Journal of Robotics, Networking and Artificial Life, Vol. 4, No. 3 (December 2017) 254–259___________________________________________________________________________________________________________

Measuring Efficiency using Dynamic Network-Based Data Envelopment Analysis
Tsutomu Ito, Katsuhiko Takahashi, Katsumi Morikawa, Takao Ito
Graduate School of Engineering, Hiroshima University,1-4-1 Kagamiyama,
Higashi-Hiroshima, 739-8527, Japan
E-mail: D152365@hiroshima-u.ac.jp
Rajiv Mehta
Martin Tuchman School of Management, New Jersey Institute of Technology, University Heights,
Newark, New Jersey, 07102-1982, U.S.
Makoto Sakamoto, Satoshi Ikeda
Faculty of Engineering, University of Miyazaki, 1-1 Gakuen Kibanadai-Nishi,
Miyazaki, 889-2192, Japan

Abstract
Enhancing efficiency is a critical objective of corporate management. While numerous approaches tomeasure efficiency have been devised, this manuscript suggests a new method referred to as dynamic
network-based Data Envelopment Analysis (DEA) as a more advanced procedure for examining
transaction priorities in any network based organization. Using dynamic network-based DEA it ispossible to detect system-wide impacts when marginal systemic changes occur. This newer method wastested using data drawn from Mazda’s Yokokai keiretsu to illustrate the effect that transactions among
member firms in the network have on sales revenues. The finding of the study are discussed based on
which managerial implications in the formulation of corporate strategy are proffered. Study drawbacks
are identified and avenues for future research are suggested.
Keywords: DEA, dynamic network-based DEA, transaction priorities, Keiretsu, Yokokai.
when marginal changes in related inter-firm phenomena
are manifest. Because of the scant research in thisdomain, this paper makes a unique contribution to theextant literature by: (1) Developing a new DEA model
based on network analysis, and (2) Underscoring its
function in corporate strategy.
This paper is organized as follows: Section 2
discusses the background and relevant literature
focusing on DEA studies. In section 3, it offers a fivenode network to illustrate the problem using a standard
DEA model, and details the process involved to resolve

1. Introduction
Ascertaining novel procedures for improving theefficiency of organizations is a continuing objective ofcorporate management. Although numerous tools toassess efficiency have been devised, this paper proposesa newer approach known as dynamic network-based
Data Envelopment Analysis (DEA) as an even more
effective approach for examining transaction priorities
in any network. This is because using dynamic networkbased DEA enables the detection of systemic impacts

Copyright © 2017, the Authors. Published by Atlantis Press.
This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
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this issue. Section 4 explicates data collection
procedures as well as calculates the efficiency of
Yokokai—a typical network organization comprising
suppliers of Mazda, a global auto manufacturer. The
findings are reported and discussed following which theconclusions are presented in the final section.

For this type of an asymmetric network, it is possible tocalculate the degree index, which can be dichotomized
into out-degree and in-degree. The findings of outdegree and in-degree are {20, 135, 115, 80, 55}, and{90, 35, 55, 45, 180} respectively. Suppose the sales ofthe five firms are 100, 900, 250, 300, and 400,
respectively. Based on the calculation of standard DEA
model, the results are reported in Table 1.

2. Background and Literature Review

Table 1. New results of Figure 1.

DEA refers to a linear programming method thatassesses the efficiency of multiple decision-making
units (DMUs) when the production process shows astructure of multiple inputs and outputs [1]. Originallyproposed in 1957 by Farrell [2], it was popularized
after Charnes, Cooper and Rhodes applied linear
programming to estimate an empirical production
technology frontier in 1978 [3]. Recently Liu and Lu
developed network-based approach in applying one
measure of the centrality—known as eigenvalue—todiscriminate efficient decision-making organizations as
determined by standard DEA modelling [4]. Chen
indicated the importance of the intermediate outputs
consumed by one sub DMU and suggested a networkDEA model with new efficiency operationalizations thatsystematically cope with the dynamic effect within a
production network, such as a keiretsu [5].
Accordingly, this paper focuses on systemic changes
in network systems to propose a new approach forcalculating efficiency within keiretsu.

A
B
C
D
E

D Efficiency
0.688
1
0.412
0.557
1

Reference set (λ)
5(0.250)2(1.000)2(0.251), 5(0.059)
2(0.297), 5(0.082)
5(1.000)

In Table 1, the efficiency of node A is 0.688, which
will improve if the out-degree and in-degree of the input
data is changed to 0.6875. After altering the input ofout-degree and in-degree from 20 and 90 to 13.75 and61.875 respectively, the newer results shows that theefficiency of node A has been improved. However, an
important aspect, which is noteworthy, is that the otherdata remain constant even though out-degree and indegree of node A is changed. This result is seemingly
inconsistent with the fact that systemic changes will bemanifest even if a marginal adjustment has transpired.
Thus, the input data should be recalculated. The new
input of out-degree and in-degree are {13.5, 135,
99.375, 80, 42.5}, and {61.8759, 28.75, 55, 45, 180},
respectively. The results using the new input data are
depicted in Table 2.

