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Integrating intra-firm and inter-firm knowledge diffusion into the knowledge diffusion model
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Expert Systems with Applications Expert Systems with Applications 34 (2008) 1423–1433 www.elsevier.com/locate/eswa
Integrating intra-firm and inter-firm knowledge diffusion into the knowledge diffusion model Chih Ming Tsai Department of Marketing and Distribution Management, Tung-Fang Institute of Technology, No. 110, Dongfang Rd., Hunei Township, Kaohsiung County 82941, Taiwan, R.O.C.
Abstract Knowledge value and enterprise benefits are closely related. The performance of a knowledge management system can be evaluated when the dynamic relationship between knowledge value and its corresponding enterprise benefits is identified quantitatively. This study introduces five kinds of knowledge diffusion patterns, including knowledge internalization, knowledge externalization, knowledge improvement, external knowledge acquisition, and internal knowledge release, to construct the knowledge diffusion model which integrates the intra-firm and inter-firm diffusion processes simultaneously. An illustrative case demonstrates the feasibility of the proposed model successfully. In addition to the estimation of all parameters involved in the model, the parameter analysis provides some managerial insights into the implementation of the knowledge management system. Therefore, it follows that knowledge can be managed more effectively, and as a result the appropriate knowledge strategies can also be established for enhancing competitiveness. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Knowledge diffusion model; Intra-firm knowledge diffusion; Inter-firm knowledge diffusion; Knowledge value; Enterprise benefits
1. Introduction Knowledge value and its corresponding enterprise benefits are considered to be closely related (Bassi & Van Buren, 1999; Kreng & Tsai, 2003; Wilkins, van Wegen, & de Hoog, 1997). In order to discuss the dynamic relationship between knowledge value and enterprise benefits, Kreng and Tsai (2003) proposed the original knowledge diffusion model to help managers understand the performance of a knowledge management system and develop a set of knowledge management strategies. The concept of the original knowledge diffusion model, which is based on the Bass diffusion model (Bass, 1969) and the Activity Based Costing (ABC) model (Dekker & de Hoog, 2000; Wilkins et al., 1997), is that knowledge value can be transformed into increasing enterprise benefits through knowledge externalization, and then the existing enterprise benefits can also be transformed back into the increase of knowledge value through knowledge
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internalization. Numerous related parameters involved in the original knowledge diffusion model also reveal the different knowledge characteristics for demonstrating the feasibility and rationality. Accordingly, not only can the performance of knowledge management system be traced, but the knowledge management strategies can also be amplified by analyzing these related parameters. Knowledge management should be implemented in the open system where the internal organization can be interacted with the external environment. Based on the knowledge transformation cycle (Carlile & Rebentisch, 2003), the knowledge storage stage, which is the first stage of the cycle, serves as a source of knowledge retrieval and usage. After the transformation stage, the used knowledge is accumulated in the repository for the retrieval and usage in the next cycle. Under this circulation of knowledge storage, retrieval, and transformation, the internal and external knowledge diffusion should be involved simultaneously to implement this cycle. The knowledge management life cycle also includes four stages: create, capture, organize, and disseminate/share (Satyadas, Harigopal, & Cassaigne, 2001).
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Knowledge that is created, captured, and organized is ready for publishing to internal and external users. According to the knowledge chain model (Holsapple & Singh, 2001), the five primary and four secondary knowledge management activities involved in the knowledge chain model result in organizational learning and projection. Organizational learning is regarded as the process of knowledge diffusion occurring in the internal organization and projection is regarded as the process of knowledge diffusion interacting with the external environment. The knowledge chain model starts knowledge acquisition, which is the process of identifying the appropriate external knowledge and then transforming the captured knowledge into usable representations for subsequent use within the organization. After knowledge selection, generation, and internalization, existing knowledge is transformed into organizational outputs eventually for release into the environment by knowledge externalization. Since a successful knowledge management system has to be implemented in the internal organization and external environment simultaneously, intra-firm and inter-firm knowledge diffusion are presented here to exhibit the internal and external knowledge diffusion executed in the open environment, respectively. Intra-firm knowledge diffusion is defined as the processes that show how knowledge interacts with the internal organization, and the inter-firm knowledge diffusion is defined as the processes that reveal how knowledge interacts with the external environment. Under the intrafirm knowledge diffusion model, the sources of knowledge are existing internal knowledge retrieval and internal knowledge improvement due to continuous investment. The total knowledge value is summed up by the above knowledge sources and transformed into increased enterprise benefits through knowledge externalization activities. Then, the enterprise benefits are accumulated continuously and transformed back into increased knowledge value through knowledge internalization activities. Compared to intra-firm knowledge diffusion, inter-firm knowledge diffusion involves external knowledge resources acquisition and the release of enterprise benefits that are published to
the external environment. Accordingly, the total knowledge value used to transform into increased enterprise benefits increases because of external knowledge resources acquisition. Furthermore, enterprise benefits that used to be transform to increased knowledge value decreases since parts of the enterprise benefits have been published in the external environment through knowledge release process. The original knowledge diffusion model proposed by Kreng and Tsai (2003) constructed the intra-firm diffusion formulae as internal knowledge usage, learning and improvement; however, the model ignores the effect of inter-firm diffusion. Since both intra-firm and inter-firm diffusion occur at the same time, the means to coordinate the various diffusion conditions for expanding the original knowledge diffusion model is the primary objective of this study. The original estimation equations presented by Kreng and Tsai (2003) have also been modified to enhance the accuracy of investigating each parameter, besides investigating the interaction between intra-firm and inter-firm diffusion to figure out the corresponding diffusion formulae. Finally, a case study is also used to illustrate the feasibility of the proposed model, in which the results are demonstrated for better performance while comparing them with the original knowledge diffusion model of Kreng and Tsai (2003). 2. The original knowledge diffusion model of single knowledge Real knowledge value can be evaluated from enterprise benefits through the ABC model (Dekker & de Hoog, 2000; Wilkins et al., 1997). In order to identify the dynamic relationship between knowledge value and enterprise benefits in a given period, Kreng and Tsai (2003) combined the ABC model with the Bass diffusion model (Bass, 1969) to present the knowledge diffusion process shown in Fig. 1. At a given time t, the knowledge value, K*(t), is equal to K(t) + K 0 (t) where K(t) is the original knowledge value and K 0 (t) is the incremental knowledge value stemming from the investment in knowledge improvement. The K*(t) is Enterprise benefits X(t)
Knowledge value K(t)
Knowledge Investment I(t)
Knowledge value K*(t)
Added value V(t+1)
Knowledge Externalization
Knowledge Internalization
Increased benefits S(t+1) || Enterprise benefits X(t+1)
|| Knowledge value K(t+1) Fig. 1. The original knowledge diffusion process (Kreng & Tsai, 2003).
C.M. Tsai / Expert Systems with Applications 34 (2008) 1423–1433
transformed to increased benefits, S(t + 1), through the knowledge externalization, and then the total enterprise benefits at the next time, X(t + 1), are equal to X(t) + S(t + 1) where X(t) is the original enterprise benefits. After knowledge internalization at the next time, the total knowledge value, K(t + 1), is equal to K*(t) + V(t + 1) where V(t + 1) is the contributions externalized from X(t + 1). Since the diffusion process is a continuous cycle, X(t + 1) and K(t + 1) will take the place of X(t) and K(t), respectively, and then begin to evolve into X(t + 2) and K(t + 2) by the same mechanism. Kreng and Tsai (2003) concluded that the increased benefits are the existence of bell-shaped curves under the diffusion cycle. In the beginning, the increased benefits have moderate initial growth due to the continuous use of knowledge and sustained knowledge investment. After a period of time, the growth rate will decelerate because of the law of diminishing returns. Then, the increased benefits will start to decrease while the peak of the bell-shaped curves is reached. Finally, the enterprise benefits cannot be enhanced anymore since the saturation level of externalization has been reached. Since the V(t + 1) is affected by enterprise benefits, the changes of V(t + 1) are similar to a bell-shaped curve as well. Kreng and Tsai (2003) present three different diffusion patterns to reveal the dynamic diffusion processes. An illustrative case is used to figure out the related parameters embedded in the knowledge diffusion model through the diffusion equations. Since the original knowledge diffusion model only investigates intra-firm diffusion, the original model has to be expanded so that intra-firm and inter-firm diffusion can be considered at the same time. In fact, external knowledge is often introduced as additive knowledge so as to expand existing knowledge value (Argote, McEvily, & Reagans, 2003; Hall & Andriani, 2002). Accordingly, the total enterprise benefits increased will be externalized from the following three sources: (1) the use of existing knowledge inside the enterprise; (2) the increment of existing knowledge due to knowledge improvement driven by the investment; and (3) the adoption of external knowledge (i.e. additive knowledge) from other companies or research institutes. Since parts of the total enterprise benefits have been released to the external environment due to inter-firm diffusion, the rest are transformed into increased knowledge value by knowledge internalization. These intra-firm and inter-firm diffusion patterns are discussed in the next section. In addition, the estimating equations developed by Kreng and Tsai (2003) are also modified in this study to improve the performance of the knowledge diffusion model. 3. The knowledge diffusion model with intra-firm and inter-firm diffusion A complete knowledge management system should include various sub-systems such as internalization, externalization, acquisition, learning, dissemination, storage,
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innovation, improvement, management, etc. (Argote et al., 2003; Birchall & Tovstiga, 2002; Caloghirou, Kastelli, & Tsakanikas, 2004; Chait, 1998; Carlile & Rebentisch, 2003; Choi & Lee, 2002; Hall & Andriani, 2002; Holsapple & Singh, 2001; Korot & Tovstiga, 1998; Kreng & Tsai, 2003; Malone, 2002; Michael, 1999; Nonaka, Toyama, & Konno, 2000; Satyadas et al., 2001). If a vague interaction can be quantified by specific formulae successfully, an enterprise can, therefore, understand the relationship between knowledge value and enterprise benefits and further develop appropriate knowledge management strategies. The original knowledge diffusion model only emphasizes the effect of intra-firm diffusion which implies that all knowledge management processes are manipulated within the enterprise (Kreng & Tsai, 2003). Under an open system where the knowledge can flow between the internal organization and the external environment without obstruction, inter-firm knowledge diffusion, including knowledge acquisition and knowledge release, should be integrated into the original knowledge diffusion model. External knowledge can be adopted via knowledge acquisition activities referred to in the knowledge chain model (Holsapple & Singh, 2001). Hall and Andriani (2002) present that introducing external knowledge is important to bridge the knowledge gaps which result from the differences between the existing knowledge framework and future knowledge requirements. Furthermore, knowledge is often released from the internal organization into the external environment via dissemination (Satyadas et al., 2001). Accordingly, the external environment can be regarded as a huge repository which acts as an interface among numerous enterprises for external knowledge acquisition and internal knowledge release. Under the interactive processes of intra-firm and interfirm knowledge diffusion shown in Fig. 2, the existing knowledge value at time t, K*(t), is increased by the incremental value generated from the external knowledge acquisition, K00 (t), besides K(t) and K 0 (t) processed inside the organization originally. After knowledge externalization of K(t), K 0 (t) and K00 (t), respectively, the total enterprise benefits at time t + 1, X(t + 1), can be expressed as X ðt þ 1Þ ¼ X ðtÞ þ S ðt þ 1Þ
ð1Þ
where S ðt þ 1Þ ¼ Sðt þ 1Þ þ S 0 ðt þ 1Þ þ S 00 ðt þ 1Þ S*(t + 1) is the total increased enterprise benefits at time t+1 S(t + 1) is the increased enterprise benefits externalized by K(t) at time t + 1 S 0 (t + 1) is the increased enterprise benefits externalized by K 0 (t) at time t + 1 S00 (t + 1) is the increased enterprise benefits externalized by K00 (t) at time t + 1 If the knowledge release effect (inter-firm diffusion) is considered as well, parts of the enterprise benefits will be
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External Environment
External Knowledge Repository
Knowledge Acquisition
Knowledge Release
Inter-firm Diffusion Intra-firm Diffusion
Knowledge value K(t)
Knowledge Investment I(t)
Enterprise benefits X(t)
Existing Knowledge value K*(t)a
Knowledge Externalization
Increased benefits S*(t+1) b
Knowledge Internalization Added value V(t+1)
Enterprise benefits X(t+1)c
Knowledge value K(t+1)d
Knowledge Accumulation
Fig. 2. The processes of intra-firm and inter-firm knowledge diffusion. aThe existing knowledge value K*(t) = K(t) + K 0 (t) + K00 (t). If t = 0, K*(0) will be equal to V(0). bThe increased benefits S*(t + 1) = S(t + 1) + S 0 (t + 1) + S00 (t + 1). cThe total enterprise benefits at time t + 1,X(t + 1) = X(t) + S*(t + 1). If t = 0, X(0) will be equal to S*(0). dThe knowledge value at time t + 1, K(t + 1) = K*(t) + V(t + 1). Since the diffusion processes are cyclic, the X(t + 1) and K(t + 1) will take the place of X(t) and K(t), respectively, and then start to evolve the X(t + 2) and K(t + 2) by the same mechanism.
