018]) indicate that an actor's positional advantages in the network, such as centrality, contribute to its influence on other actors. For example, J. Moody [Moody, 2004] indicates that actors with higher centrality gain higher prestige and connections that affect the decision of new actors to be the main target of collaboration more than other collaborative partners. Organizations in the central positions with a large number of ties have information advantages and can influence other collaborative network partners through lowering their level of uncertainty, providing necessary resources such as knowledge, etc. [Powell, Koput, Smith-Doerr, 1996]. Although there are several different measures of centrality in the literature such as degree centrality, Katz-Bonacich centrality and betweenness centrality [Freeman, 1979], Katz-Bonacich's centrality, used by several studies on identifying the leader (e.g., [Zhou, Chen, 2016]), is more efficient in measuring centrality relative to the entire network (see [Ballester, Calvo-Armengol, Zenou, 2006]). Organizations occupying a central position in networks can acquire non-redundant and diverse information more quickly than others. Central organizations also have better access to the resources and capabilities (e.g., [Powell, Koput, Smith-Doerr, 1996]) and are able to have better outcomes such as innovation and performance. L. Freeman [Freeman, 1979] also emphasizes network central-ity as an important structural feature that affects efficiency.
Therefore, based on this argument network centrality as the second main attribute of leaders in a research collaborative network is considered to identify a leader. The combination of reputation and centrality increases the attractiveness of a company as a non-market leader in a research collaborative network for other collaborative partners.
Efficiency measurement for identifying a research collaborative leader. There are different efficiency analysis approaches in the literature, including deterministic frontier analysis (DFA), stochastic frontier analysis (SFA) [Aigner, Lovell, Schmidt, 1977], and data envelopment analysis (DEA) [Charnes, Cooper, Rhodes, 1978]. This research will focus on the DEA approach as the most widely used method in this regard, with advantages over DFA and SFA [Hjalmarsson, Kumbhakar, Heshmati, 1996]. It provides a simple method to deal with multiple inputs and outputs in examining relative efficiency and handles large numbers of variables, constraints, and data [Charnes, Cooper, Rhodes, 1978; Kiani Mavi, Kazemi, Jahangiri, 2013].
DEA is a non-parametric fractional mathematical modeling as a ratio of a weighted sum of the outputs to a weighted sum of the inputs for measuring the relative efficiency of a homogeneous group of DMUs by multiple inputs and outputs [Charnes, Cooper, Rhodes, 1978]. Many additional theoretical developments in the field have adapted the models to deal with different problems in practice [Adler, Friedman, Sinuany-Stern, 2002]. Since the advent of DEA in 1978, there has been extensive growth in theoretical developments and applications in its basic models, focusing on the various models, data, status of variables, and approaches to incorporating restrictions on multipliers [Kao, 2009].
According to the proposed definition of a leader in a research collaborative network, the leader will be a company with higher efficiency based on the two main attributes of centrality and reputation. As above-mentioned, these two attributes affect particular types of resources and outcomes of organizations in interorganizational relationships. Therefore, it is required to consider these two attributes in different dimensions with related inputs and outputs. Accordingly, this research aims to develop an MDCW based on DEA to calculate efficiency scores by proposing a full ranking of organizations through implementing the common weight (CW) approach [Kiani Mavi, Kazemi, Jahangiri, 2013]. The proposed model will realize its high-efficiency score on the most influential leading organization in a research collaborative network based on the two main attributes including the network centrality and reputation.
Restrictions and variables. Typically, there are two basic structures in production systems of DMUs including series processes and parallel processes [Kao, 2009], which constitute two important parts of DEA studies known as "Network DEA" (e.g., [Zhang, Chen, 2018]) and "Parallel DEA" (e.g., [Kao, 2009]). For example, L. Zhang and Y. Chen [Zhang, Chen, 2018] have used the input-oriented additive two-stage network DEA model with predetermined weights and compared two approaches for solving this model. However, weights have been applied directly by the decision-maker in a series process of network DEA.
This study focuses on the parallel systems as DMUs usually use various sets of inputs, which separately lead to various outputs through parallel functions toward outcomes (see Figure 1).
There are no clearly defined and agreed-on input and output relationships in many cases for implementing multiple inputs and outputs. This issue highlights the importance of classifying inputs versus outputs in separate dimensions and determining their extent in efficiency measurement to better discriminate among DMUs. Accordingly, measuring efficiency based on only some dispersed criteria with different significance for the managers may lead to inaccurate and unsatisfactory results. This system is following our proposed leader's attributes as we argued that the reputation and centrality affect related inputs and outputs of each organization in n separate dimensions.
Incorporating appropriate sets of inputs and outputs is critical for the managers to decide how to consume inputs and produce outputs efficiently while they are taking the advantages of reputation and network centrality. However, some inputs are exogenously fixed and beyond managers' discretionary control [Banker, Morey, 1986].
