A Research on Inter-Firms Relationship Using Network-Based DEA -A Case Study of Mazda Yokokai
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Recent Advances in Energy and Environment Integrated Systems A Research on Inter-firms Relationship Using Network-Based DEA -A Case Study of Mazda Yokokai- TAKAO ITO, SHINYA TAGAWA Department of Business Administration Ube National College of Technology) 2-14-1 Tokiwadai, Ube City, Yamaguchi Prefecture, 755-8555 JAPAN [email protected], [email protected] RAJIV MEHTA School of Management New Jersey Institute of Technology University Heights, Newark, NJ 07102-1982 USA [email protected] MAKOTO SAKAMOTO, SATOSHI IKEDA Department of Engineering University of Miyazaki 1-1, Gakuen Kibanadai-nishi, Miyazaki-shi, 889-2192 JAPAN [email protected], [email protected] Abstract: - This is a paper focused on the research of inter-firms relationship using network-based DEA (Data Envelopment Analysis). Efficiency is an important issue in corporate management. Many effective tools to measure the efficiency have been developed. DEA is one of the most effective tools. In the DEA, efficiency is calculated as the ratio of multiple inputs and multiple outputs. All of the data is considered as independent and separate variant. As far as we know, the society we are living is a networked society. The whole system will be impacted strongly even if a small change happened. Therefore, in this paper, the authors reviewed the literature associated with the DEA, and proposed a new approach called network-based DEA. In order to identify the formation process of corporate strategy, the authors collected the data from the keiretsu of Mazda, Yokokai, and measured the importance of the firms in the transaction network. Key-Words: - DEA, degree, efficiency criterion, network, corporate performance, Yokokai necessary to measure the efficiency. Many effective tools 1 Introduction to measure the efficiency have been developed. DEA Keiretsu is commonly recognized as one of the (Data Envelopment Analysis) is one of the typical tools. competitive sources of Japanese firms. The In this paper, the authors reviewed the literature characteristics of Japanese keiretsu are 1) access to stable associated with the DEA and proposed the new financing, 2) insulation from market pressures, 3) risk approach called network-based DEA. Furthermore, the reduction, monitoring benefits and reduction of authors calculated the efficiency of each firms in information asymmetries, and 5) mutual assistance [1]. Yokokai, and revealed the relationship between inter- In order to understand the relationship between inter- firms relationship and corporate performance. firms relationship and corporate performance, it is ISBN: 978-1-61804-181-4 92 Recent Advances in Energy and Environment Integrated Systems Out-degree In-degree Sales 2 Problem Formulation 1 20 0 1,000 In order to identify the rational inter-firms relationship, a 2 135 20 2,000 number of papers have been published. The typical study 3 0 30 4,000 4 0 45 200 is the research of stability and influence of inter-firms 5 0 60 9,000 relationship in Mazda’ Yokokai published by Ito et al [2], structural analysis of the Yokokai presented by Tagawa Then the result of DEA model will be obtained as shown et al. [3], and the centrality study of Yokokai [4]. At the in Table 2. same time, many tools to measure efficiency have been developed and published. DEA is a very practical way to Table 2 Results of Fig. 1 assess performance and relative efficiency using a linear D Efficiency Reference set v1 v2 programming-based method [5]. The typical research of 1 1.000 1(1.000) 0.050 0.150 DEA and its application are the study of the efficiency of 2 0.205 1(0.385);5(0.068) 0.005 0.015 banks in transition published by Igor and Boris [6], 3 0.889 5(0.444) 0.011 0.033 simultaneous analysis of the interrelationships among 4 0.030 5(0.022) 0.007 0.022 economic growth, environmental pollution and energy 5 1.000 5(1.000) 0.006 0.017 consumption reported by Christina and George [7]. All of the data including input and output in the DEA are In Table 2, v1 and v2 means out-degree and in-degree considered independently and separately. In other words, respectively. The efficiency of node 2 is 0.205. The all of the data can be changed freely. But in real society, efficiency of node 2 will be improved if the out-degree as we know, all of the data should be connected with and in-degree are to change 0.005 and 0.015 times each other. In other words, the whole system will be respectively. changed