3. Research Method
A diagrammatic depiction among members of a small
network of firms—as illustrated in Figure 1—reveals anasymmetric group of interconnected firms composed offive nodes. Nodes are called DMUs in standard DEA.

Table 2. New results of Figure 1.
A
B
C
D
E

D Efficiency
0.773
1
0.365
0.543
1

Reference set (λ)
E(0.250)B(1.000)
B(0.246), E(0.072)
B(0.294), E(0.089)
E(1.000)

The efficiency of node A is 0.773, which is smaller
than 1, which indicates that the DEA is not sufficiently
suitable for detecting real systemic changes.
Consequently, the DEA should be modified when it isused to measure efficiency. Thus, it is necessary to findan answer that makes the result of node A = 1. The best
method is to employ a heuristic approach and calculate
the input data at different levels. In this case, theefficient of node A will be 1 if the input data will be
fixed at 45 percent (0.45). The results of the input data
analysis are reported in Figure 2.

Figure 1. A five-node network.

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Journal of Robotics, Networking and Artificial Life, Vol. 4, No. 3 (December 2017) 254–259___________________________________________________________________________________________________________As shown in Table 3, D efficiency is computed
using original input data set and D efficiency after
removing 50% (i.e., 50% of 20) is recalculated with the
input data set employing standard DEA modelling. The
difference score is defined as the gap between D
Efficiency and D Efficiency after removing a certain
amount, say 50% ― as it is in this example. The
efficiency has improved if the value is positive. The
difference score of node A is 0.312, which is suggestivethat the efficiency will change if the transaction between
node A and B decreases by 50%. The difference scoreof node B is zero. Evidently, there is no impact on node
B if the amount between node A and B will be reduced
to 10. Conversely, the efficiency will be low if theamount between node A and E decreases. Therefore,
node A will have benefits if node A changes thetransaction amount with node B.
The groups can be trichotomized in this transaction
network. The first group is the selected nodes, thesecond group refers to the nodes dealing with theselected node, and the third group comprises theremainder of the nodal firms. However, it excludes theselected node and the respective nodes dealing with theselected nodes. Next, it is necessary to calculate thedifference score of these three groups and determine thepriority of each node based on the results of the selected
node. The difference score of the three groups is shownin Figure 3.

Figure 2. Heuristic results of the input data at different levels.

These findings are dependent on inputs that are
difficult to adjust. Moreover, not all firms arenecessarily completely efficient. Hence, setting theefficiency to one is an ideal objective. The DEA shows
the reference set for improving efficiency, but does notprovide any detailed directions for providing the
optimal solution. Indeed, one of its limitations is that ittreats the detailed information as a “black box.”
However, it is important to identify the importance ofeach company that it has ties with for the purposes ofstrategy formulation. Accordingly, this paper proposes a
new index—known as the efficiency criterion—that isbased on the simulation result of dynamic networkbased DEA. Therefore, the DEA is a useful tool not
only to calculate the efficiency, but also to identify the
relative importance of the relationship in any networkbased organization. Many methods, such as incremental
approach and decremented approach, are considered
useful.
Next, we test the new index known as the efficiency
criterion to illustrate a detailed approach for Mazda’s
Yokokai using decremented approach. For purposes ofillustration, we calculate the efficiency criterion using
the data before discussing its implications for Mazda’s
Yokokai. Evidently, as shown in Figure 1, node A has
three connections with B, C, and E. The value between
node A and B is 20, which means node A sells its 20
percent parts to node B. The efficiency of all nodes iscomputed after removing a certain amount, for instance,
fifty percent (see Table 3).

Figure 3. Difference score of node A with B, C, and E.

Table 3. Difference score of the trasanction of node A with B.
D Efficiency
A
B
C
D
E

0.688
1
0.324
0.557
1

D Efficiency after
removing 50%
1
1
0.321
0.551
0.928

The summation of the difference score—called thedifference criterion—will be considered as an index that
identifies the transaction priority in any network. The
difference criterion refers to the summation of the gapof all nodes’ efficiency between the efficiency of the
new system after changing a certain amount and theoriginal system when the solution is fixed at one

Difference
score
0.312
0
-0.003-0.006-0.072256

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5) Finding new results: The calculation will becompleted if the answer of the selected node is 1;
otherwise, the answer should be ascertained by
employing heuristic approach.
6) Determining the priorities: Finally, it is necessary
to calculate the difference scores and difference
criterion of three groups to determine the priority ofeach node deal with the selected node.

selected node. Essentially, this indicates the impact ofeach node. The difference criterion of node A is shownas in Figure 4.