Figure 1. A general parallel system of operations for each DMU
N o t e s: x — input; y — output. Adapted fro m: [Kao, 2009, p. 1108].
These inputs, which are known as non-discretionary (ND) variables, affect the efficiency score indirectly and have been studied in several studies to enhance efficiency measurement (e.g., [Banker, Morey, 1986]). Non-discretionary variables affect organizations' efficiency scores by contributing to their resources and outcomes, such as age and size [Haveman, 1993]. This research also considers this type of data to enhance the accuracy of the efficiency measurement.
MODEL DEVELOPMENT
A common weight model with an ideal point approach. While the efficiency scores of DMUs using basic DEA models are between zero and one inclusively, it is impossible to reach a full rank of DMUs when some are efficient with the efficiency scores of one [Kiani Mavi, Kazemi, Jahangiri, 2013]. N. Adler with coauthors propose a review of the studies and techniques which focus on the differential capabilities of DEA to rank both effcient and ineffcient DMUs fully [Adler, Friedman, Sinuany-Stern, 2002]. However, several studies (e.g., [Kiani Mavi, Kazemi, Jahangiri, 2013]) have mentioned that CW models are the most popular approach for assessing and fully ranking all DMUs. These models focus on an identical criterion to select the most favorable set of weights and reduce the flexibility of weights assigned to all inputs and outputs of DMUs [Kiani Mavi, Kazemi, Jahangiri, 2013]. Several methods have been developed in the DEA literature for obtaining common weights (CWs) for DMUs, which have led to a wide range of contributions in this realm and reviewed by several studies (e.g., [Sun, Wu, Guo, 2013]).
This research focuses on the ideal point (IP) method introduced by [Sun, Wu, Guo, 2013] for driving CWs as it is always feasible and provides a better insight into the main purpose of developing a model to find the leader as the best performing DMU. Also, as we mentioned before, the ND inputs will be implemented in model development to enhance the accuracy of the efficiency measurement.
Therefore, this research will focus on the proposed model by [Kiani Mavi, Kazemi, Jahangiri, 2013] as a common weight model with an ideal point method and implementing ND inputs (CW-IP-ND model). In this regard, we first assume that there are a set of J DMUs and each DMUj, j = 1, ..., J produces s different discretionary outputs yjr, r = = 1, ..., s with consuming m different discretionary inputs Xji, i = 1,..., m and t different non-discretionary inputs Zji, l = 1, ..., t. In the next step, we define an ideal point DMU as follows.
Definition 1. The ideal DMU is a DMU that its inputs are at the minimum level, and its outputs are at the maximum level among all DMUs and are shown by
DMU = (X, Z,Y) where X, Z, and Y respectively denote the discretionary inputs, non-discretionary inputs, and discretionary outputs of the ideal unit, Xi = min{xji } zl = min{zjl},
and y = max{y r},j = 1, ...,J. Finally, the CW-IP-ND model is presented as Model (1)
r j j
[Kiani Mavi, Kazemi, Jahangiri, 2013]:
J
min 0 = S
j=i
s.t.
m
S V(xj< - Xi )
i=1
+
j=1
I
S qi (zl - Zi)
l=1
J
+S
j=1
■> _
S ur (yr - yjr )
r=1
S ury}r-S v>xp-S qz» -0 j=1 •••,J;
r=1 i=1 l=1
m
S viXi = 1
(Model 1)
i=1
S uryr-S qiZi = 1
r=1
l=1
Vik, Urk, qi > £ Vi, yr, Vl,
where (v, u, q)e R(m+s+t) is the common set of weights and the constraints ^ vixi = 1 and
¿=1
Z uryr — Z Z i = 1 ensure that the ideal DMU is efficient. Finally, the efficiency
s
zu* yjr
r s r r=1 /=1
score of DMUj (Ej) is measured by implementing the following ratio: E. =
r=1
j m
S
i=1
*
v*xji
We will develop this model based on a parallel system of multiple operating dimensions and two separate weights which we will describe in the model development section.
Developing a multidimensional CW-IP-ND model (MDCW-IP-ND). In this section, a multidimensional common weight model with ideal point method (CW-IP) and ND inputs is proposed as a newly developed version of the model (1) by considering the following five steps.
Step 1. According to the traditional denotations in DEA, we consider a set of k homogeneous DMUs, denoted DMUj, j = 1, ..., J. However, instead of assuming that these DMUs consume multiple inputs to produce multiple outputs [Charnes, Cooper, Rhodes, 1978], we will define inputs and outputs in n separate dimensions (equivalent to the parallel system) and a particular weight assigned to each dimension to show the importance of each dimension. Accordingly, we consider that DMUj consumes m different inputs, Xjik, i = 1, ..., mk, to produce s different outputs, yjrk, r = 1, ..., sk, in k different dimensions, k = 1, ., n.
