The construct and application of knowledge diffusion model

Expert Systems with Applications 25 (2003) 177–186 www.elsevier.com/locate/eswa

The construct and application of knowledge diffusion model Victor B. Krenga,*, Chih Ming Tsaib b

a Department of Industrial Management Science, National Cheng-Kung University, No. 1 University Road, Tainan 701, Taiwan, ROC Graduate School of Industrial Management Science, National Cheng-Kung University, No. 1 University Road, Tainan 701, Taiwan, ROC

Abstract How to measure knowledge value has become an extremely important issue for enterprise. Only through understanding the change of knowledge value, the performance of knowledge management can be fully investigated. Although activity based costing (ABC) model can evaluate the corresponding knowledge value from the standpoint of enterprise benefits, it cannot predict the future change of knowledge value. Therefore, enterprises have to construct a dynamic model to evaluate and further forecast knowledge value. Since knowledge possesses characteristics of diffusion, depreciation, and growth with time, this study is, therefore, based on diffusion model to construct knowledge diffusion process for single knowledge. In addition, UPEC (Uni-President Enterprise Corporation) of Taiwan promoting quality control circle (QCC) system will be utilized as a case study to illustrate the proposed model. Furthermore, this study will also analyze parameters in the model to help develop a set of effective knowledge management strategies. q 2003 Elsevier Science Ltd. All rights reserved. Keywords: Knowledge diffusion model; Knowledge value; Enterprise benefits

1. Introduction During recent years, the importance of knowledge has attracted more and more attention from enterprises. Many enterprises regard knowledge management as their foundation of value creation due to improvement of innovation and adaptability. Simply stated, the practice of knowledge management will make enterprises utilize their inside knowledge more effectively, and further enhance the enterprises benefits and competitive advantages in the future (Shin, Holden, & Schmidt, 2001). Knowledge value and enterprise benefits are closely linked (Wilkins, van Wegen, & de Hoog, 1997). Although many studies of exploring the framework and procedures of knowledge management had been presented in the past (Holsapple & Singh, 2001; Ndlela & du Toit, 2001; Shin et al., 2001), the dynamic relationship between knowledge value and enterprise benefits has rarely been discussed. Hence, how to systematically measure the intangible value of knowledge is a vital issue for enterprises. The ABC model presented by Wilkins et al. (1997) helps enterprises identify the relationship between knowledge value and * Corresponding author. Tel.: þ886-6-2757575x53145; fax: þ 886-62362162. E-mail addresses: [email protected] (V.B. Kreng); r3890107@ ccmail.ncku.edu.tw (C.M. Tsai)

enterprise benefits, and calculate the real value of the knowledge from enterprise benefits. Nevertheless, the above model can only obtain the knowledge value within a certain period without being able to predict future dynamic changes. Similar to physical products, knowledge also possesses characteristics of diffusion, depreciation, and growth with time. As a result, this study adopts the product diffusion model presented by Bass (1969) to infer the knowledge diffusion model so as to help enterprises precisely predict the changing relationship between knowledge value and enterprise benefits. Accordingly, enterprises can understand the performance of the knowledge, and, thereby, develop a set of knowledge management strategies.

2. Literature review 2.1. Measurement of knowledge value Knowledge management is a business approach that urges enterprise as well as individual to improve through learning and sharing of knowledge. Namely, enterprises can classify, select, use, and store knowledge in order to enhance their profits and competitive ability. In the process of conducting knowledge management, the knowledge chain model (Holsapple & Singh, 2001) is composed of five major knowledge activities including knowledge

0957-4174/03/$ - see front matter q 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0957-4174(03)00045-9