4. Measurements and Discussion
To study inter-firm relationships among keiretsu
members, transaction data were obtained from Mazda’s
Yokokai, which represents a typical automotive
manufacturer and parts-supplier keiretsu to calculate theefficiency of each company. It is noteworthy that the
number of the firms dealing with Mazda usuallyfluctuates year to year. The total membership of the
Yokokai in 2004 was 188, but the total firms Mazda
dealt with was 91.
The linkage between two firms is expressed as
degree. Degree, including out-degree and in-degree, arecalculated. Out-degree means that one company sells
parts to other company, and in-degree means that one
company purchases the parts from that same supplierfirm. Degree is considered as the input data, and sales
revenues are considered as the output data.
Mazda’s Yokokai is divided into two groups
comprising suppliers and automotive manufacturers. In
the auto manufacturer group, the top three companies
are No. 39, Pioneer Corporation, No.76, Matsushita
Electric Industrial Co., Ltd., and No.45, Bosch
Corporation. The efficiency of Pioneer Corporation andMatsushita Electric Industrial Co., Ltd. is one.
Moreover, the efficiency of Bosch Corporation is 0.954.
Conversely, the efficiency of No.55 of Aisin AI Co.,
Ltd. and No. 21 of Jatco Ltd., are the lowest as they are
0.002 and 0.003, respectively. They are subsidiaries ofToyota, and the distance to Mazda is considered as longthan other suppliers. In the group of automakers, thehighest value of efficiency is Toyota (0.01), and thelowest is Mazda (0.001).
To ascertain the detailed approach for improving afirm’s efficiency, the first step is to compute theefficiency of all firms in Yokokai. To determine the bestsolution for suppliers, Unipres is selected for illustrative
purposes. The primary business of Unipres, one ofseveral Yokokai members, is to manufacture automotive
and electronic parts that are sold to not only Mazda, but

Figure 4 Difference criterion of node A with B, C, and E.

Accordingly, the priority of node A improving its
efficiency is to focus on nodes B, and C. Node E should
be excluded because its value is negative. As such, theefficiency criterion can be considered as an index of the
impact of the selected company. This reveals that as theefficiency criterion gets larger, its impact gets stronger.
The step-wise procedure of the dynamic networkbased DEA is described next.
1) Building problem formulation: Many types of the
DEA have been developed; the most typical one is
known as the Charnes-Cooper-Rhodes (CCR) model.
The generalized model of the CCR model is formulated
as follows:max 𝜃 =

Subject to∑𝑠𝑟=1 𝑢𝑟 𝑦 𝑗
𝑢 𝑦 + 𝑢2 𝑦2𝑗 +∙∙∙ +𝑢𝑠 𝑦𝑠𝑠
𝑟 = 1 1𝑗∑𝑚𝑣
𝑥𝑣
1 𝑥1𝑗 + 𝑣2 𝑥2𝑗 +∙∙∙ +𝑣𝑚 𝑥𝑚𝑚
𝑖=1 𝑖 𝑖𝑖𝑢𝑟 ≥ 0𝑣𝑖 ≥ 0(𝑟 = 1, 2, … , 𝑠)(𝑖 = 1, 2, … , 𝑚)

(1)

(2)
(3)
(4)

2) Calculating Efficiencies: The efficiencies arecalculated using input and output data. The solution, or
reference set, for a selected node with lower efficiency
can, thus, be found.
3) Recalculating Data Set: The input and/or output
data should be recalculated based on the reference set
using the network model.
4) Recalculating Efficiencies: The efficiencies should
be recalculated using the new data set calculated in third
step. New results will be ascertained.