kept in the internal organization and the rest will be released to the external environment. Subsequently, the total increased transformed value, V*(t + 1), stemming from enterprise benefits, X(t + 1), is converted into added knowledge value, V(t + 1), and the released value, L(t + 1). The V(t + 1) is accumulated to the increment of knowledge value, K(t + 1), and the L(t + 1) is transformed into a supplement to external knowledge value. The relationship is V ðt þ 1Þ ¼ V ðt þ 1Þ þ Lðt þ 1Þ
ð2Þ
where V(t + 1) is internalized from X(t + 1) by knowledge internalization at time t + 1 L(t + 1) is released from X(t + 1) by knowledge release at time t + 1. Teng, Grover, and Gu¨ttler (2002) present four fundamental diffusion models: (1) external influence model; (2) internal influence model; (3) Gompertz function; and (4) Bass model. All of these models are based on a common hypothesis: the rate of diffusion is proportional to the number of potential adopters at a given time. In the case of the application of the diffusion model, Kreng and Tsai (2003) are the forerunners of adopting the diffusion model to develop the original knowledge diffusion model for dynamic knowledge value evaluation. The purpose of this study is not only to revise the imperfections in the original knowledge diffusion model, but also to apply the original knowl-
edge diffusion model to an open system where the intra-firm and inter-firm diffusion are integrated simultaneously. In order to formulate the knowledge diffusion model, the patterns used for illustrating the diffusion processes and all involved parameters should be redefined and represented. In addition to the references to Bass (1969), Teng et al. (2002), and Kreng and Tsai (2003), these patterns have also been demonstrated by related experts who have specialized in knowledge management for at least two years. Assuming that p(t), p 0 (t), and p00 (t) are the likelihood of increased enterprise benefits externalized by using K(t), K 0 (t), and K00 (t), respectively; q(t) is the likelihood of the added knowledge value internalized by the enterprise benefits which have not yet been transformed back to knowledge; and r(t) is the likelihood of the released value transformed from the generated enterprise benefits which has been released to the external environment. Since parts of the enterprise benefits have been released to the external environment, the enterprise benefits kept in the organization are reduced, which implies that the added knowledge value internalized by the enterprise benefits is also decreased. f ðtÞ ¼ a þ bF ðtÞ F ðtÞ f 0 ðtÞ p0 ðtÞ ¼ ¼ cF 0 ðtÞ þ d 1 F 0 ðtÞ f 00 ðtÞ ¼ eF 00 ðtÞ p00 ðtÞ ¼ 1 F 00 ðtÞ
pðtÞ ¼
ð3Þ ð4Þ ð5Þ
C.M. Tsai / Expert Systems with Applications 34 (2008) 1423–1433
qðtÞ ¼
fb ðtÞ ¼ fF b ðtÞ þ g 1 F b ðtÞ
ð6Þ
rðtÞ ¼
fr ðtÞ ¼ h iF r ðtÞ F r ðtÞ
ð7Þ
where f(t) is the likelihood of the increased enterprise benefits contributed by the original knowledge K(t) at time t F(t) is the likelihood of the total increased enterprise benefits contributed by the original knowledge K(t) during the (0, t) interval f 0 (t) is the likelihood of the increased enterprise benefits contributed by the improved knowledge K 0 (t) via investment at time t F 0 (t) is the likelihood of the total increased enterprise benefits contributed by the improved knowledge K 0 (t) via investment during the (0, t) interval f00 (t) is the likelihood of the increased enterprise benefits contributed by the acquired external knowledge K00 (t) at time t F00 (t) is the likelihood of the total increased enterprise benefits contributed by the acquired external knowledge K00 (t) during the (0, t) interval fb(t) is the likelihood of the added value of knowledge K internalized by enterprise benefits at time t Fb(t) is the likelihood of the total added value of knowledge K internalized by enterprise benefits during the (0, t) interval fr(t) is the likelihood of the released value transformed from internal organization to external environment at time t Fr(t) is the likelihood of the total released value transformed from internal organization to external environment during the (0, t) interval parameter ‘‘a’’ represents the externalization effect on enterprise benefits contributed by continuous usage of original knowledge parameter ‘‘b’’ represents the knowledge appreciation/ depreciation effect parameter ‘‘c’’ represents the externalization effect on enterprise benefits contributed by the knowledge improvement due to continuous investment parameter ‘‘d’’ represents the improvement effect on enterprise benefits generated by the knowledge improvement due to continuous investment parameter ‘‘e’’ represents the acquisition effect on enterprise benefits generated by adopting new external knowledge parameter ‘‘f’’ represents the internalization effect on knowledge value internalized from enterprise benefits parameter ‘‘g’’ represents the knowledge learning effect parameter ‘‘h’’ represents the organizational knowledge release effect parameter ‘‘i’’ represents the organizational knowledge retaining effect
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In Eq. (3), the enterprise benefits externalized by using original knowledge are generated by the subjected enterprise benefits which have been accumulated. The enterprise benefits externalized by using improved knowledge and by using external knowledge shown in Eqs. (4) and (5), respectively, are generated through the subjected enterprise benefits which have not yet been accumulated. Eq. (6) indicates that the added knowledge value internalized by enterprise benefits is also generated through the subjected added value which has not yet been accumulated. In Eq. (7), the released value derived from the knowledge release process is generated by the subjected released value which has been accumulated. The formulae p(t), p 0 (t), and q(t) which are the representations of conducting intra-firm diffusion are analogous to the study of Kreng and Tsai (2003). Compared with the study of Kreng and Tsai (2003), the definitions of the involved parameters ‘‘c’’, ‘‘d’’, ‘‘f’’, and ‘‘g’’ are the same except for the parameters ‘‘a’’ and ‘‘b’’. Since the externalized enterprise benefits are contributed by the usage of original knowledge, the externalization effect shown as the parameter ‘‘a’’ is constant when other conditions are unchanged. In addition, the organizational capability of using knowledge (Caloghirou et al., 2004; McNamara, Baxter, & Chua, 2004), the imitation of other companies (Kreng & Tsai, 2003), and the obsolescence of original knowledge (Wilkins et al., 1997) can also result in the knowledge appreciation/depreciation effect on the enterprise benefits externalization which is shown as the parameter ‘‘b’’. The formulae p00 (t) and r(t) with the three involved parameters ‘‘e’’, ‘‘h’’, and ‘‘i’’ are the new diffusion patterns used to represent the inter-firm diffusion. The acquisition effect shown as the parameter ‘‘e’’ is the organizational capability for adopting external knowledge. The more appropriate external knowledge sources are obtained, the more enterprise benefits will be externalized. Since the external environment has been considered as a huge knowledge repository, the organizational knowledge release effect shown as the parameter ‘‘h’’ indicates that parts of the enterprise benefits are transformed into the released value and then released to the external environment; however, the released value is reduced by the organizational capability of retaining the knowledge inside which is defined as the organizational knowledge retaining effect shown as the parameter ‘‘i’’. Holsapple and Joshi (2001) and Malone (2002) consider that the organization is the aggregation of all kinds of knowledge. The organizational performance often depends on the organizational capability of using internal knowledge and of acquiring external knowledge (Caloghirou et al., 2004). Since organizational capability can be accumulated during continuous knowledge management processes, an organization should possess the abilities to use the internal and to acquire external knowledge initially which are assumed to be m1 and m2, respectively, i.e. F(0) = m1 and F00 (0) = m2. The initial accumulation of improving knowledge, the initial accumulation of knowledge value internalized by enterprise benefits, and the ini-
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tial accumulation of released value transformed from enterprise benefits to the external environment are equal to 0 because knowledge investment, knowledge internalization and knowledge release are not driven until diffusion begins, i.e. F 0 (0) = 0, Fx(0) = 0, and Fb(0) = 0. Accordingly, the equations are obtained as: a F ðtÞ ¼ ð8Þ b b þ ma1 expat dF ðtÞ a eat 2 ¼a bþ ð9Þ f ðtÞ ¼ h i2 dt m1 b ðb þ ma1 Þexpat F 0 ðtÞ ¼
1 expðcþdÞt 1 þ dc expðcþdÞt
f 0 ðtÞ ¼
dF 0 ðtÞ ðc þ dÞ2 expðcþdÞt ¼ 2 dt d 1 þ c expðcþdÞt
ð10Þ ð11Þ
d
F 00 ðtÞ ¼
1
1 expet dF 00 ðtÞ 1 ¼e 1 h f 00 ðtÞ ¼ dt m2 1þ
ð12Þ
1 m2
expet i2 ð13Þ 1 þ m12 1 expet
F b ðtÞ ¼
1 expðf þgÞt 1 þ fg expðf þgÞt
ð14Þ
fb ðtÞ ¼
dF b ðtÞ ðf þ gÞ2 expðf þgÞt ¼ h i2 dt g 1 þ fg expðf þgÞt
ð15Þ
h i ði hÞexpht dF r ðtÞ expht ¼ h2 ði hÞ fr ðtÞ ¼ dt ½i ði hÞexpht 2 F r ðtÞ ¼
ð16Þ ð17Þ
In order to estimate the parameters involved in the model precisely, the estimating equations should be considered individually to investigate the related parameters directly because all data have been separated by the ABC model in advance. According to Fig. 2 and Eqs. (3)–(7), the estimating equations can be obtained as: SðtÞ ¼ K max f ðtÞ ¼ a Y s ðtÞ þ 0
c
0
