SUGISAKAMASANORI

Journal of Advances in Artificial Life Robotics
Vol. 1(4); March (2021), pp. 175–180
ON LINE ISSN 2435-8061; ISSN-L 2435-8061
https://alife-robotics.org/jallr.html

Research Article

Predicting the State of Interfirm Relationships:
An Empirical Investigation Using Integrative Forecasting
Techniques
Takao Ito1, Tsutomu Ito2, Rajiv Mehta3, Seigo Matsuno2, Makoto Sakamoto4

Graduate School of Advanced Science and Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi Hiroshima, 739-7527, Japan
Department of Business Administration, National Institute of Technology, Ube College, 2-14-1 Tokiwadai, Ube City, Yamaguchi Pref.,755-8555, Japan
3
Martin Tuchman School of Management, New Jersey Institute of Technology, Newark, New Jersey, 07102-1982, U.S.A.
4
Faculty of Engineering, University of Miyazaki, 1-1 Gakuen Kibanadai-Nishi, Miyazaki, 889-2192, Japan
12ARTICLE INFO
Article History
Received 11 November 2019
Accepted 07 September 2020
Keywords
Out-degree
Rate of changeInterfirm relationship
Cross-sectional interaction
YokokaiABSTRACT

The formation of successful corporate strategy among vertically integrated organizations ispredicated upon a plethora of dynamic relationships among buyer-seller firms. Albeit growing ininterest, there is a paucity of research that focuses on predicting the nature of interfirm
relationships among Japanese keiretsu members. Discerning this knowledge can help formulate
successful strategic decisions, such as whether to continue procuring parts or increasing future
investments in partner firms. As studies on predicting interfirm relationships among keiretsu
member firms has been scant, this research offers insights by illustrating a newer approach formaking decisions regarding corporate strategy. Using data collected on transaction from
Yokokai—parts suppliers of Mazda—in this study a new model is developed to predict the natureof interfirm relationships using the degree index and DEA model. The primary contribution ofthis research is that interfirm relationships not only depend on future trends, but are also
determined by the interactions among member firms of a keiretsu.

© 2022 The Author. Published by Sugisaka Masanori at ALife Robotics Corporation Ltd.
This is an open access article distributed under the CC BY-NC 4.0 license(http://creativecommons.org/licenses/by-nc/4.0/).

investments in partner firms. Accordingly, this study
makes a contribution to the extant literature byillustrating a novel integrative forecasting approach forpredicting the state of interfirm relationships, which is
not only dependent on future economic conditions, butalso determined by the interactive relationships amongkeiretsu member organizations. This manuscript isstructured as follows. Section 2 reviews the relevant
literature on forecasting methods and interfirm
relationships. In Section 3, the model building procedureand process for predicting interfirm relationships using
our new proposed method is explicated. In Section 4, theapplication of the integrative forecasting approach isexemplified. In Section 5, the results of this empirical
study using the data drawn from Yokokai, Mazda’s

1. Introduction
In vertically integrated arrangements, formulation of
successful corporate strategy is predicated upon aplethora of dynamic interrelationships among memberorganizations, such as frequently engaging in interfirm
transactions, cross-firm investments, and jointly coalesce
towards attaining collective, supra-organizational goals.
Although there is growing interest, research on these
vertically integrated organizational forms has been
fragmentary. Indeed, research that focuses on predicting
the nature of interfirm relationships among Japanesekeiretsu members is scant. Discerning this knowledge
can direct determine strategic decisions, such as whether
to continue procuring parts or increasing future

Corresponding author’s E-mail: itotakao@hiroshima-u.ac.jp, t_ito@ube-k.ac.jp, Mehta@njit.edu, matsuno@ube-k.qac.jp,
sakamoto@cc.miyazaki-u.ac.jp

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in case of network organizations, all indexes areconnected with each other; thus, the criterion variable
will vary if one of the indexes, such as degree andinfluence change [4], [5]. Consequently, the prediction ofinterfirm relationships basically comprises two aspects.
The first is future trends, which may exhibit increasing ordecreasing values. And, the second is the rate of change
for time series data. Thus, future trend will be determinedby not only time series change, but also cross-sectional
interaction of interfirm relationship. In this paper, timeseries change can be measured by least square method,and future trend will be identified by using comparative
study between different term’s efficiency. That isindicative of a strong incentive to develop nexttransaction if the t+1 term’ efficiency is larger than its
previous term. Therefore, to calculate relative efficiency
another forecasting method—the DEA procedure—isproposed. Cross-sectional interaction can be calculatedusing graph theory, such degree, and influence ofinterfirm relationships. Accordingly, the procedure canbe shown as below.
1. Collect adjacent matrix data from Keiretsu.
2. Calculate network indexes such as degree usinggraph theory. In asymmetric network, degree will be
divided into out-degree and in-degree. They willused as input data sets in DEA model. Degree will
be calculated as below.