Step 2. We implement a weight (Dk) to control the importance of each dimension over other dimensions which have been proposed in step 1 for efficiency measurement. This will illustrate the importance of the decision-maker in characterizing the leader. Step 3. In the next step of development, we multiplied a weight (Wjk) to each DMU's
J
inputs and outputs in each dimension while ^Wjk = 1, Vk.
j=1
These weights contribute to discriminating between DMUs regarding better influencing other collaborative network partners through implementing the network centrality and reputation. In other words, a leader should take advantage of network position and visibility in accessing inputs and producing outputs efficiently.
Step 4. Considering the previous definition of ideal DMU, we will define an ideal DMU based on multiple dimensions and the defined weights as follow.
Definition 2. The ideal DMU is a virtual DMU that possesses minimum discretionary and non-discretionary inputs and maximum discretionary outputs among all DMUs. It
is shown by DMU = (X, Z, Yk), where Xk and Yk respectively denote the vector of discretionary inputs and outputs of the ideal unit in each dimension and Z refers to the vector of non-discretionary inputs without having a particular dimension. Accordingly, we have XN=( X11, ..., XmU X12, ..., Xm22; ...; Xln, ..., Xmkn), xa = min{wjk .Xji }, j = 1, •••, J,
—k — Y =(y 1
■> ySli; y^---' y
s, 2 ' ■ ■ ■
y i„
' y$kn ^ yr
h
= minj^k -Zji} •
maxi
j
W,k •yjrk Ü j = 1,-5 j , and
Step 5. Different modifications have been made to develop corresponding models for controlling non-discretionary variables (e.g., [Banker, Morey, 1986]). R. Banker and R. Morey [Banker, Morey, 1986] were the first scholars who addressed ND variables by proposing different alterations to the original DEA models for measuring technical efficiency. Their approach has become the standard way of controlling ND inputs in DEA [Golany, Roll, 1993], which is considered in this research as Zj, l = 1,..., t.
Therefore, after following these five steps, we will have the final model as follow:
min
j
+X
j=i
in 9 = X
j=i
k =1 i=1
V
" _ k _ k Z Dk ZWjk -^k .Xjikvk Xk
i =1
j j=1
( t
t ^
Z q •ziq h
i=1
i=1
k=1 r=1
V
" fc _ k
Z Dk Z urk •yrk -ZWjk-urk •yjrk
r=1
(Model 2)
s.t.
k=1 i=1
V
" k 1 " k ZDk ZWk-vik-xpk +Zq-zfl-ZDk ZWk-urk• y.
1=1
k=1 r=1
V
> 0, j = 1,-, J
k
Dk Ii -X-k = = k = l,...,n
i=i V
' 'k t
Dk I urk ■yFk -h<i- -lki== = =
r =1 V l=1
, n
Vik, Urk, qi > s; k = 1, ..., n; l = 1, ..., t; i = 1, ..., mk; r = 1, ..., sk, where £ is a non-Archimedean infinitesimal epsilon that is imposed to avoid ignoring any factor in calculating efficiency [Kiani Mavi, Kazemi, Jahangiri, 2013]. The calculated weights of vik and urk are the assigned weights to the discretionary input i and output r, respectively in dimension k. The weight of qi is also the calculated weight assigning to non-discretionary input I by the model.
The objective function of the model measures the total virtual distances between
each DMU and the DMU [Kiani Mavi, Kazemi, Jahangiri, 2013] based on the given inputs and outputs and the corresponding weights. In other words, the total horizontal distances will be
j
I
j=i
IDk IWjk
-Ivik -Xu
j
+ I
j=i
f t t I q ■zji -I q z
for both discretionary and ND inputs, and the total vertical distances will be
i f si si A
I
j=i
I Dk I urk -yrk -IWjk -urk -yFk
In this model, the external weights of each dimension (Dk) can be in two states, including variable states, with determining their optimal scores by the Model (2) and parameter states to determine their scores by the manager. The amount of internal weight for each DMU and its inputs and outputs in each dimension (Wjk) are parameters that will be defined and predetermined based on the case study and two main interorgani-zational and network characteristics of DMUs. As the assumptions mentioned above, these weights are essential in leaders characterizing and discriminating between DMUs regarding resource accessibility. Previous studies have used external weights in the network DEA (e.g., [Zhang, Chen, 2018]).
Finally, after calculating variables by Model (2), we need to calculate each DMU's efficiency score. Following [Kiani Mavi, Kazemi, Jahangiri, 2013], the following definition will complete this efficiency measurement procedure.
Definition 3. The efficiency of DMUj is better than other DMUs if its objective function which measures the distance in Model (2) is less than the objective function
of other DMUs. In other words, the distance between the DMUj and DMU is less than the other distances. The purpose of Model (2) is to obtain an optimal solution of (D1, ..., Dk; v*, ..., v*k; u*, ..., u*k; q1, ..., q*) to make the total distances between all
DMUs and DMU as short as possible [Sun, Wu Guo, 2013]. Afterward, we can calculate the efficiency of each DMUj with the optimal CWs using Equation (1) [Kiani Mavi, Kazemi, Jahangiri, 2013]:
E* =
I Dk XWjk .u*k j
f t \ *
I9 Zj
(1)
I Dk %Wjk .v*k j
The DMU with a higher value of E* will be considered as the leader in the horizontal network among a set of homogenous and related organizations.