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acquisition, knowledge selection, knowledge generation, knowledge internalization, and knowledge externalization. In general, the enterprise benefits can be illustrated by financial and non-financial indicators such as product benefits, sales volume, and customer satisfaction etc. in which the intangible knowledge value is very difficult to be measured directly. Wilkins et al. (1997) and Dekker and de Hoog (2000) presented the ABC model shown in Fig. 1, which uses the concept of knowledge item defined by Wiig, de Hoog, & van der Spek, (1997) to represent the knowledge applied to produce products. Dekker and de Hoog (2000) further applied the ABC model by Wilkins et al. (1997) to a bank to calculate the value of every knowledge item. They thought that such measurement on the basis of process could help enterprises in process reengineering as well. In addition, Wilkins et al. (1997) stated that original knowledge assets would devaluate with time, if they were not renewed and amended. 2.2. Product diffusion model The basic diffusion model of first-purchase products presented by Bass 1969 described the growth condition of a product. If FðtÞ is defined as the cumulative percentage of potential market in which customers have adopted the product in the ð0; tÞ interval, then, f ðtÞ ¼ dFðtÞ=dt is the percentage of potential market in which customers adopt the product at time t: The likelihood of purchase at time t given that no purchase has yet been made is given in Eq. (1). f ðtÞ ¼ p þ qFðtÞ 1 2 FðtÞ

from Eq. (2). f ðtÞ ¼

dFðtÞ ¼ p þ ðq 2 pÞ £ FðtÞ 2 qF 2 ðtÞ dt

1 2 e2ðpþqÞt FðtÞ ¼ q e2ðpþqÞtþ1 p

ð2Þ ð3Þ

Since f ðtÞ is the likelihood of purchase at time t and m is the potential purchasing figures during the whole period, the total purchasing volume YðtÞ in the ð0; tÞ interval and purchasing volume at time t are given in Eqs. (4) and (5). ðt YðtÞ ¼ SðtÞdt ¼ m £ FðtÞ ð4Þ 0

SðtÞ ¼ m £ f ðtÞ ¼ PðtÞ½m 2 YðtÞ ¼ pm þ ðq 2 pÞYðtÞ 2

q 2 Y ðtÞ m

ð5Þ

There is a questionable assumption in the Bass diffusion model, in which this model only considers the first-purchase customers. However, most of products usually own customers with both first purchase and repeated purchase simultaneously. Similar to physical products, knowledge not only can be repeatedly used, but also can be introduced to novices by means of various acquisition activities. Therefore, in order to realize the dynamic change of knowledge value while conducting knowledge internalization and externalization activities, this study combines the ABC model and products diffusion model to construct knowledge diffusion model, which is expected to realistically represent the characteristics of knowledge.

ð1Þ 3. Model construction

The parameters, p and q; respectively represent the innovation coefficient and imitation coefficient of products purchase because the model divides first-purchase consumers into innovators and imitators. The importance of innovators will be greater at first but will diminish monotonically with time, while the importance of imitators will increase with time (Norton & Bass, 1987). Eq. (1) can be transformed to Eq. (2). With the initial condition Fð0Þ ¼ 0; the solution of Eq. (3) can be obtained

Fig. 1. The concepts in activities based costing model (Wilkins et al., 1997; Dekker & de Hoog, 2000).

Among the five major activities defined by the knowledge chain model, when introducing a new knowledge, enterprises normally continuously use it and also keep investing to strengthen its mergence and innovation. At last, enterprises can transform knowledge to enterprise benefits or product profits through externalization, and further transform from existing enterprise benefits back into knowledge value through internalization. According to the ABC model, the dynamic relationship between the value of knowledge item and enterprise benefits will be explored in this study. Under the circumstances of other factors unchanged, assumed that Xð0Þ is the initial enterprise benefit; Kð0Þ is the initial value inside enterprise; Ið0Þ is the initial investment in knowledge K: Besides the original knowledge value Kð0Þ; the value of knowledge K is expected to increase by introduction, with the increment of K0 (0) after investment. Therefore, the total knowledge value at time 0, K p ð0Þ; is equal to Kð0Þ þ K 0 ð0Þ: The total enterprise benefits of next time, Xð1Þ; is equal to Xð0Þ þ Sð1Þ; assumed that Sð1Þ is the increased enterprise benefits through the use of the knowledge K: The increased