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Journal of Robotics, Networking and Artificial Life, Vol. 4, No. 3 (December 2017) 254–259___________________________________________________________________________________________________________

Two additional examples are Japan Climate Systems
Corporation and the renowned Sumino, which are
members of Yokokai. Climate Systems is a firm that
manufactures air-conditioning, condensers, and engine
cooling systems. In 2004, Climate Systems sold its parts
to Mazda while it purchased from Sumino, a renowned
manufacturer of precision press welding components forautomobiles in Yokokai. The detailed transaction information of Climate Systems is shown in Table 5 and 6.

also non-keiretsu members, such as Nissan, Isuzu,
Toyota and Jatco. Unipres also purchases parts fromYorozu Corporation, which also manufactures
automobile suspension systems. Moreover, Unipres andYorozu are members of an independent group of autopart suppliers.
The efficiency of Unipres is 0.0261. From theseresults, it can be determined that the objective ofUnipres is to improve its efficiency, which can beaccomplished by changing its input data for out-degree
and in-degree 0.0261 times. Thus, this results in an
efficiency of Unipres of 0.996 when the input data ischanged 0.0261 times.
Based upon efficiency results, and the procedure of
dynamic network-based DEA, D efficiency is calculated. The value is 0.0258 if D efficiency is set as 1.
Next, to find the optimal solution of Unipres, thedetailed transaction information in Yokokai should beanalyzed, which is reported in Table 4. Unipres
purchases the parts from Yorozu and sells its products
to Mazda, Calsonic Kansai, Jatco, Nissan and Isuzu.
Difference score of all firm inter-relationships with
Unipres are depicted in Figure 5.

Table 5. Transaction of Climate Systems in Yokokai.
To Climate
Systems

0
0
0
0
0
1.6

0

92

Sumino

2

0

0
0
0

2
2
83

0,0035

0,003

0,003

0,017

0,00250,002
0,0015

0,001

0,001
0,0005

0,016

0

0,014
0,012

Mazda

SuminoFigure 6. Difference criterion of Climate Systems.

0,01
0,008
0,006

0,003

0,004
0,002
0

0,001

0
Mazda

Calsonic
Kansei

0,012

0,003

Jatco

Nissan

Isuzu

0,011

0,01

0

Differencce Criterion

Difference criterion

From Sumino

Difference criterion of all firms associated with Climate
Systems and Sumino are illustrated in Figures 6 and 7.

From Unipres
1.1
3.5
10.8
58.9
0.7
0

0,018

To Sumino
Climate Systems
NSK
Mazda

Difference Criterion

To Unipres

Mazda

Table 6. Transaction of Sumino in Yokokai.

Table 4. Transaction of Unipres in Yokokai.
Mazda
Calsonic Kansei
Jatco
NissanIsuzu
YorozuFrom Climate
Systems

YorozuFigure 5. Difference score of Unipres.

The Difference criterion between Unipres andYorozu is 0.017, and the value between Unipres andNissan and Calsonic Kansai is 0.003 respectively.
Therefore, Unipres should prioritize its business with
Yorozu, Nissan, and Jatco.

0,008
0,006
0,004

0,005
0,003

0,002
0

Climate System

NSK

Mazda

Figure 7. Difference criterion of Sumino.

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efficiency of all member firms were calculated. The
paper also suggested a new index—the efficiency
criterion—to determine the importance of each firm in agiven network.
A key limitation of this paper, however, is that only
one network index—degree—is used. Additional
network indices, such as betweenness, and density,
should be investigated. Furthermore, in future research
investigations not only transactional data, but also crossshareholdings among member firms, should be applied,which will enhance our understanding of how keiretsus
can be strategically managed to yield higher
performance objectives.

Figure 6 indicates that Climate Systems should
prioritize the number of transactions with Sumino andMazda. Figure 7 shows that the priority of transactionsof Sumino is NSK, Mazda, and Climate Systems.
Therefore, not only Climate Systems and Sumino, butalso Mazda has the opportunity to improve theirefficiency if the data between Climate Systems andSumino is altered. Moreover, it is a mutual but
asymmetric relationship between Climate Systems andSumino, The priority of Climate Systems is Sumino andMazda, but the priority of Sumino is NSK, Mazda, andClimate Systems. Climate Systems will get much more
benefits to adjust its transaction amount compared withthat of Sumino.
The results of this study makes several contributions
to the extant literature to yield some implications thatoffer guidelines for managerial actions. Morespecifically, to augment corporate efficiency, thefollowingsuggestions
formanaging
theinterrelationships among keiretsu members are
identified: First, this study proposed a new approach toidentify systemic changes in a given network system. It
clarified the internal solutions to link with the DEA
model and network approach. In this paper, theefficiency of all firms was measured as well as thepriority of the different firms was determined. Second,
new indexes, such as differece sores and difference
criterion were proposed. These new indexes express thechanges after the data are modified. Third, calculating
the efficiency in a given network is a useful tool
because the relationship between a member vis-à-vis thewhole network system can be developed.

Acknowledgements
This work was supported by JSPS KAKENHI Grant
Number 16K01243.
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5. Conclusion
In this paper, dynamic network-based DEA wasproposed as a new approach for analyzing
interrelationships among members of a keiretsu. Using
transaction data drawn from Mazda’s Yokokai, the259