ILLUSTRATIVE CASE STUDY
In this section, the developed Model (2) is applied to evaluate the performance of R&D centers' as the numerical example for the leader investigation.
Problem description. This research focuses on R&D networks as an example of a research collaborative network, which has received increasing academic interest in recent years (e.g., [He et al., 2018]) to illustrate the applicability of the proposed model for identifying the leader. Shortcomings in fundamental technologies and technological and scientific capabilities highlight the importance of R&D efficiency improvement [He et al., 2018]. Therefore, R&D leaders' role is becoming increasingly important to find, invest in, and pay greater attention to different network levels for establishing R&D policy and resource allocation. This study identifies a leader among 47 R&D centers in medical universities in Iran where lecturers, researchers, and budget will be employed to deliver scientific outcomes in terms of meetings and new knowledge in the form of papers. In this regard, we implemented our proposed model, the network structure, and collected data to investigate a leading DMU by measuring the efficiency of DMUs based on the network centrality and reputation as two leader's attributes.
To define the network structure, we have investigated strategic collaborative relationships based on joint papers published by these R&D centers (Figure 2).
Accordingly, G is defined as the symmetric adjacency matrix of research collaborative relationships between R&D centers. Elements of gj in matrix G are the link between DMUj and DMUj - and defined with a value of 1 if DMUj has collaborated with DMUj - and 0 otherwise, also gjj=0 which indicates there is no self-loop.
Data collection. For the data analysis, the input and output variables are selected based on the literature (e.g., [Qin, Du, 2018; Yang, Fukuyama, Song, 2018]). For example, S. Zemtsov and M. Kotsemir [Zemtsov, Kotsemir, 2019] presented a literature review on the most applicable inputs and outputs for measuring the efficiency of innovation systems and R&D centers. In this research, Human Capital inputs including R&D research staff and researchers, and R&D and education expenditures are two main categories of inputs, and Patents and Publications are two main categories of outputs
Figure 2. The research collaborative network of 47 medical R&D centers
based on the previous literature. In this research, according to the particular strategies of R&D centers in Iranian Universities and the available data, the categorizing inputs and related outputs in different dimensions is exclusively related to current research that can be different in other collaborative research networks in other countries.
Hence, we assume that the operations of these medical R&D centers are based on two parallel sets of inputs and outputs as two dimensions. In the first dimension, it is assumed that the budget of R&D centers1 (input) leads to their scientific meetings and conferences (output). In other words, R&D centers in universities consume their budget to hold scientific meetings and conferences as an important attribute of knowledge level and productivity indicator of scientists in R&D centers [Lopes, Lanzer, 2002]. In the second dimension, we assume that students and lecturers (input) in each R&D center contribute to the national and international published articles (output) that is based on the dominant strategy to increase publications in Iranian universities by students and lecturers [Kharabaf, Abdollahi, 2012].
These dimensions can be different in other similar networks for different countries. The efficiency of individual scientists also can be inferred in terms of consuming their knowledge and creativity to develop knowledge in terms of publications. We have also considered universities' age as a non-discretionary factor as it is an uncontrollable input for managers and affects level of prior knowledge in R&D centers and their efficiency [Beier, Ackerman, 2003]. The corresponding data was collected from the UniRef2 database and the universities' website in 2018 (Appendix).
However, for collecting data regarding the other defined variables, we will perform as bellow:
♦ the reputation of universities affects some parts of their resources and, accordingly, the relevant outcomes. The high reputed universities cause managers to enhance their budget for holding scientific meetings. This research used universities' rank-ing3 to measure their reputation and normalized them as the ratio to the sum of the rankings. In this way, the sum of reputation scores of universities is one;
♦ there are several measures of centrality in the literature [Freeman, 1979]. However, Katz-Bonacich's centrality is more popular for finding the leader in the networks (e.g., [Zhou, Chen, 2016]), and is more efficient in measuring centrality relative to the whole network [Ballester, Calvo-Armengol, Zenou, 2006]. The Katz-Bonacich centrality of a DMU counts the number of paths that stem from the DMU exponentially discounted based on the length of paths [Ballester, Calvo-Armengol, Zenou, 2006] and is calculated using the network structure and the following Equation (2) in the matrix form:
1 All universities are public universities and they have annual budget, which is approved by the Ministry of Science.
2 Database www.uniref.ir introduces and ranks Iranian universities based on clear and documented data from internal conference and journal papers as well as published papers in international journals indexed by Science Citation Index (SCI).