V.B. Kreng, C.M. Tsai / Expert Systems with Applications 25 (2003) 177–186

enterprise benefits Sð1Þ at time 1 is given in Eq. (6) from two different diffusion sources. Sð1Þ ¼ SK!X ð1Þ þ SI!K!x ð1Þ

ð6Þ

where SK!X ð1Þ represents the increased enterprise benefits generated by the original knowledge Kð0Þ at time 1 SI!K!X ð1Þ represents the increased enterprise benefits generated by the incremental original knowledge K 0 ð0Þ at time 1. According to the ABC model, the increased value of knowledge K at time 1 can also be obtained from the enterprise benefits Xð1Þ: Assumed that the contribution from Xð1Þ to knowledge K at time 1 is Vð1Þ; the total value of knowledge K at time 1, Kð1Þ; will become K p ð0Þ þ Vð1Þ: In this way, not only enterprise benefits but also knowledge value will raise higher and higher through continuous use of and occasional investment in knowledge K: The relationship among enterprise benefits, knowledge value, and knowledge investment is shown in Fig. 2. With the continuous use of and occasional investment in the knowledge K; the increased enterprise benefits SðtÞ at time t is given in Eq. (7). SðtÞ ¼ SK!X ðtÞ þ SI!K!X ðtÞ

ð7Þ

In the beginning, SK!X ðtÞ will increase gradually; nevertheless, with the learning effect of knowledge K decelerating inside enterprises and the disseminating rates of external knowledge increasing, SK!X ðtÞ will start to decrease. Similarly, SI!K!X ðtÞ will have an moderate initial growth;

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however, due to the restriction of enterprise budget, investment in other substitutional knowledge and smaller range of knowledge innovation are expected. Therefore, SI!K!X ðtÞ will also decreases with time. Under the circumstances of smaller and smaller SðtÞ; the incremental knowledge value VðtÞ from enterprise benefits XðtÞ gradually decreases with time as well. The mutual relationship of the above is shown in Eqs. (8) – (11). SðtÞ ¼ Sk!x ðtÞ þ SI!k!x ðtÞ ¼ Kmax £ fk!x ðtÞ þ Imax £ fI!k!x ðtÞ ðt Ys ðtÞ ¼ SðtÞ ¼ Kmax £ Fk!x ðtÞ þ Imax £ FI!k!x ðtÞ

ð8Þ ð9Þ

0

VðtÞ ¼ Xmax £ fx!k ðtÞ ðt Yv ðtÞ ¼ VðtÞ ¼ Xmax £ Fx!k ðtÞ

ð10Þ ð11Þ

0

where Xmax is the maximum of enterprise benefits Kmax is the maximum of knowledge value Imax is the maximum of knowledge investments Ys ðtÞ is the total increased enterprise benefits in the ð0; tÞ interval Yv ðtÞ is the total added value of knowledge K in the ð0; tÞ interval fk!x ðtÞ is the likelihood of the increased enterprise benefits contributed by existing knowledge K at time t Fk!x ðtÞ is the likelihood of the increased enterprise benefits contributed by existing knowledge K during the ð0; tÞ interval

Fig. 2. The relationship among enterprise benefits, knowledge value, and knowledge investment.

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fI!k!x ðtÞ is the likelihood of the total increased enterprise benefits contributed by knowledge innovation via investment at time t FI!k!x ðtÞ is the likelihood of the total increased enterprise benefits contributed by knowledge innovation via investment during the ð0; tÞ interval fx!k ðtÞ is the likelihood of the added value of knowledge K internalized by enterprise benefits at time t Fx!k ðtÞ is the likelihood of the added value of knowledge K internalized by enterprise benefits during the ð0; tÞ interval At time t; the likelihood of increased enterprise benefits due to usage of the original knowledge KðtÞ can be indicated in Eq. (12). The likelihood of increased enterprise benefits generated by original knowledge K 0 ðtÞ because of investment can be indicated in Eq. (13). fk!x ðtÞ ¼ aFk!x ðtÞ 2 b Fk!x ðtÞ