S ðtÞ ¼ I max f ðtÞ ¼
I max
b K max
Y 2s0 ðtÞ
Y 2s ðtÞ
ð18Þ
e Y 2s00 ðtÞ þ e Y s00 ðtÞ ð20Þ Emax f V ðtÞ ¼ Bmax fb ðtÞ ¼ Y 2v ðtÞ þ ðf gÞ Y v ðtÞ þ g Bmax Bmax S 00 ðtÞ ¼ Emax f 00 ðtÞ ¼
ð21Þ LðtÞ ¼ Rmax fr ðtÞ ¼
Rmax
The maximum of enterprise benefits, Xmax, is equal to the sum of Bmax and Rmax. Compared to the original knowledge diffusion model presented by Kreng and Tsai (2003), the added value should be internalized by Bmax instead of Xmax because Rmax is released to the external environment and only Bmax is kept in the organization. When both intra-firm and inter-firm knowledge diffusions are considered simultaneously, Eqs. (18), (19), and (21) which exhibit intra-firm knowledge diffusion are similar to the presentation of Kreng and Tsai (2003), and the inter-firm knowledge diffusion is presented by Eqs. (20) b i and (22). Since only K max and Rmax can be obtained while estimating parameters, the equations which indicate the relationship between intra-firm and inter-firm knowledge diffusion are developed so that all of the parameters in the model can be estimated plausibly. K max ¼ K ð0Þ þ
Z
1
V ðtÞdt ¼ K ð0Þ þ Bmax 0
X max ¼ Bmax þ Rmax ¼ X ð0Þ þ
Z
ð23Þ
1
SðtÞdt ¼ X ð0Þ þ K max þ I max þ Emax
0
ð24Þ
þ ðc dÞ Y s0 ðtÞ þ d I max
ð19Þ
i
Emax is the maximum of external knowledge acquisition value Bmax is the maximum of enterprise benefits kept in the internal organization Rmax is the maximum of enterprise benefits released to the external environment Ys(t) is the total increased enterprise benefits externalRt ized by S(t) during the (0, t) interval, i.e. Y s ðtÞ ¼ 0 SðtÞ Y s0 ðtÞ is the total increased enterprise benefits externalRt ized by S 0 (t) during the (0, t) interval, i.e. Y s0 ðtÞ ¼ 0 S 0 ðtÞ Y s00 ðtÞ is the total increased enterprise benefits externalized byR S00 (t) during the (0, t) interval, i.e. t Y s00 ðtÞ ¼ 0 S 00 ðtÞ Yv(t) is the total added value of knowledge K internalized by Renterprise benefits during the (0, t) interval, i.e. t Y v ðtÞ ¼ 0 V ðtÞ YL(t) is the total value released form internal organization to external R t environment during the (0, t) interval, i.e. Y L ðtÞ ¼ 0 LðtÞ
Y 2L ðtÞ þ h Y L ðtÞ
ð22Þ
where Kmax is the maximum of knowledge value Imax is the maximum of internal knowledge improvement value
In Eq. (23), the knowledge value is internalized from the amount of the enterprise benefits kept in the internal organization. Eq. (24) implies that the total enterprise benefits are externalized from the three knowledge sources including original knowledge, improved knowledge, and external acquired knowledge which have been integrated by organization beforehand. When only intra-firm diffusion is considered in knowledge diffusion, the Bmax and Rmax disappear, and then the diffusion model is degenerated to the original model proposed by Kreng and Tsai (2003). In the next section, a real case study which is the same as the study done by Kreng and Tsai (2003) is used to demonstrate the feasibility of the proposed model. The results are also compared with the conclusions of
C.M. Tsai / Expert Systems with Applications 34 (2008) 1423–1433
Kreng and Tsai (2003) so that the difference between the original diffusion model and the new diffusion model can be highlighted. 4. Model demonstration The Uni-President Enterprise Corporation (UPEC) established in 1967 is the largest food company in Taiwan in recent years. Using the strategies of high quality and customer satisfaction, the UPEC has implemented a QCC (Quality Control Circle) system for more than twenty years. The QCC system has created more than 500 million NT dollars for UPEC. In order to compare the conclusions presented by Kreng and Tsai (2003), this study uses the same case to identify the relationship between knowledge value and enterprise benefits under inter-firm and interfirm knowledge diffusion. According to the original data from 1980 to 1991 presented by Kreng and Tsai (2003), the relevant data are re-identified and shown in Table 1 where S*(t) and V*(t) are the total increased enterprise benefits externalized by all knowledge sources and the total increased transformed value converted from the enterprise benefits, respectively. The basic model is shown in Eqs. (18)–(22). In estimating all involved parameters from these discrete time series data, the following analogue can be used (Bass, 1969; Kreng & Tsai, 2003): SðtÞ ¼ a Y s ðt 1Þ þ b Y 2s ðt 1Þ
ð25Þ
S 0 ðtÞ ¼ d Y 2s0 ðt 1Þ þ k Y s0 ðt 1Þ þ q
ð26Þ
S 00 ðtÞ ¼ p Y 2s00 ðt 1Þ þ u Y s00 ðtÞ
ð27Þ
V ðtÞ ¼ g Y 2v ðt 1Þ þ l Y v ðt 1Þ þ h
ð28Þ
LðtÞ ¼ f Y 2L ðt 1Þ þ t Y L ðt 1Þ
ð29Þ
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and Tsai (2003) where S*(t) and V*(t) are used to investigate all involved parameters, a new estimating method which uses Eqs. (25)–(29) to estimate the corresponding parameters is presented here. The adjusted R2 value and the p value of the original estimating method are unacceptable, whereas the adjusted R2 value and the p value of the new estimating method show substantial improvement. Therefore, the rationality and preciseness of the new estimating method are, indeed, better than the original one. According to the regression results of the new estimating method, the predicted/actual values of S*(t) and V*(t) are shown in Figs. 3 and 4, respectively, where the predicted value of S*(t) is equal to the sum of the predicted values of S(t), S 0 (t), and S00 (t) and the predicted value of V*(t) is equal to the sum of the predicted values of V(t) and L(t). Kreng and Tsai (2003) consider that the proposed model should be adopted to predict future changes of knowledge value and enterprise benefits so as to develop appropriate knowledge management strategies. In the prediction process, the bias, e, which can be estimated by the formula f ðtÞ 1 ¼ F ðtþ1ÞF for any probability distribution, should be e ðtÞ added to the prediction equations (Bass, 1969). As a result, the prediction equations, S(t), S 0 (t), S00 (t), V(t) and, L(t), are reconstructed as the following analogue after including the biases e1 to e5. SðtÞ ¼ a0 Y s ðt 1Þ þ b0 Y 2s ðt 1Þ 0
S ðtÞ ¼ d Y 2s0 ðt 1Þ þ k0 Y s0 ðt 1Þ þ q S 00 ðtÞ ¼ p0 Y 2s00 ðt 1Þ þ u0 Y s00 ðt 1Þ V ðtÞ ¼ g0 Y 2v ðt 1Þ þ l0 Y v ðt 1Þ þ h LðtÞ ¼ f0 Y 2L ðt 1Þ þ t0 Y L ðt 1Þ 0
ð30Þ ð31Þ ð32Þ ð33Þ ð34Þ
where
where a ¼ a; b ¼ g¼
b K max
;d ¼
c I max
; k ¼ ðc dÞ; q ¼ d I max ; p ¼
e Emax
; u ¼ e;
f i ; l ¼ ðf gÞ; h ¼ g Bmax ; f ¼ ;t ¼ h Bmax Rmax
a0 ¼ a0 ¼ a e1 ; b0 ¼ d0 ¼
The regression results are listed in Table 2. Compared with the original estimating method presented by Kreng
p0 ¼
c0 I 0max 0
e E0max
b0 b ¼ e21 ; K 0max K max
c
e22 ; k0 ¼ ðc0 d 0 Þ ¼ ðc dÞ e2 ; I max e ¼ e23 ; u0 ¼ e0 ¼ e e3 ; Emax
¼
Table 1 The re-identified data from 1980 to 1991 in UPEC (unit: million NT dollars) Time 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991
(t = 0) (t = 1) (t = 2) (t = 3) (t = 4) (t = 5) (t = 6) (t = 7) (t = 8) (t = 9) (t = 10) (t = ll)
S*(t)
S(t)
S 0 (t)
S00 (t)
V*(t)
V(t)
L(t)
21 22.18 14.04 23.28 23.28 27.6 33.68 26.46 17.55 17.737 24.426 16.887
6.268 6.661 6.12 9.596 10.608 14.147 21.45 17.114 12.295 11.5596 20.7621 15.1983
1.05 2.218 2.106 4.656 5.82 8.28 8.42 6.615 3.51 3.5474 3.6639 1.6887
13.682 13.301 5.814 9.028 6.852 5.173 3.81 2.731 1.745 2.63 0 0
5.25 6.654 4.914 9.312 11.64 16.56 25.26 21.6972 15.444 16.31804 23.44896 16.71813
4.16 3.284 3.858 6.57 10.34 12.53 13.22 14.69 14.347 13.142 17.4581 14.325
1.09 3.37 1.056 2.742 1.3 4.03 12.04 7.0072 1.097 3.17604 5.99086 2.39313
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Table 2 The regression results of the knowledge diffusion model New method
Adjusted R2
Estimates
Std. Err.
p value
Parameters
S(t)
0.9101
a = 0.4264 b = 0.0025
0.0657 0.0006
0.0001 0.0027
S 0 (t)
0.7957
S00 (t)
0.7879
V(t)
0.8507
L(t)
0.6360
d = 0.0103 k = 0.4944 q = 1.7790 p = 0.0086 u ¼ 0:5511 g = 0.0020 l = 0.3161 h = 3.1929 n = 0.0137 t = 0.6106
0.0016 0.0828 0.7577 0.001 0.0938 0.0005 0.0590 1.2487 0.0047 0.1677
0.0002 0.0003 0.0468 0.0005 0.0002 0.0054 0.0007 0.0338 0.0175 0.0054
Kmax = 175.7137a a = 0.4264 b = 0.4393a Imax = 5 1.6063 c = 0.5289 d = 0.0345 Emax = 64.0814 e = 0.5511 Bmax = 171.5537 f = 0.3347 g = 0.0186 Rmax = 140.8477b i = 1.9296b h = 0.6106
Original method S*(t)
0.4290
V*(t)
0.8129
a = 0.9608 b = 0.0042 d = 0.0224 k = 0.0187 q = 43.7036 p = 0.0470 u ¼ 1:7998 g = 0.0008 l = 0.6577 h = 1.9167 n = 0.0302 t = 0.1331
2.4002 0.0074 0.0320 3.9526 14.8457 0.0276 1.6498 0.0036 0.4520 2.5297 0.0284 1.3241
0.7094 0.5985 0.5222 0.9965 0.0422 0.1641 0.3366 0.8297 0.1959 0.4473 0.3290 0.9232
–c
—c
a
The parameters Kmax and ‘‘b’’ are obtained by Eq. (23) where K*(0) = V(0) = 4.16. The parameters Rmax and ‘‘i’’ are obtained by Eq. (24) where X(0) = S*(0) = 21. c The parameters of S*(t) and V*(t) are not necessary to calculate since the adjusted R2 of original method is smaller than the one of new method and the estimates are not significant. b
S*(t) actual value
V*(t) actual value
S*(t) predictd value
V*(t) predictd value 30 million NT dollars
million NT dollars
40 30 20 10 0
1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 Year Fig. 3. The predicted value and actual value of S*(t).
25 20 15 10 5 0
1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 Year Fig. 4. The predicted value and actual value of V*(t).
f0 f ¼ e24 ; l0 ¼ ðf 0 g0 Þ ¼ ðf gÞ e4 ; B0max Bmax i0 i e25 ; t0 ¼ h0 ¼ h e5 f0 ¼ 0 ¼ Rmax Rmax
1 cþd 1 ¼ ¼ lnðc0 þ d 0 þ 1Þ e2 ðexpðcþdÞ 1Þ c0 þ d 0
ð36Þ
1 e 1 ¼ 0 lnðe0 þ 1Þ ¼ e e3 ðexp 1Þ e
ð37Þ
For small values of t, the biases can be obtained, and then the correct parameters which have been adjusted by biases can be figured out.