3 From www.webometrics.info
w = [I- SG]-1SG1 (2)
where w is the vector of centralities, 1 is the /-dimensional vector of 1s, and I denotes the identity matrix [Ballester, Calvo-Armengol, Zenou, 2006]. Also, S is a discount factor between 0 and the inverse of the largest eigenvalue, 1/(\Max(G)) to compute the discounted sum of walks emanating from the node j to j (j Finally, after calculating the centrality of each university, the values have been normalized by the sum of centralities.
Results and discussion. This part presents the efficiency scores derived from the formulating developed model using GAMS software and collected data from 47 R&D centers in medical universities. In this regard, we presumed that there are two dimensions of inputs and outputs regarding each DMU for the leader's investigation. Also, for differentiating between outputs of R&D centers in terms of produced paper, we considered that the weight of international papers (u22) is more than double the weight of internal papers (u12).
Furthermore, the optimization technology in the GAMS software adjust the weights of dimensions (Dk) with the weights of inputs (vk) and outputs (urk) for solving the proposed model. This adjustment leads to similar rankings of DMUs for different status of Dk (to be as a parameter or variable). To prevent such adjusting weights, we measure the efficiency scores through two rounds of calculation. In the first round of efficiency calculation, we derive the optimal weights of inputs and outputs where the status of Dk is variable (Table l).
Table 1. Optimal weights of inputs and outputs
Variable With Without
Dk and Wjk Dk and Wjk
Vil 0.42E-4 0.08E-5
V*12 38.7374 0.01587
V21 0.01E-4 0.01E-4
«il 1.82915 0.72E-4
«21 1.82915 0.03571
«22 0.01561 0.00014
qi 0.01E-4 0.01E-4
For efficiency calculation, we selected a non-maximum value arbitrarily for the epsilon (g=10-6)) to achieve feasible solutions due to the existence of large values. Then, through fixing these weights as the optimal results for Vik, Urk, and qi we recalculate the efficiency scores in the second round of efficiency measurement. Here, a sensitivity analysis also on the values of Dk has been performed for a better understanding of its impact on efficiency scores (Table 2).
Finally, we compared the results of this proposed model with a simple situation where there is no Dk and Wjk in the model. We also implemented the normalization of the efficiency scores to produce efficiencies between 0 and 1 with at least one efficient unit. Based on the efficiency calculations and sensitivity analysis in Table 3, the following results can be inferred:
a) the comparison between the cases in which there are different weights of Dk for each dimension (the first and third columns of efficiency scores) and the case without considering weights of dimensions (the last column of efficiency scores) or with equal weights (the second column of efficiency scores) illustrates that the external weights of dimensions (Dk) or the manager's preferences increase the discrimination power of the moedel in order to have a more precices and fair efficiency scores concerning each DMU;
b) the comparison between the case in which there is a simple CWs model with ND inputs without considering Dk and Wjk (the last column of efficiency scores) and the case without considering weights of dimensions or with equal weights (the second column of efficiency scores) demonstrates that internal weights (Wjk) affect efficiency scores;
c) the results confirm that ignoring the above weights in this research (Dk and Wjk) for measuring efficiency based on DEA may cause inaccurate and biased results. Consequently, the leader can vary based on managers' preferences and the external network characteristics that affect the resource availability and outcomes of DMUs;
d) the results demonstrate that the leader will be the R&D center in Tehran University of Medical Sciences (DMU 1), one of the reputable universities with the highest reputation among other medical universities in Iran. However, this university's efficiency decreases compared to other universities when we incorporate the considerably higher weight of reputation compared to the centrality in the model. In other words, the University of Tehran, with its high reputation compared to the other universities, is not efficient in exploiting its reputational advantages to produce higher levels of outcomes;
e) finally, the R&D spillover is not completely evident. On the one hand, social media and electronic communications will facilitate joint research and papers without the barrier of distance. On the other hand, the magnitude of different levels of reputation and centrality of universities in the same province creates competition between these DMUs. Only those universities which have high and relatively close knowledge accessibility, reputation, and mutual dependency (for example, universities number 1 with 4, 28 with 7) have more tendency to create mutual strategic relations to keep their competitiveness and not to lose their power advantages. The competition among these universities for higher reputation and centrality to gain a higher budget and other valuable resources is for higher knowledge and innovation creation. Therefore, competition among universities to gain a leading position is linked to their network efficiencies.