Keiretsu, is compared and contrasted to validate our new
proposed integrative forecasting method vis-à-vis
traditional prediction methods and approaches. Section 6
identifies limitations and offers directions for future
research.
2. BackgroundAs well-known organizational structures, Japanesekeiretsu typically comprise a family of interfirm
cooperative arrangements among member automotive
manufacturers and their component parts suppliers. It iswidely recognized that the success of corporate
management of these inter-family structured businessconstellations and alliances depends to a large extent oninterfirm relationships among partner firms. A plethoraof studies on interfirm relationships have been published.
For instance, Bensaou illustrated a framework for
managing a portfolio of relationships among partner
firms. More specifically, he (a) proposed the type ofrelation design a firm should choose under different
external contingencies, and (b) what is the appropriate
way to manage different types of relationships [1]. In
another investigation, Mathijs De Vaan clarified how thecomposition and stability of network ties affect firm
performance in industries characterized by rapid
technological change [2]. All of these research studies
focused on the interfirm relationships using past data sets.
While offering explanations to past occurrences isimportant, forecasting the future developmental trends ofinterfirm relationships would be even more salient.
Indeed, businesses place tremendous importance on theprediction in different fields, such as weather forecasting,and stock price movements [3]. In the context of keiretsu,
as studies on prediction of interrelationships amonginterfirm partners have been sparse, this research offers
insights by showing a newer approach for making
decisions regarding corporate strategy. Using datacollected on transaction from Yokokai—parts suppliersof Mazda—in this study a new model is developed toforecast interfirm relationship using graph theory.

3.

Deg = ∑𝑛𝑛𝑖𝑖 𝑎𝑎(𝑝𝑝𝑖𝑖 , 𝑝𝑝𝑘𝑘 )Put the network indexes as input data set into DEA
model with output data set. The generalized modelof the CCR model is formulated as follows:
Objective function∑𝑠𝑠

Subject tomax θ = ∑𝑟𝑟=1𝑚𝑚

𝑢𝑢𝑟𝑟 𝑦𝑦𝑟𝑟𝑟𝑟

𝑖𝑖=1 𝑣𝑣𝑖𝑖 𝑥𝑥𝑖𝑖𝑖𝑖∑𝑠𝑠𝑟𝑟=1 𝑢𝑢𝑟𝑟𝑦𝑦𝑟𝑟𝑟𝑟∑𝑚𝑚𝑖𝑖=1 𝑣𝑣𝑖𝑖 𝑥𝑥𝑖𝑖𝑖𝑖

4.

Generally, all forecasting methods, which include
moving average and ARMA models, have focus on
future trends and rate of change for time series data
depending on past values of the variable being forecastedand on past prediction errors. Moreover, the input data
sets are basically independent with each other. However,5.

𝑣𝑣𝑖𝑖 ≥ 0 (i = 1,2, ⋯ , m)

(4)
(5)

Select specific firm from the keiretsu and forecast
the value of interfirm relation using regression
model.
Calculate the rate of change of the specific firm. The
rate of change r will be calculated as below.
r=176

(2)

(3)

≤1𝑢𝑢𝑟𝑟 ≥ 0 (r = 1,2, ⋯ , s)

3. Model Building(1)

𝐷𝐷𝐷𝐷𝐷𝐷𝑡𝑡+1 −𝐷𝐷𝐷𝐷𝐷𝐷𝑡𝑡
𝐷𝐷𝐷𝐷𝐷𝐷𝑡𝑡≤1(6)and E will be 31.25, and 68.75, respectively. The newvalue of interfirm relation of D-C and D-E are 0.505, and0.482, respectively. They are less than θ 0=0.543;
therefore, the direction of the future trend will be
negative. The prediction value of D-C and D-E will be
18.75, and 41.25. It means that the relationship between
D and C, and D and E will be weaker than before.