ð12Þ

fI!k!x ðtÞ qðtÞ ¼ ¼ cFI!k!x ðtÞ þ d 1 2 FI!k!x ðtÞ

ð13Þ

pðtÞ ¼

Since Fk!x ðt ¼ 0Þ ¼ 2b and FI!k!x ðt ¼ 0Þ ¼ 0; the constant n1 ¼ ð1=bÞlnðða þ 1Þ=aÞ; and n2 ¼ 2ð1=c þ dÞlnðc=dÞ; Fk!x ðtÞ; fk!x ðtÞ; FI!k!x ðtÞ; and fI!k!x ðtÞ can be represented as follows: b ð20Þ Fk!x ðtÞ ¼ a 2 ða þ 1Þebt fk!x ðtÞ ¼

dFk!x ðtÞ ebt ¼ b2 ða þ 1Þ £ dt ½a 2 ða þ 1Þebt 2

1 2 e2ðcþdÞt c 1 þ e2ðcþdÞt d dFI!k!x ðtÞ fI!k!x ðtÞ ¼ dt FI!k!x ðtÞ ¼

¼

ðc þ dÞ2 £  d

ð21Þ ð22Þ

e2ðcþdÞt 2 c 1 þ e2ðcþdÞt d

ð23Þ

Accordingly, the relationship between SðtÞ and YsðtÞ is given in Eq. (24). SðtÞ ¼ Kmax £ fk!x ðtÞ þ Imax £ fI!k!x ðtÞ

where

2 ¼ Kmax £ ðaFk!x ðtÞ 2 bFk!x ðtÞÞ þ Imax

parameter ‘a’ represents the usage of knowledge results in the externalization effects of enterprise benefits parameter ‘b’ represents the knowledge depreciation parameter ‘c’ represents the externalization effects of enterprise benefits generated by the knowledge expansion parameter ‘d’ represents the innovative effects of enterprise benefits generated by the knowledge expansion due to continuous investment.

2 £ ð2cFI!k!x ðtÞ þ ðc 2 dÞFI!k!x ðtÞ þ dÞ 2 ðtÞ 2 b £ Kmax £ Fk ðtÞ 2 c ¼ a £ Kmax £ Fk!x 2 £ Imax £ FI!k!x ðtÞ þ ðc 2 dÞ £ Imax £ FI!k!x ðtÞ

þ d £ Imax ¼

Eqs. (12) and (13) lead to the differential Eqs. (14) –(17). dFk!x ðtÞ 2 fk!x ðtÞ ¼ ¼ aFk!x ðtÞ 2 bFk!x ðtÞ dt 1 dFk!x ðtÞ ¼ dt 2 aFk!x ðtÞ 2 bFk!x ðtÞ fI!k!x ðtÞ ¼

1 dFI!k!x ðtÞ ¼ dt 2 ðtÞ þ ðc 2 dÞFI!k!x ðtÞ þ d 2 cFI!k!x

b að1 2 ebðtþn1Þ Þ

FI!k!x ðtÞ ¼

1 c 2 de2ðcþdÞðtþn2Þ £ c ð1 þ e2ðcþdÞðtþn2Þ Þ

c Imax

2 £ YI!k!x ðtÞ þ ðc 2 dÞ £ YI!k!x ðtÞ þ d £ Imax

ð24Þ

Based on the above, the total contribution of enterprise benefits by knowledge K in the ð0; tÞ interval is as follows:

ð15Þ

YsðtÞ ¼ YK!X ðtÞ þ YI!K!X ð1Þ

ð25Þ

where

ð16Þ ð17Þ

Because aFk!x 2 b . 0; the solution of Eqs. (15) and (17) can be obtained as Eqs. (18) and (19), respectively. Fk!x ðtÞ ¼