Table 2. The comparison of efficiency scores
DMU D/t and Wjit are both parameters (a sensitivity analysis on Dk) Dk is variable and Wß is parameter Without Die and Wjk
£*(£>! = 0.01, £>2=0.99) Rank E"j(D1 = 0.5, D2 = 0.5) Rank E"j(D1 = 0.99, D2 = 0.01) Rank £*(£>! = 0.9, £>2 = 0.1) Rank E; Rank
1 2 3 4 5 6 7 8 9 10 11
1 1.0000 1 0.5741 4 0.5461 9 0.2523 15 1.0000 1
2 0.7408 3 0.5122 6 0.7506 4 0.3614 8 0.8022 3
3 0.7300 4 0.4407 9 0.5049 11 0.2294 16 0.7344 4
4 0.0747 40 0.1114 39 0.6196 5 0.1709 21 0.5277 7
5 0.5203 11 0.2880 18 0.0852 30 0.0994 30 0.2621 24
6 0.9183 2 0.5807 3 0.4945 12 0.3236 9 0.6611 5
7 0.7034 5 0.4318 10 0.2823 22 0.2173 17 0.4403 10
8 0.5368 9 0.3447 14 0.4201 14 0.2084 18 0.5154 8
9 0.4579 13 0.2759 19 0.1611 27 0.1310 25 0.2943 21
10 0.2934 28 0.4583 7 0.9847 2 0.5981 2 0.6301 6
11 0.5956 7 0.2883 17 0.0048 37 0.0467 33 0.2800 22
12 0.4451 15 0.3040 16 0.3836 18 0.2058 19 0.4290 12
13 0.3636 22 0.2223 28 0.1591 28 0.1127 27 0.2520 25
14 0.4483 14 0.3583 13 0.2994 21 0.2614 12 0.3202 17
15 0.4426 16 0.2749 20 0.1681 24 0.1395 23 0.2439 26
16 0.2736 33 0.2261 26 0.3089 20 0.1934 20 0.2786 23
17 0.4872 12 0.4181 11 0.5719 8 0.3686 7 0.5038 9
18 0.3138 27 0.1583 34 0.0053 35 0.0322 37 0.1227 38
19 0.3738 21 0.2401 25 0.1658 25 0.1322 24 0.2301 29
20 0.3329 24 0.1707 33 0.0094 32 0.0388 35 0.1882 33
21 0.2873 29 0.2741 22 0.4105 16 0.2655 11 0.3341 16
22 0.0518 42 0.0240 44 0.0001 47 0.0031 46 0.0243 44
un
o\
End ofthe Table 2
s e x
aj
1 2 3 4 5 6 7 8 9 10 11
23 0.2870 30 0.1431 36 0.0036 38 0.0272 38 0.1170 40
24 0.6782 6 0.5681 5 1.0000 1 0.5179 3 0.8141 2
25 0.3629 23 0.2249 27 0.0984 29 0.1050 29 0.1589 35
26 0.2786 31 0.1368 38 0.0027 40 0.0238 40 0.1289 36
27 0.3824 20 0.1914 32 0.0051 36 0.0371 36 0.2310 28
28 0.5373 8 0.2747 21 0.0135 31 0.0612 31 0.3035 19
29 0.4008 18 0.5930 2 0.3932 17 0.4790 5 0.3152 18
30 0.0384 44 0.0782 43 0.3186 19 0.1257 26 0.1704 34
31 0.0652 41 0.2113 29 0.4192 15 0.3043 10 0.2211 30
32 0.1939 38 0.0977 42 0.0031 39 0.0197 42 0.0991 41
33 0.4285 17 0.3279 15 0.4535 13 0.2613 13 0.4350 11
34 0.0345 46 0.0174 46 0.0004 45 0.0035 45 0.0156 46
35 0.2625 34 0.4467 8 0.5949 6 0.5095 4 0.3508 15
36 0.2765 32 0.1374 37 0.0027 41 0.0255 39 0.0937 42
37 0.0976 39 0.1073 41 0.1614 26 0.1120 28 0.1224 39
38 0.2611 35 0.2464 24 0.5374 10 0.2573 14 0.4049 14
39 0.0346 45 0.0176 45 0.0006 44 0.0037 44 0.0171 45
40 0.3888 19 0.1974 31 0.0074 34 0.0419 34 0.2203 31
41 0.5289 10 0.2667 23 0.0088 33 0.0542 32 0.2323 27
42 0.2579 36 0.2029 30 0.1998 23 0.1534 22 0.2044 32
43 0.2254 37 0.1101 40 0.0020 42 0.0187 43 0.0874 43
44 0.3146 26 0.1497 35 0.0019 43 0.0224 41 0.1287 37
45 0.3261 25 0.3797 12 0.5825 7 0.4086 6 0.4215 13
46 0.0475 43 1.0000 1 0.8045 3 1.0000 1 0.2946 20
47 0.00507 47 0.00229 47 0.00008 46 0.00023 47 0.0015 47
CONCLUSION AND FUTURE RESEARCH
An increasing interest in the investigation and identification of supply network leaders is evident in recent studies by incorporating various leadership characteristics in the literature. In this research, we focused on evaluating based on efficiency through developing a multidimensional CW model and incorporating various attributes of a leader, especially in a research collaborative network.
The proposed model can consider various importance of inputs and outputs by bearing in mind two main internal and external coefficients for each dimension. The external coefficient is to handle the significance of each dimension based on the preferences of managers. This feature illustrates that efficiency scores and types of inputs and outputs are inextricably bound up for efficiency calculation, which was not considered before. On the other hand, inputs and outputs in each dimension have a different significance for each company's network regarding their access to the resources and the market. This importance also was considered as an internal coefficient for each input and output per DMU in all dimensions.