whereDegt+1 predicted value of degree at t+1 term
Degt existed value of degree at t term
6. Input the degree index as input data into DEA model,
and calculate the relative efficiency (θ0).
7. Determine the transaction firms of the specific firm,and predict the value of interfirm relation using therate of change for each firms.
8. Calculate degree index again, and input the degree
as input data sets of DEA model; calculate theefficiencies of each firms: θ1,θ2,…θn.
9. Determine the direction of the transaction firms, tokeep going up if θi≥θ; Otherwise keep going down.
10. Predict the values of interfirm relationship.
11. Check the difference between prediction andobserved value, find the reason if the big gap exists.

5. Empirical Studies
In order to predict the relationship of the keiretsu, datafor the duration 2004 to 2008 was obtained from Yokokai,a network organization of the automotive parts suppliers.
The network of Yokokai in 2004 is illustrated as in Fig.

4. An Example
Suppose a five node network shown in Fig. 1 is given

Fig. 2. An Example of Transaction of Yokokai in 2004.

2.
To predict interfirm relationships in 2008, the out-degreeof Hiroshima Aluminum are calculated in Table 2.
Table 2. Out-degree of Hiroshima Aluminum.
Out-degree

Fig. 1. An Example of Five-node Network.

[4].

2004

76.5

Based on degree equation, in-degree and out-degree will
be calculated in Table 1 as below.

2005762006

792007

78.8

ABCDE

Table 1. This is the caption.
Out-degreeIn-degree
2090
13535
11555
804555180

The relative efficiency of Hiroshima Aluminum is 0.04.
The prediction value of out-degree in 2008 will becalculated as 80.05 using regression model. The observed
value in 2008 is 81.2. The rate of change will becalculated as 1.58%. There are four companies havetransactions with Hiroshima Aluminum in 2007. Theyare Mazda, Honda, Jatco, and Aishin AW. This rate isused to calculate the relationship and efficiency. The new
efficiencies of Mazda, Honda, Jatco, and Aishin AW are
0.039, 0.092, 0.088, and 0.101, respectively. Thus, only
the efficiency with Mazda is less than the former. It
indicates that the future trend of the relationship with

The relative efficiency of the five firms are 0.714, 1,0.322, 0.543, 1 respectively when the sales revenue of thefive firms are 100, 90, 250, 300, and 400 respectively.
Suppose the regression model of out-degree of node D isy=20x-100 based on data sets of 9 historical term. Thus,
the out-degree of B in next term will be 100. The rate ofchange is 0.25. Consequently, the relationships with C,

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Mazda will be negative. The results of prediction andefficiency can be shown in Table 3 below.

15

Table 3. Prediction Results and Observed Data.
Prediction

10Observed Data Set

Mazda

53.04

48

Honda

8.84

6.9

Jatco

10.46

11.5

Aishin AW

5.99

14.8

50Observed data

Observed data

Prediction1Prediction2

In this paper, a new method using two integrative
forecasting techniques was proposed. Using transaction
data drawn from Mazda’s Yokokai, the value of interfirm
relationship of Hiroshima Aluminum and KYB wereselected and predicted. The results validate andcorroborate that the newer method has met with empiricalsupport.
A limitation of this paper, however, is that only one
network index—degree—is used. Additional network
indices, such as influence and closeness, should also beinvestigated to test the validity of the newer forecastingmodel. Furthermore, in future research studies not onlytransactional data, but also cross-shareholdings among
member firms, should be employed.

20
JatcoPrediction1

Suzuki

6. Conclusion

40

NissanMitsubishi

This study corroborates that the result of our newer
proposed method is much more accurate than thetraditional approach. Accordingly, the results obtained inthis empirical investigation find validation and support ofour integrative forecasting method.

60

ToyotaNissanFig. 4. Prediction Results of the Relationships between theKYB and its Suppliers.

Basically, the traditional approach of prediction is only
to calculate the trend based on time series change. To
compare the traditional approach with our newer
proposed method, the prediction of interfirm
relationships is conducted. The value of interfirm ofHiroshima Aluminum with Mazda, Honda, and Jatco are
54.7, 7.2, and 11.25 respectively using the regression
model without considering the interaction among firms
to predict. The relationship with Aishin AW cannot becalculated because of lack of data. Using the observed
data, prediction using our proposed method, versus
prediction without considering the interaction isillustrated in Fig. 3.