1 f þg 1 ¼ ¼ lnðf 0 þ g0 þ 1Þ e4 ðexpðf þgÞ 1Þ f 0 þ g0
ð38Þ
1 a 1 ¼ lnða0 þ 1Þ ¼ e1 ðexpa 1Þ a0
1 h 1 ¼ 0 lnðh0 þ 1Þ ¼ h e5 ðexp 1Þ h
ð39Þ
g0 ¼
ð35Þ
C.M. Tsai / Expert Systems with Applications 34 (2008) 1423–1433
Table 3 The re-identified data from 1997 to 1999 in UPEC (unit: million NT dollars) Time
S*(t)
S(t)
S 0 (t)
S00 (t)
V*(t)
V(t)
L(t)
1997 (t = 0) 1998 (t = 1) 1999 (t = 2)
22.219 26.818 37.830
9.843 10.933 18.612
2.222 4.023 6.758
10.154 11.862 12.46
10.079 17.786 28.240
8.248 14.357 21.36
1.831 3.429 6.88
0
0
a = 1.3042 b 0 = 0.0197
Parameters
Biases
Parameters
a = 1.3042 K ¼ 0:0197 K0
1 e1
¼ 0:6400
I 0max 0
1 e2
¼ 0:7012
1 e3
¼ 0:5863
1 e4
¼ 0:6872
1 e5
¼ 0:3639
a = 0.8347 Kmax = 129.3419a b = 1.0437a Imax = 61.971 c = 0.6368 d = 0.0358 Emax = 56.5303 e = 0.9872 Bmax = 121.0939 f = 0.6405 g = 0.0681 Rmax = 148.9863b i = 3.2490b h = 0.7912
0
max
d = 0.0209 k 0 = 0.8570 q = 2.222 p 0 = 0.0508 - ¼ 1:6837 g 0 = 0.0112 l 0 = 0.8329 h = 8.248 v 0 = 0.1647
¼ 43:452 c = 0.9081 d 0 = 0.0511 E0max ¼ 33:1437 e 0 = 1.6837 B0max ¼ 83:2157 f 0 = 0.9320 g 0 = 0.0991 i0 ¼ 0:1647 R0
m 0 = 2.1743
h 0 = 2.1743
max
S 0 (t)
S00 (t)
V*(t)
2.222
10.154
10.079
8.248
1.831
10.933
4.023
11.862
17.786
14.357
3.429
37.830
18.612
6.758
12.46
28.240
21.36
6.88
41.932
20.358
8.296
13.278
29.579
23.188
6.391
38.743
21.066
10.358
7.319
30.005
22.833
7.172
27.104
14.756
10.946
1.402
22.853
16.925
5.928
15.298
6.071
9.172
0.0550
12.191
8.986
3.205
7.268
1.478
5.789
0.001
4.635
3.540
1.095
3.034
0.270
2.764
0
1.431
1.160
0.271
1.122
0.045
1.077
0
0.41
0.351
0.059
Time
S*(t)
1997 (t = 0) 1998 (t = 1) 1999 (t = 2) 2000 (t = 3) 2001 (t = 4) 2002 (t = 5) 2003 (t = 6) 2004 (t = 7) 2005 (t = 8) 2006 (t = 9)
22.219
9.843
26.818
S(t)
V(t)
L(t)
more resources have been devoted to knowledge improvement. Thus, the reason for the increase of Imax for the period S*(t) V*(t) 50 40 30 20 10 0 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 Year
Fig. 5. The predictions of S*(t) and V*(t) resulting from the prediction model.
Table 4 All parameters of the prediction model Estimates
Table 5 The results of the prediction model (unit: million NT dollars)
million NT dollars
The data used for the prediction are the same as the original data presented by Kreng and Tsai (2003). Since interfirm and intra-firm diffusion are considered simultaneously, these data should also be re-identified. The re-identified data are shown in Table 3. Thus all prediction equations can be established according to the equations from (30) to (35), and the results are shown in Table 4. The maximum enterprise benefits of this period, Xmax, are equal to 270.0622. Since all the parameters appear to be plausible, the predictions of both S*(t) and V*(t) can be obtained in Table 5 and Fig. 5. The parameters of the period from 1980–1991 and of from the period 1997–2006 are shown in Table 6. The situations for conducting knowledge management can be identified by parameter analysis since all parameters involved in the knowledge diffusion model possess managerial implications. For the period 1997–2006, the QCC knowledge has become mature knowledge because the knowledge has been adopted by a great many Taiwanese companies. The Kmax and Xmax of the period 1997–2006 are lower than those of the period 1980–1991 inevitably. The parameter ‘‘a’’ is increased in the period 1997–2006 which implies that the capability for enterprise benefits externalization by using original knowledge has been strengthened; however, the rate of depreciation shown as parameter ‘‘b’’ becomes more rapid. That is, the original knowledge has been less and less valueless because of the knowledge depreciation. In order to put new added value on the QCC knowledge, more and
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a The parameters Kmax and ‘‘b’’ are obtained by Eq. (23) where K*(0) = V(0) = 8.248. b The parameters Rmax and ‘‘i’’ are obtained by Eq. (24) where X(0) = S*(0) = 22.219.
Table 6 The parameters of period 1980–1991 and of period 1997–2006 Period
1980–1991
1997–2006
Increase/Decrease
Kmax a b Imax c d Emax e Bmax f g Rmax h i Xmax
175.7137 0.4264 0.4393 51.6063 0.5289 0.0345 64.0814 0.5511 171.5537 0.3347 0.0186 140.8477 1.9296 0.6106 312.4014
129.3419 0.8347 1.0437 61.971 0.6368 0.0358 56.5303 0.9872 121.0939 0.6405 0.0681 148.9683 0.7912 3.2490 270.0622
Decrease Increase Increase in the absolute value Increase Increase Increase Decrease Increase Decrease Increase Increase Increase Decrease Increase Decrease
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C.M. Tsai / Expert Systems with Applications 34 (2008) 1423–1433
1997–2006 can also be demonstrated. The parameters ‘‘c’’ and ‘‘d’’ have increased in the period 1997–2006 which demonstrates that the efficiency of making enterprise benefits from improved knowledge has also been enhanced. The results can be interpreted as being due to the capability of the related staff has been strengthened. At the present time, UPEC is promoting a new quality system so as to maintain profitability and to remain competitiveness in the future. In addition, the Emax of the period 1997-2006 has decreased, which means that the dependence on external knowledge resource has been reduced since knowledge can be developed more effectively within the internal organization. Even so, the parameter ‘‘e’’ is showing increase in this period because the external knowledge can be integrated into the existing knowledge system more successfully, and then more enterprise benefits can also be generated. The manager considers the new QCC knowledge acquired from the cooperative Japanese company after 1996 to be quite novel. Much included know-how seems to be unfamiliar in the beginning; however, the execution and adopting of new knowledge has been achieved in the end due to the extensive experience the staff has accumulated. Under an open knowledge system of the period 1997–2006, the decrease of Bmax with the increase of Rmax is a necessary result since the release process is processed much more frequently than before. The parameters ‘‘f’’ and ‘‘g’’ of the period 1997–2006 have increased, which implies that the knowledge value is internalized from enterprise benefits more successfully, i.e. the capabilities of absorbing and of learning knowledge have been enhanced. Finally, the knowledge release effect from the internal organization to the external environment is decreased, whereas the knowledge retaining effect is enhanced for the period 1997–2006. The presentation of the parameters ‘‘h’’ and ‘‘i’’ means that the knowledge management system is executed fairly successfully since more and more knowledge is kept inside the organization. Many Taiwanese companies often promote technical exchange or cooperation to transfer new knowledge or technologies from other overseas companies. Therefore, the proposed knowledge diffusion model integrating intra-firm and inter-firm diffusion is much more appropriate to describe the relationship between knowledge value and its corresponding enterprise benefits. Moreover, the performance of executing the knowledge management system is also investigated by the parameter analysis so that effective knowledge management strategies are developed in advance.
5. Conclusion Implementing the knowledge management system for competitive success has been an increasingly vital issue for enterprises recently. The performance of knowledge management can be investigated only by realizing the relationship between knowledge value and enterprise benefits. Since knowledge management is conducted in an open
system, both intra-firm diffusion, and inter-firm diffusion processes exist between the interaction of the internal organization and the external environment simultaneously. In addition to the patterns including knowledge internalization, externalization, improvement, and learning presented by Kreng and Tsai (2003), the knowledge acquisition and knowledge release are also integrated into the new knowledge diffusion model. The new estimating method is more appropriate than the original one presented by Kreng and Tsai (2003) for investigating all involved parameters, since the adjusted R2 values of all estimating equations have improved. Accordingly, the feasibility of the new knowledge diffusion model is demonstrated as well. The performance of executing knowledge management in different periods can be traced by further parameters analysis. Since the inference provided by parameters analysis has been successfully connected with actual situations after confirming with the related managers, effective knowledge strategies can be identified to enhance the competitiveness of an enterprise, and as a result, a successful knowledge management system can also be facilitated. The knowledge diffusion model is a novelty; however, this model still provides some insights into the problem. In addition to revising and expanding the model continuously, further discussion on knowledge substitutive or complementary effects is another theme for future study. References Argote, L., McEvily, B., & Reagans, R. (2003). Managing knowledge in organizations: an integrative framework and review of emerging themes. Management Science, 49(4), 571–582. Bass, F. M. (1969). A new product growth for model consumer durables. Management Science, 15(5), 215–227. Bassi, L. J., & Van Buren, M. E. (1999). Valuing investment in intellectual capital. International Journal of Technology Management, 18(5), 414–432. Birchall, D. W., & Tovstiga, G. (2002). Assessing the firm’s strategic knowledge portfolio: a framework and methodology. International Journal of Technology Management, 24(4), 419–434. Caloghirou, Y., Kastelli, I., & Tsakanikas, A. (2004). Internal capabilities and external knowledge sources: complements or substitutes for innovative performance? Technovation, 24, 29–39. Chait, L. (1998). Creating a successful knowledge management system. Prism(Second Quarter Issue), 83. Carlile, P. R., & Rebentisch, E. S. (2003). Into the black box: the knowledge transformation cycle. Management Science, 49(9), 1180–1195. Choi, B., & Lee, H. (2002). Knowledge management strategy and its link to knowledge creation process. Expert Systems with Applications, 23(3), 173–187. Dekker, R., & de Hoog, R. (2000). The monetary value of knowledge assets: a micro approach. Expert Systems with Applications, 18(2), 111–124. Hall, R., & Andriani, P. (2002). Managing knowledge for innovation. Long Range Planning, 35, 29–48. Holsapple, C. W., & Joshi, K. D. (2001). Organizational knowledge resources. Decision Support Systems, 33, 39–54. Holsapple, C. W., & Singh, M. (2001). The knowledge chain model: activities for competitiveness. Expert Systems with Applications, 20(1), 77–98.
C.M. Tsai / Expert Systems with Applications 34 (2008) 1423–1433 Korot, L., & Tovstiga, G. (1998). Profiling the 21st century knowledgebased organization. In Conference on globalization and emerging business: Strategies for the 21st century, McGill University, Montreal, Canada, 26–28 September. Kreng, V. B., & Tsai, C. M. (2003). The construct and application of knowledge diffusion model. Expert Systems with Applications, 25(2), 177–186. Malone, D. (2002). Knowledge management a model for organizational learning. International Journal of Accounting Information System, 3, 111–123. McNamara, C., Baxter, J., & Chua, W. F. (2004). Making and managing organizational knowledge(s). Management Accounting Research, 15, 56–76. Michael, H. Z. (1999). Developing a knowledge strategy. California Management Review, 41(3), 125–145.