Finally, an R&D network was selected as a numerical example to test the applicability of our proposed model and framework for leader identification among 47 R&D centers in medical universities in Iran. The results demonstrate that R&D centers with different positions in the network structure and specific popularity in terms of reputation have particular access to resources and specific capability to produce outputs. The network externality is based on the network centrality, and the reputation affects the relevant dimension of each R&D center in the network, which influences their efficiency scores. Finally, selecting a leader based on the efficiency of DMUs is sensitive to managers' preferences about the importance of each dimension.
This study offers considerable contributions in evaluating and suggest further investigation of both DEA model developments and leader identification realms. Some scholars may be interested in selecting a set of leaders. In this case, the current procedure for model development can be applied to the conventional DEA models [Charnes, Cooper, Rhodes, 1978], where some DMUs may receive higher efficiency scores. Finally, this study suggests incorporating the strength of the links among DMUs (weak and strong ties) in the next studies to gain better insights into the dependencies and knowledge spillover.
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Received: January 30, 2021 Accepted: March 10, 2021
Contact information
Sajad Kazemi — Postgraduate Student; s.kazemi_ie@yahoo.com
ВЫЯВЛЕНИЕ ЛИДЕРА В СОВМЕСТНОЙ ИССЛЕДОВАТЕЛЬСКОЙ СЕТИ
С. Каземи
Санкт-Петербургский государственный университет, Российская Федерация, 199034, Санкт-Петербург, Университетская наб., 7-9
Для цитирования: Kazemi S. 2021. Leader identification in a research collaborative network. Вестник Санкт-Петербургского университета. Менеджмент 20 (1): 58-85. http://doi.org/10.21638/11701/spbu08.2021.103
Существует множество эмпирических данных о преимуществах межорганизационных исследовательских сетей сотрудничества между обществами и исследовательскими институтами, такими как центры исследований и разработок (R&D) и университеты. Определение лидера в этих условиях важно как с теоретической (для изучения лидерства), так и с практической точки зрения (для эффективного распределения государственного финансирования и частных инвестиций). Непоследовательные определения и неоднородные атрибуты с одномерными подходами к измерению (например, субъективное измерение силы или рассмотрение центральной компании в качестве лидера) сделали неэффективными предыдущие усилия для выявления лидеров в межорганизационной среде. Поэтому настоящее исследование направлено на установление лидирующей организации среди множества центров НИОКР в контексте совместной исследовательской сети путем реализации концепции главного лидера в разных измерениях. В статье разработана многомерная модель с общими весами на основе подхода анализа свертки данных (DEA) в параллельной системе с несколькими операционными измерениями, каждое из которых потребляет набор входных данных (бюджет, преподаватели и студенты) для достижения набора результатов (научные встречи и конференции, национальные и международные документы). Центральность и видимость — два основных свойства лидеров, которые вместе с эффективностью влияют на вклад и результаты каждого сетевого партнера. Показано, как предложенная модель реализует самый высокий уровень эффективности
Исследование выполнено при поддержке гранта Санкт-Петербургского государственного университета (проект № 60419633).
в наиболее влиятельном центре НИОКР, названном «лидером», среди 47 центров НИОКР в медицинских университетах Ирана. Сравнительный анализ результатов управления показывает, что репутация в данном случае имеет большее значение при определении лидера, чем центральность. Результаты математических расчетов показали надежную различительную способность при измерении эффективности в рамках представленной модели. Ключевые слова: совместная исследовательская сеть, лидер, анализ свертки данных, общие веса, недискреционные переменные, эффективность, центральность сети, репутация.
Статья поступила в редакцию 30 января 2021 г. Статья рекомендована в печать 10 марта 2021 г.