0Toyota

Aishin AWPrediction2

Fig. 3. Prediction Results of the Relationships between
Hiroshima Aluminum and its Suppliers.

References

Prediction 1 indicates the proposed method, which iscompared with the results of Prediction 2 (or thetraditional approach) in Fig. 3. All other firms exhibit
similar results. Similarly, we selected KYB andcompared the results using the same method, which isreported in Fig. 4.

1. Bensaou, Portfolio of buyer-supplier relationships, Sloan
management Review, summer 1999.
2. Mathijs de Vaan, Inter-firm networks and firm
performance in the face of technological discontinuities,
the DIME-DRUID Academy winter conference 2011,
Comwell Rebild Bakker, Aalborg, Denmark, January 2022, 2011.
3. Forecasting.
4. Tsutomu Ito, The influence of inter-firm relationships on
corporate performance, Scholars’ Press, 2018.
5. T. Ito, M. Sakamoto, R. Mehta, and S. Ikeda: Examining
Inter-Firm Relationships Using Network-Based DEA: A178

Case Study of Mazda Yokokai, International Journal of
Mathematical Models and Methods in Applied Sciences,
Volume 8, 2014, pp. 516-521, November 2014.

Dr. Rajiv Mehta

Dr. Rajiv Mehta (Ph.D., DrexelUniversity) is Professor of Marketing atMartin
TuchmanSchoolofManagement, New Jersey Institute ofTechnology, USA. Previously, heworked
foraninternationalmanufacturer of steel cables. He has coauthored four university textbooks,including Sales Force Management, 2ne ed. (2020). Focusing
on sales management, global marketing channels, Keiretsus,
and international strategic alliances, his research is publishedin Sloan Management Review, Journal of BusinessResearch, Industrial Marketing Management, European
Journal of Marketing, International Marketing Review, andArtificial Life and Robotics, among others.

Authors Introduction
Dr. Takao Ito
He is Professor of Management ofTechnology (MOT) in Graduate Schoolof Engineering at Hiroshima University.
He is serving concurrently as Professorof Harbin Institute of Technology(Weihai) China. He has publishednumerous papers in refereed journals andproceedings, particularly in the area of management science,and computer science. Dr. Ito earned his Doctor degree ofEconomics from Kyoto University and Ph. D. ofEngineering from Miyazaki University, Japan. Dr. Ito was avisiting research professor of School of Management, New
Jersey Institute of Technology (NJIT) from March 29 2008
to March 28, 2009.
Dr. Tsutomu Ito
He is Assistant Professor of theDepartment of Business Administration
at National Institute of Technology, Ube
College, Japan. He has published many
papers in refereed journals andproceedings, particularly in the area ofindustrial management, and computerscience. His current research interests
include internet of things (IoT), mechanical engineering,artificial intelligence (AI), automata theory, quantitative
analysis of Japanese Keiretsu. He was one of the winners ofthe Best Paper Award in the International Conference on
Artificial Life and Robotics (ICAROB) in 2015and 2016.
Dr. Ito earned his Doctor degree of Engineering fromHiroshima University, Japan in 2018.

179Dr. Seigo Matsuno

He is Professor of the Department ofBusiness Administration at National
Institute of Technology, Ube College,
Japan. He received his Ph.D. degree in
Economics from Kyushu University,
Japan in 2004. His current researchinterests are in the areas of IT
management and strategy, information systems outsourcing,and interfirm relationship management. Dr. Matsuno has
published several research papers and books in that area. He
is a member of the Board of the Directors of Japan Society
for Information and Management.
Dr. Makoto Sakamoto
He received the Ph.D. degree incomputer science and systems
engineering
fromYamaguchi
University in 1999. He is presently anassociate professor in the Faculty ofEngineering, University of Miyazaki.
He is a theoretical computer scientist,and his current main research interests
are automata theory, languages andcomputation. He is also interested in digital geometry,
digital image processing, computer vision, computer
graphics, virtual reality, augmented reality, entertainment
computing, complex systems, data science, and so forth.

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