Kmax

2 £ Yk!x ðtÞ 2 b £ Yk!x ðtÞ 2

ð14Þ

dFI!k!x ðtÞ dt

2 ¼ 2cFI!k!x ðtÞ þ ðc 2 dÞFI!k!x ðtÞ þ d

a

ð18Þ ð19Þ

YK!X ðtÞ represents the total increased enterprise benefits during the ð0; tÞ interval generated by using the original knowledge K: YI!K!X ð1Þ represents the total increased enterprise benefits during the ð0; tÞ interval generated by the increment of the original knowledge K from investment. Assumed that during the ð0; tÞ interval, Eq. (26) represents the likelihood of the incremental knowledge value generated by the portion that enterprise benefits have not yet transformed back to knowledge K: rðtÞ ¼

fx!k ðtÞ ¼ eFx!k ðtÞ þ f 1 2 Fx!k ðtÞ

ð26Þ

V.B. Kreng, C.M. Tsai / Expert Systems with Applications 25 (2003) 177–186

dFx!k ðtÞ 2 ¼ 2eFx!k ðtÞ þ ðe 2 f ÞFx!k ðtÞ þ f dt 1 dFx!k ðtÞ ¼ dt 2 2 eFx!k ðtÞ þ ðe 2 f ÞFx!k ðtÞ þ f

fx!k ðtÞ ¼

Fx!k ðtÞ ¼

1 e 2 f e2ðeþf Þðtþn3Þ £ e ð1 þ e2ðeþf Þðtþn3Þ Þ

ð27Þ ð28Þ ð29Þ

where parameter ‘e’ represents the internalization of knowledge value used by enterprise benefits parameter ‘f’ represents the learning effects of knowledge Because of Fx!k ðt ¼ 0Þ ¼ 0 and n3 ¼ 2ð1=e þ f Þlnðe=f Þ; Fx!k ðtÞ and fx!k ðtÞ can be found as follows: Fx!k ðtÞ ¼

fx!k ðtÞ ¼

1 2 e2ðeþf Þt e 1 þ e2ðeþf Þt f

ð30Þ

dFx!k ðtÞ ðe þ f Þ2 e2ðeþf Þt ¼ £   dt f e 2ðeþf Þt 2 1þ e f

ð31Þ

According to the above, the relationship between VðtÞ and Yv ðtÞ can be obtained in the following. VðtÞ ¼ Xmax £ fx!k ðtÞ 2 ¼ Xmax £ ð2eFx!k ðtÞ þ ðe 2 f ÞFx!k ðtÞ þ f Þ 2 ðtÞ þ ðe 2 f Þ £ Xmax £ Fx!k ðtÞ ¼ 2e £ Xmax £ Fx!k

þ f £ Xmax ¼2

e Xmax

£ Yv2 ðtÞ þ ðe 2 f Þ £ Yv ðtÞ þ f £ Xmax

ð32Þ

Since only a=Kmax can be found while estimating parameters, Eq. (33) is again used to obtain Kmax and to get the parameter a: Finally, all of the parameters in the model can be estimated. ð1 Xmax ¼ Xð0Þ þ SðtÞ dt 0

¼ Xð0Þ þ Kmax

ð1 0

fk!x ðtÞdt þ Imax

¼ Xð0Þ þ Kmax þ Imax

ð1 0

fI!k!x ðtÞ ð33Þ

4. Case study 4.1. Introduction to UPEC The Uni-President Enterprise Corporation (UPEC) established in 1967 is the largest public food company in