dramatically even if a small change happened. We will get the new results shown in Table 3 after using Suppose a small network is given as follows. the solution shown in the Table 2. Table 3 New results of Fig. 1 D Efficiency Reference set v1 v2 1 1.000 1(1.000) 0.050 6.552 2 1.000 2(1.000) 1.417 0.075 60 3 0.889 5(0.444) 0.630 0.033 4 0.030 5(0.022) 0.420 0.022 5 1.000 5(1.000) 0.315 0.017 Table 3 shows that the efficiency of node 2 has been improved. But one of the important things should not be overlooked is that out-degree and in-degree of node 2 are changed from 135 and 20 in Table 1 to 0.675 and 0.3 Fig. 1 A five-node network respectively. The other data still remain same. It is inconsistent with the fact that whole system will be Fig. 1 is composed of five nodes. Node may be human, changed even if a small change happened. Thus, the computer or company. This is an asymmetric network; input data should be recalculated. The results are shown we may calculate the degree including in-degree and out- as in Table 4. degree based upon degree equation. Suppose the node is company, and output is sales. Suppose all of the input Table 4 New Input and output data of Fig. 1 and output data are given in Table 1. Input data Output data Out-degree In-degree Sales 1 0.300 0 1,000 Table 1 Input and output data of Fig. 1 2 0.675 0.300 2,000 Input data Output data ISBN: 978-1-61804-181-4 93 Recent Advances in Energy and Environment Integrated Systems 3 0 0.150 4,000 5) Efficiency comparison 4 0 0..225 200 The new solution will be found after comparing the 5 0 0.300 9,000 efficiencies between 2) and 4). 6) Criterion calculation The efficiency of node 2 is 0.178, smaller than 0.205. In order to find the importance of each node, Then we begin to understand that the DEA is not good efficiency criterion and its square value will be enough to find the best way of improvement. The DEA calculated if no difference between 2) and 4) exists. should be modified when we use it to measure the An efficiency criterion is defined as the summation efficiency. of all nodes’ efficiency when the solution is fixed at one specific company. And its square value is 3 Problem Solution defined as the summation of the square of all nodes’ efficiency. The former means that the impact of In this paper, we propose a new approach using DEA each node’, and the later means the importance of based upon network model. each node’. 3.1 Procedure of Network-based DEA 3.2 Measurement and Results The procedure of the network-based DEA is as follows. In order to identify inter-firms relationship in the keiretsu, 1) Problem formulation the authors collected the transaction data from Mazda’s Many types of DEA have been developed; the most Yokokai, a typical keiretsu of car-maker and parts- basic one is CCR (Charnes-Cooper-Rhodes) model. suppliers keiretsu, and calculated the efficiency of each The generalized model of the CCR is formulated as company. Degree including out-degree and in-degree are follows. calculated. Out-degree means that one company sells s parts to other company, and in-degree means that one = e Maximum∑ur y r (1) company purchases the parts from other company. In r =1 this paper, degree is considered as the input, and sales are Subject to considered as the output. The efficiency of all companies m is shown in Table 5. v x = 1 (2) ∑ l l l =1 Table 5 Efficiency of the firm in Mazda Yokokai s (selected part) u y ∑ r rj D v1 v2 u1 r=1 ≤ ;1 j=1, 2, ……, n (3) Efficiency (out-degree) (in-degree) (sales) m Mazda 0 0 1 0 ∑vl x lj l=1 Ishizaki 0.386 67 85,109 18 Honten v1, v 2, ⋅⋅⋅⋅⋅⋅ , vm ≥ 0 (4) Keylex 0.298 42 53,647 11 Kurashiki 0.404 90 113,851 24 u, u⋅⋅⋅⋅⋅⋅ , u ≥ 0 (5) Kako 1 2, m Sumino 0.303 207 262,696 56 2) Efficiency calculation Nishikawa 0.552 50 64,085 14 The efficiency will be calculated using input and Rubber output data and then the solution for lower Japan 0.038 6 8,005 2 Climate efficiency will be found. systems 3) Data recalculation Hiluta 0.321 66 84,043 18 The input and/or output data should be recalculated Kogyo based on the solution using network model. Hiroshima 0.353 37 47,075 1 4) Finding new result Aluminiu The efficiency should be recalculated using the new m data in 3). New result will be found. Molten 0.675 92 117,163 25 ISBN: 978-1-61804-181-4 94 Recent Advances in Energy and Environment Integrated Systems Ring Techs 0.332 144 183,101 39 Hiroshima Akebono 0.405 12 15,066 3 Brake Asumo 0.322 8 9,771 2 Usui 0.429 33 41,902 9 Kokusai Sangyo NOK 0.386 6 7,385 2 Kayaba 0.009 0 246 0 Industries Calsonic 0.013 0 115 0 Fig.