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Nonaka, I., Toyama, R., & Konno, N. (2000). SECI, Ba and leadership: a unified model of dynamic knowledge creation. Long Range Planning, 33(1), 5–34. Satyadas, A., Harigopal, U., & Cassaigne, N. P. (2001). Knowledge management tutorial: an editorial overview. IEEE Transactions on Systems, Man, and Cybernetics – Part C: Applications and Reviews, 31(4), 429–437. Teng, J. T. C., Grover, V., & Gu¨ttler, W. (2002). Information technology innovations: general diffusion patterns and its relationships to innovation characteristics. IEEE Transactions on Engineering Management, 49(1), 13–27. Wilkins, J., van Wegen, B., & de Hoog, R. (1997). Understanding and valuing knowledge assets: overview and method. Expert Systems with Applications, 13(1), 55–72.
Expert Systems with Applications Expert Systems with Applications 34 (2008) 1423–1433 www.elsevier.com/locate/eswa
Integrating intra-firm and inter-firm knowledge diffusion into the knowledge diffusion model Chih Ming Tsai Department of Marketing and Distribution Management, Tung-Fang Institute of Technology, No. 110, Dongfang Rd., Hunei Township, Kaohsiung County 82941, Taiwan, R.O.C.
Abstract Knowledge value and enterprise benefits are closely related. The performance of a knowledge management system can be evaluated when the dynamic relationship between knowledge value and its corresponding enterprise benefits is identified quantitatively. This study introduces five kinds of knowledge diffusion patterns, including knowledge internalization, knowledge externalization, knowledge improvement, external knowledge acquisition, and internal knowledge release, to construct the knowledge diffusion model which integrates the intra-firm and inter-firm diffusion processes simultaneously. An illustrative case demonstrates the feasibility of the proposed model successfully. In addition to the estimation of all parameters involved in the model, the parameter analysis provides some managerial insights into the implementation of the knowledge management system. Therefore, it follows that knowledge can be managed more effectively, and as a result the appropriate knowledge strategies can also be established for enhancing competitiveness. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Knowledge diffusion model; Intra-firm knowledge diffusion; Inter-firm knowledge diffusion; Knowledge value; Enterprise benefits
1. Introduction Knowledge value and its corresponding enterprise benefits are considered to be closely related (Bassi & Van Buren, 1999; Kreng & Tsai, 2003; Wilkins, van Wegen, & de Hoog, 1997). In order to discuss the dynamic relationship between knowledge value and enterprise benefits, Kreng and Tsai (2003) proposed the original knowledge diffusion model to help managers understand the performance of a knowledge management system and develop a set of knowledge management strategies. The concept of the original knowledge diffusion model, which is based on the Bass diffusion model (Bass, 1969) and the Activity Based Costing (ABC) model (Dekker & de Hoog, 2000; Wilkins et al., 1997), is that knowledge value can be transformed into increasing enterprise benefits through knowledge externalization, and then the existing enterprise benefits can also be transformed back into the increase of knowledge value through knowledge
E-mail address: [email protected] 0957-4174/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2007.01.027
internalization. Numerous related parameters involved in the original knowledge diffusion model also reveal the different knowledge characteristics for demonstrating the feasibility and rationality. Accordingly, not only can the performance of knowledge management system be traced, but the knowledge management strategies can also be amplified by analyzing these related parameters. Knowledge management should be implemented in the open system where the internal organization can be interacted with the external environment. Based on the knowledge transformation cycle (Carlile & Rebentisch, 2003), the knowledge storage stage, which is the first stage of the cycle, serves as a source of knowledge retrieval and usage. After the transformation stage, the used knowledge is accumulated in the repository for the retrieval and usage in the next cycle. Under this circulation of knowledge storage, retrieval, and transformation, the internal and external knowledge diffusion should be involved simultaneously to implement this cycle. The knowledge management life cycle also includes four stages: create, capture, organize, and disseminate/share (Satyadas, Harigopal, & Cassaigne, 2001).
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Knowledge that is created, captured, and organized is ready for publishing to internal and external users. According to the knowledge chain model (Holsapple & Singh, 2001), the five primary and four secondary knowledge management activities involved in the knowledge chain model result in organizational learning and projection. Organizational learning is regarded as the process of knowledge diffusion occurring in the internal organization and projection is regarded as the process of knowledge diffusion interacting with the external environment. The knowledge chain model starts knowledge acquisition, which is the process of identifying the appropriate external knowledge and then transforming the captured knowledge into usable representations for subsequent use within the organization. After knowledge selection, generation, and internalization, existing knowledge is transformed into organizational outputs eventually for release into the environment by knowledge externalization. Since a successful knowledge management system has to be implemented in the internal organization and external environment simultaneously, intra-firm and inter-firm knowledge diffusion are presented here to exhibit the internal and external knowledge diffusion executed in the open environment, respectively. Intra-firm knowledge diffusion is defined as the processes that show how knowledge interacts with the internal organization, and the inter-firm knowledge diffusion is defined as the processes that reveal how knowledge interacts with the external environment. Under the intrafirm knowledge diffusion model, the sources of knowledge are existing internal knowledge retrieval and internal knowledge improvement due to continuous investment. The total knowledge value is summed up by the above knowledge sources and transformed into increased enterprise benefits through knowledge externalization activities. Then, the enterprise benefits are accumulated continuously and transformed back into increased knowledge value through knowledge internalization activities. Compared to intra-firm knowledge diffusion, inter-firm knowledge diffusion involves external knowledge resources acquisition and the release of enterprise benefits that are published to
the external environment. Accordingly, the total knowledge value used to transform into increased enterprise benefits increases because of external knowledge resources acquisition. Furthermore, enterprise benefits that used to be transform to increased knowledge value decreases since parts of the enterprise benefits have been published in the external environment through knowledge release process. The original knowledge diffusion model proposed by Kreng and Tsai (2003) constructed the intra-firm diffusion formulae as internal knowledge usage, learning and improvement; however, the model ignores the effect of inter-firm diffusion. Since both intra-firm and inter-firm diffusion occur at the same time, the means to coordinate the various diffusion conditions for expanding the original knowledge diffusion model is the primary objective of this study. The original estimation equations presented by Kreng and Tsai (2003) have also been modified to enhance the accuracy of investigating each parameter, besides investigating the interaction between intra-firm and inter-firm diffusion to figure out the corresponding diffusion formulae. Finally, a case study is also used to illustrate the feasibility of the proposed model, in which the results are demonstrated for better performance while comparing them with the original knowledge diffusion model of Kreng and Tsai (2003). 2. The original knowledge diffusion model of single knowledge Real knowledge value can be evaluated from enterprise benefits through the ABC model (Dekker & de Hoog, 2000; Wilkins et al., 1997). In order to identify the dynamic relationship between knowledge value and enterprise benefits in a given period, Kreng and Tsai (2003) combined the ABC model with the Bass diffusion model (Bass, 1969) to present the knowledge diffusion process shown in Fig. 1. At a given time t, the knowledge value, K*(t), is equal to K(t) + K 0 (t) where K(t) is the original knowledge value and K 0 (t) is the incremental knowledge value stemming from the investment in knowledge improvement. The K*(t) is Enterprise benefits X(t)
Knowledge value K(t)
Knowledge Investment I(t)
Knowledge value K*(t)
Added value V(t+1)
Knowledge Externalization
Knowledge Internalization
Increased benefits S(t+1) || Enterprise benefits X(t+1)
|| Knowledge value K(t+1) Fig. 1. The original knowledge diffusion process (Kreng & Tsai, 2003).
C.M. Tsai / Expert Systems with Applications 34 (2008) 1423–1433
transformed to increased benefits, S(t + 1), through the knowledge externalization, and then the total enterprise benefits at the next time, X(t + 1), are equal to X(t) + S(t + 1) where X(t) is the original enterprise benefits. After knowledge internalization at the next time, the total knowledge value, K(t + 1), is equal to K*(t) + V(t + 1) where V(t + 1) is the contributions externalized from X(t + 1). Since the diffusion process is a continuous cycle, X(t + 1) and K(t + 1) will take the place of X(t) and K(t), respectively, and then begin to evolve into X(t + 2) and K(t + 2) by the same mechanism. Kreng and Tsai (2003) concluded that the increased benefits are the existence of bell-shaped curves under the diffusion cycle. In the beginning, the increased benefits have moderate initial growth due to the continuous use of knowledge and sustained knowledge investment. After a period of time, the growth rate will decelerate because of the law of diminishing returns. Then, the increased benefits will start to decrease while the peak of the bell-shaped curves is reached. Finally, the enterprise benefits cannot be enhanced anymore since the saturation level of externalization has been reached. Since the V(t + 1) is affected by enterprise benefits, the changes of V(t + 1) are similar to a bell-shaped curve as well. Kreng and Tsai (2003) present three different diffusion patterns to reveal the dynamic diffusion processes. An illustrative case is used to figure out the related parameters embedded in the knowledge diffusion model through the diffusion equations. Since the original knowledge diffusion model only investigates intra-firm diffusion, the original model has to be expanded so that intra-firm and inter-firm diffusion can be considered at the same time. In fact, external knowledge is often introduced as additive knowledge so as to expand existing knowledge value (Argote, McEvily, & Reagans, 2003; Hall & Andriani, 2002). Accordingly, the total enterprise benefits increased will be externalized from the following three sources: (1) the use of existing knowledge inside the enterprise; (2) the increment of existing knowledge due to knowledge improvement driven by the investment; and (3) the adoption of external knowledge (i.e. additive knowledge) from other companies or research institutes. Since parts of the total enterprise benefits have been released to the external environment due to inter-firm diffusion, the rest are transformed into increased knowledge value by knowledge internalization. These intra-firm and inter-firm diffusion patterns are discussed in the next section. In addition, the estimating equations developed by Kreng and Tsai (2003) are also modified in this study to improve the performance of the knowledge diffusion model. 3. The knowledge diffusion model with intra-firm and inter-firm diffusion A complete knowledge management system should include various sub-systems such as internalization, externalization, acquisition, learning, dissemination, storage,
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innovation, improvement, management, etc. (Argote et al., 2003; Birchall & Tovstiga, 2002; Caloghirou, Kastelli, & Tsakanikas, 2004; Chait, 1998; Carlile & Rebentisch, 2003; Choi & Lee, 2002; Hall & Andriani, 2002; Holsapple & Singh, 2001; Korot & Tovstiga, 1998; Kreng & Tsai, 2003; Malone, 2002; Michael, 1999; Nonaka, Toyama, & Konno, 2000; Satyadas et al., 2001). If a vague interaction can be quantified by specific formulae successfully, an enterprise can, therefore, understand the relationship between knowledge value and enterprise benefits and further develop appropriate knowledge management strategies. The original knowledge diffusion model only emphasizes the effect of intra-firm diffusion which implies that all knowledge management processes are manipulated within the enterprise (Kreng & Tsai, 2003). Under an open system where the knowledge can flow between the internal organization and the external environment without obstruction, inter-firm knowledge diffusion, including knowledge acquisition and knowledge release, should be integrated into the original knowledge diffusion model. External knowledge can be adopted via knowledge acquisition activities referred to in the knowledge chain model (Holsapple & Singh, 2001). Hall and Andriani (2002) present that introducing external knowledge is important to bridge the knowledge gaps which result from the differences between the existing knowledge framework and future knowledge requirements. Furthermore, knowledge is often released from the internal organization into the external environment via dissemination (Satyadas et al., 2001). Accordingly, the external environment can be regarded as a huge repository which acts as an interface among numerous enterprises for external knowledge acquisition and internal knowledge release. Under the interactive processes of intra-firm and interfirm knowledge diffusion shown in Fig. 2, the existing knowledge value at time t, K*(t), is increased by the incremental value generated from the external knowledge acquisition, K00 (t), besides K(t) and K 0 (t) processed inside the organization originally. After knowledge externalization of K(t), K 0 (t) and K00 (t), respectively, the total enterprise benefits at time t + 1, X(t + 1), can be expressed as X ðt þ 1Þ ¼ X ðtÞ þ S ðt þ 1Þ
ð1Þ
where S ðt þ 1Þ ¼ Sðt þ 1Þ þ S 0 ðt þ 1Þ þ S 00 ðt þ 1Þ S*(t + 1) is the total increased enterprise benefits at time t+1 S(t + 1) is the increased enterprise benefits externalized by K(t) at time t + 1 S 0 (t + 1) is the increased enterprise benefits externalized by K 0 (t) at time t + 1 S00 (t + 1) is the increased enterprise benefits externalized by K00 (t) at time t + 1 If the knowledge release effect (inter-firm diffusion) is considered as well, parts of the enterprise benefits will be
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External Environment
External Knowledge Repository
Knowledge Acquisition
Knowledge Release
Inter-firm Diffusion Intra-firm Diffusion
Knowledge value K(t)
Knowledge Investment I(t)
Enterprise benefits X(t)
Existing Knowledge value K*(t)a
Knowledge Externalization
Increased benefits S*(t+1) b
Knowledge Internalization Added value V(t+1)
Enterprise benefits X(t+1)c
Knowledge value K(t+1)d
Knowledge Accumulation
Fig. 2. The processes of intra-firm and inter-firm knowledge diffusion. aThe existing knowledge value K*(t) = K(t) + K 0 (t) + K00 (t). If t = 0, K*(0) will be equal to V(0). bThe increased benefits S*(t + 1) = S(t + 1) + S 0 (t + 1) + S00 (t + 1). cThe total enterprise benefits at time t + 1,X(t + 1) = X(t) + S*(t + 1). If t = 0, X(0) will be equal to S*(0). dThe knowledge value at time t + 1, K(t + 1) = K*(t) + V(t + 1). Since the diffusion processes are cyclic, the X(t + 1) and K(t + 1) will take the place of X(t) and K(t), respectively, and then start to evolve the X(t + 2) and K(t + 2) by the same mechanism.