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Taiwan nowadays. The UPEC has over 50% market share of Taiwan in the instant noodle category, and has over 30 years experience in production. The UPEC’s products line-up outside of instant noodles and cover virtually every major food and beverage category, including dairy, meat, bakery, cereals, snacks, juice products, and edible oils. The UPEC also produces animal and aquatic feeds, tin plate, rubber products … and more. In addition, the UPEC conducts many other businesses including securities, hotels, real estate, construction, and commercial banking. Under the strategy of high growth and diversification, the UPEC vigorously cooperates with European, American, and Japanese enterprises in technology. The total turnover of the whole corporation goes beyond NT 180 billion dollars, and its average growth rate maintains about 7%. Under the strategic guidance of quality and service, the UPEC set up Quality Control Circle (QCC) committee in 1970 to promote a series of QCC activities. The UPEC has promoted more than 180 QC circles so far, and the participation rate of the staff is more than 70%, which nearly create a profit of NT $500 million. Table 1 shows the history of UPEC QCC system, which can be divided into five major periods. The aim of promoting QCC system by the UPEC is to cultivate the spirit of self-management, to innovate and improve operation, to boost morale of the staff, and to achieve the mutual goal of enterprise. Owing to the introduction of QCC system, over 16000 improvement projects have been proposed until 2000. In addition, the QCC system also obtains positive benefits in talent cultivation of enterprises, technology improvement, customer satisfaction, and enterprise image. Table 2 lists the costs and benefits of the QCC system promoted by the UPEC from 1970 to 2000. 4.2. Construct the knowledge diffusion model The QCC system plays a vital role in the growth of the UPEC. In order to explore the intangible knowledge value, this study uses the enterprise benefits by UPEC promoting the QCC system to find out the value of QCC core knowledge, which is continuous innovation and improvement. In addition, the relationship between enterprise benefits and knowledge value can also be found by constructing the knowledge diffusion model mentioned in Section 3. Since the QCC system has been adopted for more than 20 years, it has already experienced the periods of introduction, growth and stagnation. In 1991, the introduction of new knowledge renovated the original QCC core knowledge transformed from stagnation to breakthrough. Since substitution between original knowledge and new knowledge are not considered in this model, the period of the UPEC promoting the QCC system from 1980 to 1991 is, then, adopted to construct the knowledge diffusion model. The relevant information is illustrated in Table 3.

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Table 1 The history of the QCC system promoted by the UPEC (Lee, 1998) Periods

Years

Relevant activities

Introduction

1970– 1984

Growth

1984– 1988

Stagnation

1988– 1991

Breakthrough

1991– 1996

Stable growth

1996-today

Establish QCC systems and introduce QCC knowledge About 70–100 circles and 50% of employees’ participation Strengthen education and training so as to cultivate QCC talents inside the UPEC Spread QCC activities to sales and service department Take part in domestic and overseas QCC conference About 110– 260 circles and 65% of employees’ participation Continuously take part in domestic and overseas QCC conference About 110– 120 circles and 55% of employees’ participation Introduce new QC concept and system into UPEC Engage professors as consultants Execute self-assessment and raise reward Continuously take part in domestic and overseas QCC conference About 120– 140 circles and 60% of employees’ participation Expand education and training of QCC Extensively take part in domestic and overseas QCC conference and publish their achievements About 150– 170 circles and 70% of employees’ participation

SðtÞ represents the newly increased enterprise benefits by promoting the QCC system in the particular year. Since enterprise benefits can be beneficial from the use of both original knowledge and new investment, SK!X ðtÞ and SI!K!X ðtÞ; respectively, represent the contribution on enterprise benefits generated by the use of original knowledge and the increment of the original knowledge after investment. According to the ABC model, correlation between enterprise benefits and knowledge value can be

found. While estimating all the parameters from discrete time series data, the following analogue are given in Eqs. (34) and (35). 2 ðt 2 1Þ 2 b £ Yk!x ðt 2 1Þ 2 d SðtÞ ¼ a £ Yk!x 2 £ YI!k!x ðt 2 1Þ þ l £ YI!k!x ðt 2 1Þ þ r

VðtÞ ¼ 2h £ Yv2 ðt 2 1Þ þ m £ Yv ðt 2 1Þ þ u

ð34Þ ð35Þ

Table 2 The costs and benefits of the QCC system (Wu, 2000) Year

QCC circles

Members

Participation rate (%)