Контактная информация
Каземи Саджад — аспирант; s.kazemi_ie@yahoo.com
oo to
The input and output data from 47 R&D centers in medical universities
APPENDIX
e *
a}
ID Universities of Medical Sciences Province Non-discretionary input Weight Discretionary input Discretionary output
Dimension 1 Dimension 2 Dimension 1 Dimension 2 Dimension 1 Dimension 2
Age Reputation: World's rank (normalized) Centrality (normalized) Budget (Million Rials) No. of lecturers No. of students No. of scientific meetings and conferences National paper International paper
1 2 3 4 5 6 7 8 9 10 11 12
1 Tehran University Tehran 85 2.168E-02 0.0925 36044870 1650 13300 28 1175 6384
2 Mashhad University Razavi Khorasan 73 2.161E-02 0.0403 23921622 911 8300 16 822 2434
3 Iran University Tehran 45 2.159E-02 0.0585 20917546 980 7206 12 700 2671
4 Shahid Beheshti University Tehran 59 2.165E-02 0.0597 22575513 1414 12600 20 675 101
5 Ahvaz Jundishapur University Khuzestan 65 2.150E-02 0.0164 18614967 646 6400 1 576 1133
6 Tabriz University East Azerbaijan 72 2.161E-02 0.0296 21368659 716 8500 8 568 2491
7 Isfahan University Isfahan 73 2.159E-02 0.0236 25106905 830 8770 5 512 2209
8 Hamedan University Hamedan 47 2.148E-02 0.0388 10359853 451 4149 4 293 875
Continuation of the Appendix
1 2 3 4 5 6 7 8 9 10 11 12
9 Yazd Shahid Sadoughi University Yazd 37 2.147E-02 0.0175 8935700 379 5400 1 272 597
10 Shiraz University Pars 74 2.149E-02 0.0191 25817719 898 10200 18 274 954
11 Kermanshah University Kermanshah 52 2.149E-02 0.0076 11655656 474 4394 0 263 1064
12 Kerman University Kerman 42 2.149E-02 0.0229 9477527 515 6136 3 227 853
13 Zahedan University Sistan and Baluchestan 38 2.137E-02 0.0222 8495336 355 4361 1 220 435
14 Mazandaran University Mazandaran 33 2.149E-02 0.0139 15687553 454 8200 3 198 757
15 Alborz University Alborz 9 2.122E-02 0.0266 8787248 209 7116 1 173 304
16 Gilan University Gilan 34 2.142E-02 0.0223 13466387 453 4805 3 162 440
17 Babol University Mazandaran 36 2.137E-02 0.0115 4930515 297 3500 2 160 528
18 Lorestan University Lorestan 26 2.141E-02 0.0244 9354725 279 2621 0 127 307
19 Kurdistan University Kurdistan 33 2.143E-02 0.0223 8858326 252 2551 1 125 335
20 Qazvin University Qazvin 36 2.136E-02 0.0266 5027122 295 2800 0 119 356
21 Golestan University Golestan 52 2.134E-02 0.0223 10404078 305 2497 3 113 311
oo
Continuation of the Appendix
e *
a}
1 2 3 4 5 6 7 8 9 10 11 12
22 Shahrekord University Chaharmahal and Bakhtiari 33 2.144E-02 0.0049 6070802 244 2385 0 108 0
23 Bushehr University Bushehr 37 2.141E-02 0.0169 6265364 200 2160 0 104 191
24 Gonabad University Razavi Khorasan 33 2.094E-02 0.0134 1254249 98 1581 1 103 228
25 Urmia University West Azerbaijan 34 2.142E-02 0.0195 16412581 313 4379 1 87 436
26 Qom University Qom 15 2.128E-02 0.0097 5208193 206 2294 0 82 202
27 Birjand University South Khorasan 35 2.139E-02 0.0087 2894542 197 3030 0 82 278
28 Kashan University Isfahan 33 2.143E-02 0.0222 3622085 212 1988 0 84 440
29 Dezful University Khuzestan 12 2.051E-02 0.0085 4341754 72 1128 1 81 79
30 Semnan University Semnan 31 2.085E-02 0.0205 3469613 244 2756 1 77 0
31 Zabol University Sistan and Baluchestan 14 2.132E-02 0.0117 3618462 138 1769 1 72 0
32 North Khorasan University North Khorasan 10 2.127E-02 0.0147 4093807 195 1805 0 68 126
33 Sabzevar University Razavi Khorasan 24 2.131E-02 0.0224 2896231 120 1783 1 65 184
34 Arak University Markazi 33 2.141E-02 0.0203 5978916 229 3471 0 67 0
End of the Appendix
1 2 3 4 5 6 7 8 9 10 11 12
35 Rafsanjan University Kerman 34 2.133E-02 0.0049 2661864 182 1874 1 55 170
36 Abadan University Khuzestan 78 2.021E-02 0.0205 3367896 81 587 0 54 68
37 Hormozgan University Hormoz 33 2.137E-02 0.0187 9125439 267 2700 1 50 84
38 Zanjan University Zanjan 32 2.145E-02 0.0223 6774793 357 4200 3 50 366
39 Ilam University Ilam 24 2.140E-02 0.0237 3863715 174 3826 0 47 2
40 Shahroud University Semnan 46 2.132E-02 0.0161 2203819 130 1370 0 34 197
41 Torbat Heydarieh University Razavi Khorasan 6 2.048E-02 0.0191 1743450 63 737 0 32 125
42 Ardabil University Ardabil 26 2.136E-02 0.0167 7499375 235 3371 1 30 240
43 Bam University Kerman 9 1.990E-02 0.0114 2242070 66 834 0 28 49
44 Yasuj University Kohgiluyeh and Boyer-Ahmad 34 2.136E-02 0.0078 5435319 174 1626 0 26 219
45 Fasa University Pars 42 2.130E-02 0.0141 2541991 95 905 1 25 117
46 Jahrom University Pars 25 2.124E-02 0.0023 2133320 113 1091 1 25 0
47 Jiroft University Kerman 11 2.027E-02 0.0103 4620888 90 227 0 4 0
oo Un