kept in the internal organization and the rest will be released to the external environment. Subsequently, the total increased transformed value, V*(t + 1), stemming from enterprise benefits, X(t + 1), is converted into added knowledge value, V(t + 1), and the released value, L(t + 1). The V(t + 1) is accumulated to the increment of knowledge value, K(t + 1), and the L(t + 1) is transformed into a supplement to external knowledge value. The relationship is V ðt þ 1Þ ¼ V ðt þ 1Þ þ Lðt þ 1Þ
ð2Þ
where V(t + 1) is internalized from X(t + 1) by knowledge internalization at time t + 1 L(t + 1) is released from X(t + 1) by knowledge release at time t + 1. Teng, Grover, and Gu¨ttler (2002) present four fundamental diffusion models: (1) external influence model; (2) internal influence model; (3) Gompertz function; and (4) Bass model. All of these models are based on a common hypothesis: the rate of diffusion is proportional to the number of potential adopters at a given time. In the case of the application of the diffusion model, Kreng and Tsai (2003) are the forerunners of adopting the diffusion model to develop the original knowledge diffusion model for dynamic knowledge value evaluation. The purpose of this study is not only to revise the imperfections in the original knowledge diffusion model, but also to apply the original knowl-
edge diffusion model to an open system where the intra-firm and inter-firm diffusion are integrated simultaneously. In order to formulate the knowledge diffusion model, the patterns used for illustrating the diffusion processes and all involved parameters should be redefined and represented. In addition to the references to Bass (1969), Teng et al. (2002), and Kreng and Tsai (2003), these patterns have also been demonstrated by related experts who have specialized in knowledge management for at least two years. Assuming that p(t), p 0 (t), and p00 (t) are the likelihood of increased enterprise benefits externalized by using K(t), K 0 (t), and K00 (t), respectively; q(t) is the likelihood of the added knowledge value internalized by the enterprise benefits which have not yet been transformed back to knowledge; and r(t) is the likelihood of the released value transformed from the generated enterprise benefits which has been released to the external environment. Since parts of the enterprise benefits have been released to the external environment, the enterprise benefits kept in the organization are reduced, which implies that the added knowledge value internalized by the enterprise benefits is also decreased. f ðtÞ ¼ a þ bF ðtÞ F ðtÞ f 0 ðtÞ p0 ðtÞ ¼ ¼ cF 0 ðtÞ þ d 1 F 0 ðtÞ f 00 ðtÞ ¼ eF 00 ðtÞ p00 ðtÞ ¼ 1 F 00 ðtÞ
pðtÞ ¼
ð3Þ ð4Þ ð5Þ
C.M. Tsai / Expert Systems with Applications 34 (2008) 1423–1433
qðtÞ ¼
fb ðtÞ ¼ fF b ðtÞ þ g 1 F b ðtÞ
ð6Þ
rðtÞ ¼
fr ðtÞ ¼ h iF r ðtÞ F r ðtÞ
ð7Þ
where f(t) is the likelihood of the increased enterprise benefits contributed by the original knowledge K(t) at time t F(t) is the likelihood of the total increased enterprise benefits contributed by the original knowledge K(t) during the (0, t) interval f 0 (t) is the likelihood of the increased enterprise benefits contributed by the improved knowledge K 0 (t) via investment at time t F 0 (t) is the likelihood of the total increased enterprise benefits contributed by the improved knowledge K 0 (t) via investment during the (0, t) interval f00 (t) is the likelihood of the increased enterprise benefits contributed by the acquired external knowledge K00 (t) at time t F00 (t) is the likelihood of the total increased enterprise benefits contributed by the acquired external knowledge K00 (t) during the (0, t) interval fb(t) is the likelihood of the added value of knowledge K internalized by enterprise benefits at time t Fb(t) is the likelihood of the total added value of knowledge K internalized by enterprise benefits during the (0, t) interval fr(t) is the likelihood of the released value transformed from internal organization to external environment at time t Fr(t) is the likelihood of the total released value transformed from internal organization to external environment during the (0, t) interval parameter ‘‘a’’ represents the externalization effect on enterprise benefits contributed by continuous usage of original knowledge parameter ‘‘b’’ represents the knowledge appreciation/ depreciation effect parameter ‘‘c’’ represents the externalization effect on enterprise benefits contributed by the knowledge improvement due to continuous investment parameter ‘‘d’’ represents the improvement effect on enterprise benefits generated by the knowledge improvement due to continuous investment parameter ‘‘e’’ represents the acquisition effect on enterprise benefits generated by adopting new external knowledge parameter ‘‘f’’ represents the internalization effect on knowledge value internalized from enterprise benefits parameter ‘‘g’’ represents the knowledge learning effect parameter ‘‘h’’ represents the organizational knowledge release effect parameter ‘‘i’’ represents the organizational knowledge retaining effect
1427
In Eq. (3), the enterprise benefits externalized by using original knowledge are generated by the subjected enterprise benefits which have been accumulated. The enterprise benefits externalized by using improved knowledge and by using external knowledge shown in Eqs. (4) and (5), respectively, are generated through the subjected enterprise benefits which have not yet been accumulated. Eq. (6) indicates that the added knowledge value internalized by enterprise benefits is also generated through the subjected added value which has not yet been accumulated. In Eq. (7), the released value derived from the knowledge release process is generated by the subjected released value which has been accumulated. The formulae p(t), p 0 (t), and q(t) which are the representations of conducting intra-firm diffusion are analogous to the study of Kreng and Tsai (2003). Compared with the study of Kreng and Tsai (2003), the definitions of the involved parameters ‘‘c’’, ‘‘d’’, ‘‘f’’, and ‘‘g’’ are the same except for the parameters ‘‘a’’ and ‘‘b’’. Since the externalized enterprise benefits are contributed by the usage of original knowledge, the externalization effect shown as the parameter ‘‘a’’ is constant when other conditions are unchanged. In addition, the organizational capability of using knowledge (Caloghirou et al., 2004; McNamara, Baxter, & Chua, 2004), the imitation of other companies (Kreng & Tsai, 2003), and the obsolescence of original knowledge (Wilkins et al., 1997) can also result in the knowledge appreciation/depreciation effect on the enterprise benefits externalization which is shown as the parameter ‘‘b’’. The formulae p00 (t) and r(t) with the three involved parameters ‘‘e’’, ‘‘h’’, and ‘‘i’’ are the new diffusion patterns used to represent the inter-firm diffusion. The acquisition effect shown as the parameter ‘‘e’’ is the organizational capability for adopting external knowledge. The more appropriate external knowledge sources are obtained, the more enterprise benefits will be externalized. Since the external environment has been considered as a huge knowledge repository, the organizational knowledge release effect shown as the parameter ‘‘h’’ indicates that parts of the enterprise benefits are transformed into the released value and then released to the external environment; however, the released value is reduced by the organizational capability of retaining the knowledge inside which is defined as the organizational knowledge retaining effect shown as the parameter ‘‘i’’. Holsapple and Joshi (2001) and Malone (2002) consider that the organization is the aggregation of all kinds of knowledge. The organizational performance often depends on the organizational capability of using internal knowledge and of acquiring external knowledge (Caloghirou et al., 2004). Since organizational capability can be accumulated during continuous knowledge management processes, an organization should possess the abilities to use the internal and to acquire external knowledge initially which are assumed to be m1 and m2, respectively, i.e. F(0) = m1 and F00 (0) = m2. The initial accumulation of improving knowledge, the initial accumulation of knowledge value internalized by enterprise benefits, and the ini-
1428
C.M. Tsai / Expert Systems with Applications 34 (2008) 1423–1433
tial accumulation of released value transformed from enterprise benefits to the external environment are equal to 0 because knowledge investment, knowledge internalization and knowledge release are not driven until diffusion begins, i.e. F 0 (0) = 0, Fx(0) = 0, and Fb(0) = 0. Accordingly, the equations are obtained as: a F ðtÞ ¼ ð8Þ b b þ ma1 expat dF ðtÞ a eat 2 ¼a bþ ð9Þ f ðtÞ ¼ h i2 dt m1 b ðb þ ma1 Þexpat F 0 ðtÞ ¼
1 expðcþdÞt 1 þ dc expðcþdÞt
f 0 ðtÞ ¼
dF 0 ðtÞ ðc þ dÞ2 expðcþdÞt ¼ 2 dt d 1 þ c expðcþdÞt
ð10Þ ð11Þ
d
F 00 ðtÞ ¼
1
1 expet dF 00 ðtÞ 1 ¼e 1 h f 00 ðtÞ ¼ dt m2 1þ
ð12Þ
1 m2
expet i2 ð13Þ 1 þ m12 1 expet
F b ðtÞ ¼
1 expðf þgÞt 1 þ fg expðf þgÞt
ð14Þ
fb ðtÞ ¼
dF b ðtÞ ðf þ gÞ2 expðf þgÞt ¼ h i2 dt g 1 þ fg expðf þgÞt
ð15Þ
h i ði hÞexpht dF r ðtÞ expht ¼ h2 ði hÞ fr ðtÞ ¼ dt ½i ði hÞexpht 2 F r ðtÞ ¼
ð16Þ ð17Þ