Completed subjects

Presented projects

Expenses (NT million dollars)

Benefits (NT million dollars)

1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 Total

84 80 80 91 125 254 277 262 152 116 111 106 121 117 127 138 132 137 147 150 175

693 733 810 941 1348 2444 2691 2550 1528 1226 1199 1155 1253 1186 1331 1428 1411 1468 1681 1723 1953

41.4 41.6 47.6 54.4 54.4 59.2 65.5 70.5 52.3 58.0 58.0 54.3 54.2 49.2 52.7 57.6 58.2 68.0 80.3 78.7 71.5

166 157 159 181 249 501 544 517 249 231 221 205 237 233 252 275 264 274 292 299 346 5884

76 53 69 104 203 722 1105 1378 670 582 647 729 975 1060 1210 1141 1073 990 1037 1121 1073 16018

0.390 0.613 0.630 0.825 0.737 1.385 1.686 0.755 0.805 1.655 1.502 1.462 1.598 2.002 2.264 2.370 2.476 2.500 2.772 2.672 2.453 35.453

21.000 22.180 14.040 23.280 23.280 27.600 33.680 26.460 17.550 17.737 24.426 16.887 31.273 26.740 16.541 20.881 19.382 22.219 26.818 37.830 45.865 496.679

V.B. Kreng, C.M. Tsai / Expert Systems with Applications 25 (2003) 177–186 Table 3 The data of SðtÞ; SK!X ðtÞ; SI!K!X ðtÞ and VðtÞ from 1980 to 1991 in UPEC Year

1980 ðt 1981 ðt 1982 ðt 1983 ðt 1984 ðt 1985 ðt 1986 ðt 1987 ðt 1988 ðt 1989 ðt 1990 ðt 1991 ðt

¼ 0Þ ¼ 1Þ ¼ 2Þ ¼ 3Þ ¼ 4Þ ¼ 5Þ ¼ 6Þ ¼ 7Þ ¼ 8Þ ¼ 9Þ ¼ 10Þ ¼ 11Þ

SðtÞ (NT million dollars)

SK!X ðtÞ (NT million dollars)

SI!K!X ðtÞ (NT million dollars)

VðtÞ (NT million dollars)

21 22.18 14.04 23.28 23.28 27.6 33.68 26.46 17.55 17.737 24.426 16.887

19.95 19.962 11.934 18.624 17.46 19.32 25.26 19.845 14.04 14.1896 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

5.25 6.654 4.914 9.312 11.64 16.56 25.26 21.6972 15.444 16.31804 23.44896 16.71813

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Table 5 The regression results of SðtÞ 2 2 Model: SðtÞ ¼ a £ Yk!x ðt 2 1Þ 2 b £ Yk!x ðt 2 1Þ 2 d £ YI!k!x ðt 2 1Þ þ l £ YI!k!x ðt 2 1Þ þ r Final loss: 128.69130538 R2 ¼ 0:77479 Variance explained: 60.029%

Estimates

Parameters

a ¼ 0:003425 b ¼ 0:585225 d ¼ 0:063749 l ¼ 2:568663 r ¼ 28:72052

Imax ¼ 49:41125 c ¼ 3:14992 d ¼ 0:58125 Kmax ¼ 138:547 a ¼ 0:47452 b ¼ 0:585225

4.3. Predict the change between SðtÞ and VðtÞ in the future where

d¼

c Imax

r ¼ d £ Imax l ¼ c 2 d ¼ d £ Imax 2

r Imax

pffiffiffiffiffiffiffiffiffiffiffiffi l ^ l2 þ 4dr Imax ¼ 2d pffiffiffiffiffiffiffiffiffiffiffiffi m ^ m2 þ 4hu Xmax ¼ 2h Tables 4 and 5 illustrate the regression results and all the parameters of the model. The R2 values of the VðtÞ and SðtÞ model are 0.82368 and 0.77479, respectively, which indicate that such model describes VðtÞ and SðtÞ rather well. In addition, the results demonstrate that the model is suitable to represent the dynamic relationship between knowledge value and enterprise benefits. Furthermore, the parameter estimates seem reasonable for the model as well. According to the models, the actual and predicted values are compared and shown in Figs. 3 and 4.