In order to estimate the parameters involved in the model precisely, the estimating equations should be considered individually to investigate the related parameters directly because all data have been separated by the ABC model in advance. According to Fig. 2 and Eqs. (3)–(7), the estimating equations can be obtained as: SðtÞ ¼ K max f ðtÞ ¼ a Y s ðtÞ þ 0
c
0
S ðtÞ ¼ I max f ðtÞ ¼
I max
b K max
Y 2s0 ðtÞ
Y 2s ðtÞ
ð18Þ
e Y 2s00 ðtÞ þ e Y s00 ðtÞ ð20Þ Emax f V ðtÞ ¼ Bmax fb ðtÞ ¼ Y 2v ðtÞ þ ðf gÞ Y v ðtÞ þ g Bmax Bmax S 00 ðtÞ ¼ Emax f 00 ðtÞ ¼
ð21Þ LðtÞ ¼ Rmax fr ðtÞ ¼
Rmax
The maximum of enterprise benefits, Xmax, is equal to the sum of Bmax and Rmax. Compared to the original knowledge diffusion model presented by Kreng and Tsai (2003), the added value should be internalized by Bmax instead of Xmax because Rmax is released to the external environment and only Bmax is kept in the organization. When both intra-firm and inter-firm knowledge diffusions are considered simultaneously, Eqs. (18), (19), and (21) which exhibit intra-firm knowledge diffusion are similar to the presentation of Kreng and Tsai (2003), and the inter-firm knowledge diffusion is presented by Eqs. (20) b i and (22). Since only K max and Rmax can be obtained while estimating parameters, the equations which indicate the relationship between intra-firm and inter-firm knowledge diffusion are developed so that all of the parameters in the model can be estimated plausibly. K max ¼ K ð0Þ þ
Z
1
V ðtÞdt ¼ K ð0Þ þ Bmax 0
X max ¼ Bmax þ Rmax ¼ X ð0Þ þ
Z
ð23Þ
1
SðtÞdt ¼ X ð0Þ þ K max þ I max þ Emax
0
ð24Þ
þ ðc dÞ Y s0 ðtÞ þ d I max
ð19Þ
i
Emax is the maximum of external knowledge acquisition value Bmax is the maximum of enterprise benefits kept in the internal organization Rmax is the maximum of enterprise benefits released to the external environment Ys(t) is the total increased enterprise benefits externalRt ized by S(t) during the (0, t) interval, i.e. Y s ðtÞ ¼ 0 SðtÞ Y s0 ðtÞ is the total increased enterprise benefits externalRt ized by S 0 (t) during the (0, t) interval, i.e. Y s0 ðtÞ ¼ 0 S 0 ðtÞ Y s00 ðtÞ is the total increased enterprise benefits externalized byR S00 (t) during the (0, t) interval, i.e. t Y s00 ðtÞ ¼ 0 S 00 ðtÞ Yv(t) is the total added value of knowledge K internalized by Renterprise benefits during the (0, t) interval, i.e. t Y v ðtÞ ¼ 0 V ðtÞ YL(t) is the total value released form internal organization to external R t environment during the (0, t) interval, i.e. Y L ðtÞ ¼ 0 LðtÞ
Y 2L ðtÞ þ h Y L ðtÞ
ð22Þ
where Kmax is the maximum of knowledge value Imax is the maximum of internal knowledge improvement value
In Eq. (23), the knowledge value is internalized from the amount of the enterprise benefits kept in the internal organization. Eq. (24) implies that the total enterprise benefits are externalized from the three knowledge sources including original knowledge, improved knowledge, and external acquired knowledge which have been integrated by organization beforehand. When only intra-firm diffusion is considered in knowledge diffusion, the Bmax and Rmax disappear, and then the diffusion model is degenerated to the original model proposed by Kreng and Tsai (2003). In the next section, a real case study which is the same as the study done by Kreng and Tsai (2003) is used to demonstrate the feasibility of the proposed model. The results are also compared with the conclusions of
C.M. Tsai / Expert Systems with Applications 34 (2008) 1423–1433
Kreng and Tsai (2003) so that the difference between the original diffusion model and the new diffusion model can be highlighted. 4. Model demonstration The Uni-President Enterprise Corporation (UPEC) established in 1967 is the largest food company in Taiwan in recent years. Using the strategies of high quality and customer satisfaction, the UPEC has implemented a QCC (Quality Control Circle) system for more than twenty years. The QCC system has created more than 500 million NT dollars for UPEC. In order to compare the conclusions presented by Kreng and Tsai (2003), this study uses the same case to identify the relationship between knowledge value and enterprise benefits under inter-firm and interfirm knowledge diffusion. According to the original data from 1980 to 1991 presented by Kreng and Tsai (2003), the relevant data are re-identified and shown in Table 1 where S*(t) and V*(t) are the total increased enterprise benefits externalized by all knowledge sources and the total increased transformed value converted from the enterprise benefits, respectively. The basic model is shown in Eqs. (18)–(22). In estimating all involved parameters from these discrete time series data, the following analogue can be used (Bass, 1969; Kreng & Tsai, 2003): SðtÞ ¼ a Y s ðt 1Þ þ b Y 2s ðt 1Þ
ð25Þ
S 0 ðtÞ ¼ d Y 2s0 ðt 1Þ þ k Y s0 ðt 1Þ þ q
ð26Þ
S 00 ðtÞ ¼ p Y 2s00 ðt 1Þ þ u Y s00 ðtÞ
ð27Þ
V ðtÞ ¼ g Y 2v ðt 1Þ þ l Y v ðt 1Þ þ h
ð28Þ
LðtÞ ¼ f Y 2L ðt 1Þ þ t Y L ðt 1Þ
ð29Þ
1429
and Tsai (2003) where S*(t) and V*(t) are used to investigate all involved parameters, a new estimating method which uses Eqs. (25)–(29) to estimate the corresponding parameters is presented here. The adjusted R2 value and the p value of the original estimating method are unacceptable, whereas the adjusted R2 value and the p value of the new estimating method show substantial improvement. Therefore, the rationality and preciseness of the new estimating method are, indeed, better than the original one. According to the regression results of the new estimating method, the predicted/actual values of S*(t) and V*(t) are shown in Figs. 3 and 4, respectively, where the predicted value of S*(t) is equal to the sum of the predicted values of S(t), S 0 (t), and S00 (t) and the predicted value of V*(t) is equal to the sum of the predicted values of V(t) and L(t). Kreng and Tsai (2003) consider that the proposed model should be adopted to predict future changes of knowledge value and enterprise benefits so as to develop appropriate knowledge management strategies. In the prediction process, the bias, e, which can be estimated by the formula f ðtÞ 1 ¼ F ðtþ1ÞF for any probability distribution, should be e ðtÞ added to the prediction equations (Bass, 1969). As a result, the prediction equations, S(t), S 0 (t), S00 (t), V(t) and, L(t), are reconstructed as the following analogue after including the biases e1 to e5. SðtÞ ¼ a0 Y s ðt 1Þ þ b0 Y 2s ðt 1Þ 0
S ðtÞ ¼ d Y 2s0 ðt 1Þ þ k0 Y s0 ðt 1Þ þ q S 00 ðtÞ ¼ p0 Y 2s00 ðt 1Þ þ u0 Y s00 ðt 1Þ V ðtÞ ¼ g0 Y 2v ðt 1Þ þ l0 Y v ðt 1Þ þ h LðtÞ ¼ f0 Y 2L ðt 1Þ þ t0 Y L ðt 1Þ 0
ð30Þ ð31Þ ð32Þ ð33Þ ð34Þ
where
where a ¼ a; b ¼ g¼
b K max
;d ¼
c I max
; k ¼ ðc dÞ; q ¼ d I max ; p ¼
e Emax
; u ¼ e;
f i ; l ¼ ðf gÞ; h ¼ g Bmax ; f ¼ ;t ¼ h Bmax Rmax
a0 ¼ a0 ¼ a e1 ; b0 ¼ d0 ¼
The regression results are listed in Table 2. Compared with the original estimating method presented by Kreng
p0 ¼
c0 I 0max 0
e E0max
b0 b ¼ e21 ; K 0max K max
c
e22 ; k0 ¼ ðc0 d 0 Þ ¼ ðc dÞ e2 ; I max e ¼ e23 ; u0 ¼ e0 ¼ e e3 ; Emax
¼
Table 1 The re-identified data from 1980 to 1991 in UPEC (unit: million NT dollars) Time 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991
(t = 0) (t = 1) (t = 2) (t = 3) (t = 4) (t = 5) (t = 6) (t = 7) (t = 8) (t = 9) (t = 10) (t = ll)
S*(t)
S(t)
S 0 (t)
S00 (t)
V*(t)
V(t)
L(t)
21 22.18 14.04 23.28 23.28 27.6 33.68 26.46 17.55 17.737 24.426 16.887
6.268 6.661 6.12 9.596 10.608 14.147 21.45 17.114 12.295 11.5596 20.7621 15.1983
1.05 2.218 2.106 4.656 5.82 8.28 8.42 6.615 3.51 3.5474 3.6639 1.6887
13.682 13.301 5.814 9.028 6.852 5.173 3.81 2.731 1.745 2.63 0 0
5.25 6.654 4.914 9.312 11.64 16.56 25.26 21.6972 15.444 16.31804 23.44896 16.71813
4.16 3.284 3.858 6.57 10.34 12.53 13.22 14.69 14.347 13.142 17.4581 14.325
1.09 3.37 1.056 2.742 1.3 4.03 12.04 7.0072 1.097 3.17604 5.99086 2.39313
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C.M. Tsai / Expert Systems with Applications 34 (2008) 1423–1433
Table 2 The regression results of the knowledge diffusion model New method
Adjusted R2
Estimates
Std. Err.
p value
Parameters
S(t)
0.9101
a = 0.4264 b = 0.0025
0.0657 0.0006
0.0001 0.0027
S 0 (t)
0.7957
S00 (t)
0.7879
V(t)
0.8507
L(t)
0.6360
d = 0.0103 k = 0.4944 q = 1.7790 p = 0.0086 u ¼ 0:5511 g = 0.0020 l = 0.3161 h = 3.1929 n = 0.0137 t = 0.6106
0.0016 0.0828 0.7577 0.001 0.0938 0.0005 0.0590 1.2487 0.0047 0.1677
0.0002 0.0003 0.0468 0.0005 0.0002 0.0054 0.0007 0.0338 0.0175 0.0054
Kmax = 175.7137a a = 0.4264 b = 0.4393a Imax = 5 1.6063 c = 0.5289 d = 0.0345 Emax = 64.0814 e = 0.5511 Bmax = 171.5537 f = 0.3347 g = 0.0186 Rmax = 140.8477b i = 1.9296b h = 0.6106
Original method S*(t)
0.4290
V*(t)
0.8129
a = 0.9608 b = 0.0042 d = 0.0224 k = 0.0187 q = 43.7036 p = 0.0470 u ¼ 1:7998 g = 0.0008 l = 0.6577 h = 1.9167 n = 0.0302 t = 0.1331
2.4002 0.0074 0.0320 3.9526 14.8457 0.0276 1.6498 0.0036 0.4520 2.5297 0.0284 1.3241
0.7094 0.5985 0.5222 0.9965 0.0422 0.1641 0.3366 0.8297 0.1959 0.4473 0.3290 0.9232
–c
—c
a
The parameters Kmax and ‘‘b’’ are obtained by Eq. (23) where K*(0) = V(0) = 4.16. The parameters Rmax and ‘‘i’’ are obtained by Eq. (24) where X(0) = S*(0) = 21. c The parameters of S*(t) and V*(t) are not necessary to calculate since the adjusted R2 of original method is smaller than the one of new method and the estimates are not significant. b
S*(t) actual value
V*(t) actual value
S*(t) predictd value
V*(t) predictd value 30 million NT dollars
million NT dollars
40 30 20 10 0
1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 Year Fig. 3. The predicted value and actual value of S*(t).
25 20 15 10 5 0
1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 Year Fig. 4. The predicted value and actual value of V*(t).
f0 f ¼ e24 ; l0 ¼ ðf 0 g0 Þ ¼ ðf gÞ e4 ; B0max Bmax i0 i e25 ; t0 ¼ h0 ¼ h e5 f0 ¼ 0 ¼ Rmax Rmax
1 cþd 1 ¼ ¼ lnðc0 þ d 0 þ 1Þ e2 ðexpðcþdÞ 1Þ c0 þ d 0
ð36Þ
1 e 1 ¼ 0 lnðe0 þ 1Þ ¼ e e3 ðexp 1Þ e
ð37Þ
For small values of t, the biases can be obtained, and then the correct parameters which have been adjusted by biases can be figured out.
1 f þg 1 ¼ ¼ lnðf 0 þ g0 þ 1Þ e4 ðexpðf þgÞ 1Þ f 0 þ g0
ð38Þ
1 a 1 ¼ lnða0 þ 1Þ ¼ e1 ðexpa 1Þ a0
1 h 1 ¼ 0 lnðh0 þ 1Þ ¼ h e5 ðexp 1Þ h
ð39Þ
g0 ¼
ð35Þ
C.M. Tsai / Expert Systems with Applications 34 (2008) 1423–1433
Table 3 The re-identified data from 1997 to 1999 in UPEC (unit: million NT dollars) Time
S*(t)
S(t)
S 0 (t)
S00 (t)
V*(t)
V(t)
L(t)
1997 (t = 0) 1998 (t = 1) 1999 (t = 2)
22.219 26.818 37.830
9.843 10.933 18.612
2.222 4.023 6.758
10.154 11.862 12.46
10.079 17.786 28.240
8.248 14.357 21.36
1.831 3.429 6.88
0
0
a = 1.3042 b 0 = 0.0197
Parameters
Biases
Parameters
a = 1.3042 K ¼ 0:0197 K0
1 e1
¼ 0:6400
I 0max 0
1 e2
¼ 0:7012
1 e3
¼ 0:5863
1 e4
¼ 0:6872
1 e5
¼ 0:3639
a = 0.8347 Kmax = 129.3419a b = 1.0437a Imax = 61.971 c = 0.6368 d = 0.0358 Emax = 56.5303 e = 0.9872 Bmax = 121.0939 f = 0.6405 g = 0.0681 Rmax = 148.9863b i = 3.2490b h = 0.7912
0
max
d = 0.0209 k 0 = 0.8570 q = 2.222 p 0 = 0.0508 - ¼ 1:6837 g 0 = 0.0112 l 0 = 0.8329 h = 8.248 v 0 = 0.1647
¼ 43:452 c = 0.9081 d 0 = 0.0511 E0max ¼ 33:1437 e 0 = 1.6837 B0max ¼ 83:2157 f 0 = 0.9320 g 0 = 0.0991 i0 ¼ 0:1647 R0
m 0 = 2.1743
h 0 = 2.1743
max
S 0 (t)
S00 (t)
V*(t)
2.222
10.154
10.079
8.248
1.831
10.933
4.023
11.862
17.786
14.357
3.429
37.830
18.612
6.758
12.46
28.240
21.36
6.88
41.932
20.358
8.296
13.278
29.579
23.188
6.391
38.743
21.066
10.358
7.319
30.005
22.833
7.172
27.104
14.756
10.946
1.402
22.853
16.925
5.928
15.298
6.071
9.172
0.0550
12.191
8.986
3.205
7.268
1.478
5.789
0.001
4.635
3.540
1.095
3.034
0.270
2.764
0
1.431
1.160
0.271
1.122
0.045
1.077
0
0.41
0.351
0.059
Time
S*(t)
1997 (t = 0) 1998 (t = 1) 1999 (t = 2) 2000 (t = 3) 2001 (t = 4) 2002 (t = 5) 2003 (t = 6) 2004 (t = 7) 2005 (t = 8) 2006 (t = 9)
22.219
9.843
26.818
S(t)
V(t)
L(t)
more resources have been devoted to knowledge improvement. Thus, the reason for the increase of Imax for the period S*(t) V*(t) 50 40 30 20 10 0 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 Year
Fig. 5. The predictions of S*(t) and V*(t) resulting from the prediction model.
Table 4 All parameters of the prediction model Estimates
Table 5 The results of the prediction model (unit: million NT dollars)
million NT dollars
The data used for the prediction are the same as the original data presented by Kreng and Tsai (2003). Since interfirm and intra-firm diffusion are considered simultaneously, these data should also be re-identified. The re-identified data are shown in Table 3. Thus all prediction equations can be established according to the equations from (30) to (35), and the results are shown in Table 4. The maximum enterprise benefits of this period, Xmax, are equal to 270.0622. Since all the parameters appear to be plausible, the predictions of both S*(t) and V*(t) can be obtained in Table 5 and Fig. 5. The parameters of the period from 1980–1991 and of from the period 1997–2006 are shown in Table 6. The situations for conducting knowledge management can be identified by parameter analysis since all parameters involved in the knowledge diffusion model possess managerial implications. For the period 1997–2006, the QCC knowledge has become mature knowledge because the knowledge has been adopted by a great many Taiwanese companies. The Kmax and Xmax of the period 1997–2006 are lower than those of the period 1980–1991 inevitably. The parameter ‘‘a’’ is increased in the period 1997–2006 which implies that the capability for enterprise benefits externalization by using original knowledge has been strengthened; however, the rate of depreciation shown as parameter ‘‘b’’ becomes more rapid. That is, the original knowledge has been less and less valueless because of the knowledge depreciation. In order to put new added value on the QCC knowledge, more and
1431
a The parameters Kmax and ‘‘b’’ are obtained by Eq. (23) where K*(0) = V(0) = 8.248. b The parameters Rmax and ‘‘i’’ are obtained by Eq. (24) where X(0) = S*(0) = 22.219.
Table 6 The parameters of period 1980–1991 and of period 1997–2006 Period
1980–1991
1997–2006
Increase/Decrease
Kmax a b Imax c d Emax e Bmax f g Rmax h i Xmax
175.7137 0.4264 0.4393 51.6063 0.5289 0.0345 64.0814 0.5511 171.5537 0.3347 0.0186 140.8477 1.9296 0.6106 312.4014
129.3419 0.8347 1.0437 61.971 0.6368 0.0358 56.5303 0.9872 121.0939 0.6405 0.0681 148.9683 0.7912 3.2490 270.0622
Decrease Increase Increase in the absolute value Increase Increase Increase Decrease Increase Decrease Increase Increase Increase Decrease Increase Decrease
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1997–2006 can also be demonstrated. The parameters ‘‘c’’ and ‘‘d’’ have increased in the period 1997–2006 which demonstrates that the efficiency of making enterprise benefits from improved knowledge has also been enhanced. The results can be interpreted as being due to the capability of the related staff has been strengthened. At the present time, UPEC is promoting a new quality system so as to maintain profitability and to remain competitiveness in the future. In addition, the Emax of the period 1997-2006 has decreased, which means that the dependence on external knowledge resource has been reduced since knowledge can be developed more effectively within the internal organization. Even so, the parameter ‘‘e’’ is showing increase in this period because the external knowledge can be integrated into the existing knowledge system more successfully, and then more enterprise benefits can also be generated. The manager considers the new QCC knowledge acquired from the cooperative Japanese company after 1996 to be quite novel. Much included know-how seems to be unfamiliar in the beginning; however, the execution and adopting of new knowledge has been achieved in the end due to the extensive experience the staff has accumulated. Under an open knowledge system of the period 1997–2006, the decrease of Bmax with the increase of Rmax is a necessary result since the release process is processed much more frequently than before. The parameters ‘‘f’’ and ‘‘g’’ of the period 1997–2006 have increased, which implies that the knowledge value is internalized from enterprise benefits more successfully, i.e. the capabilities of absorbing and of learning knowledge have been enhanced. Finally, the knowledge release effect from the internal organization to the external environment is decreased, whereas the knowledge retaining effect is enhanced for the period 1997–2006. The presentation of the parameters ‘‘h’’ and ‘‘i’’ means that the knowledge management system is executed fairly successfully since more and more knowledge is kept inside the organization. Many Taiwanese companies often promote technical exchange or cooperation to transfer new knowledge or technologies from other overseas companies. Therefore, the proposed knowledge diffusion model integrating intra-firm and inter-firm diffusion is much more appropriate to describe the relationship between knowledge value and its corresponding enterprise benefits. Moreover, the performance of executing the knowledge management system is also investigated by the parameter analysis so that effective knowledge management strategies are developed in advance.
5. Conclusion Implementing the knowledge management system for competitive success has been an increasingly vital issue for enterprises recently. The performance of knowledge management can be investigated only by realizing the relationship between knowledge value and enterprise benefits. Since knowledge management is conducted in an open
system, both intra-firm diffusion, and inter-firm diffusion processes exist between the interaction of the internal organization and the external environment simultaneously. In addition to the patterns including knowledge internalization, externalization, improvement, and learning presented by Kreng and Tsai (2003), the knowledge acquisition and knowledge release are also integrated into the new knowledge diffusion model. The new estimating method is more appropriate than the original one presented by Kreng and Tsai (2003) for investigating all involved parameters, since the adjusted R2 values of all estimating equations have improved. Accordingly, the feasibility of the new knowledge diffusion model is demonstrated as well. The performance of executing knowledge management in different periods can be traced by further parameters analysis. Since the inference provided by parameters analysis has been successfully connected with actual situations after confirming with the related managers, effective knowledge strategies can be identified to enhance the competitiveness of an enterprise, and as a result, a successful knowledge management system can also be facilitated. The knowledge diffusion model is a novelty; however, this model still provides some insights into the problem. In addition to revising and expanding the model continuously, further discussion on knowledge substitutive or complementary effects is another theme for future study. References Argote, L., McEvily, B., & Reagans, R. (2003). Managing knowledge in organizations: an integrative framework and review of emerging themes. Management Science, 49(4), 571–582. Bass, F. M. (1969). A new product growth for model consumer durables. Management Science, 15(5), 215–227. Bassi, L. J., & Van Buren, M. E. (1999). Valuing investment in intellectual capital. International Journal of Technology Management, 18(5), 414–432. Birchall, D. W., & Tovstiga, G. (2002). Assessing the firm’s strategic knowledge portfolio: a framework and methodology. International Journal of Technology Management, 24(4), 419–434. Caloghirou, Y., Kastelli, I., & Tsakanikas, A. (2004). Internal capabilities and external knowledge sources: complements or substitutes for innovative performance? Technovation, 24, 29–39. Chait, L. (1998). Creating a successful knowledge management system. Prism(Second Quarter Issue), 83. Carlile, P. R., & Rebentisch, E. S. (2003). Into the black box: the knowledge transformation cycle. Management Science, 49(9), 1180–1195. Choi, B., & Lee, H. (2002). Knowledge management strategy and its link to knowledge creation process. Expert Systems with Applications, 23(3), 173–187. Dekker, R., & de Hoog, R. (2000). The monetary value of knowledge assets: a micro approach. Expert Systems with Applications, 18(2), 111–124. Hall, R., & Andriani, P. (2002). Managing knowledge for innovation. Long Range Planning, 35, 29–48. Holsapple, C. W., & Joshi, K. D. (2001). Organizational knowledge resources. Decision Support Systems, 33, 39–54. Holsapple, C. W., & Singh, M. (2001). The knowledge chain model: activities for competitiveness. Expert Systems with Applications, 20(1), 77–98.
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