In Section 4.2, every parameter in knowledge diffusion model can be effectively estimated based on the historical information. As a result, the QCC core knowledge still belongs to the period of stable growth inside UPEC after 1996, which does not yet experience the recession period. Accordingly, a prediction model have to be obtained to further an effective strategy to cope with the changes of knowledge value. In the process of estimation, the bias has to be added to the prediction model in order to close to reality (Bass, 1969). According to the above knowledge diffusion model, after adding the bias, the prediction models, SK!X ðtÞ; SI!K!X ðtÞ; and VðtÞ; have been transformed into Eqs. (36) and (37). 2 SðtÞ ¼ a £ 121 £ Yk!x ðt 2 1Þ 2 b £ 11 £ Yk!x ðt 2 1Þ 2 d 2 £ 122 £ YI!k!x ðt 2 1Þ þ l £ 12 £ YI!k!x ðt 2 1Þ þ r 2 ¼ a0 £ Yk!x ðt 2 1Þ 2 b0 £ Yk!x ðt 2 1Þ 2 d0 2 £ YI!k!x ðt 2 1Þ þ l0 £ YI!k!x ðt 2 1Þ þ r

ð36Þ

VðtÞ ¼ 2h £ 123 £ Yv2 ðt 2 1Þ þ m £ 13 £ Yv ðt 2 1Þ þ u Table 4 The regression results of VðtÞ

¼ 2h0 £ Yv2 ðt 2 1Þ þ m0 £ Yv ðt 2 1Þ þ u

Model: VðtÞ ¼ 2h £ Yv2 ðt 2 1Þ þ m £ Yv ðt 2 1Þ þ u Final loss: 142.46555312 R2 ¼ 0:82368 Variance explained: 67.844% Estimates

Parameters

h ¼ 0:001768 m ¼ 0:348514 u ¼ 4:37215

Xmax ¼ 208:958 e ¼ 0:36944 f ¼ 0:02092

Fig. 3. The actual and predicted values of VðtÞ:

ð37Þ

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Thus, 1=1i can be obtained as follows:

Fig. 4. The actual and predicted values of SðtÞ:

Table 6 The data of SðtÞ SK!X ðtÞ SI!K!X ðtÞ and VðtÞ from 1997 to 1999 in UPEC Year

1997 ðt ¼ 0Þ 1998 ðt ¼ 1Þ 1999 ðt ¼ 2Þ

SðtÞ (NT million dollars)

SK!X ðtÞ (NT million dollars)

SI!K!X ðtÞ (NT million dollars)

VðtÞ (NT million dollars)

22.219 26.818 37.830

19.997 22.795 31.072

2.222 4.023 6.758

10.079 17.786 28.240

1 b 1 ¼ £ lnð1 2 b0 Þ ¼ 11 2 b0 ð1 2 e2b Þ

ð38Þ

1 cþd 1 ¼ ðcþdÞ £ lnðc0 þ d0 þ 1Þ ¼ 0 12 c þ d0 2 1Þ ðe

ð39Þ

1 eþf 1 ¼ ðeþf Þ £ lnðe0 þ f 0 þ 1Þ ¼ 0 13 e þ f0 2 1Þ ðe

ð40Þ

Table 6 illustrates the information of UPEC promoting the QCC system from 1997 to 1999. All equations can be established by Eqs. (36) and (37), and the solutions are shown in Table 7. Sk!xð0Þ ¼ 22:795 ¼ 399:88 £ a0 2 19:997 £ b0 Sk!x ð1Þ ¼ 31:072 ¼ 1831:156 £ a0 2 42:792 £ b0 SI!k!x ð0Þ ¼ 2:222 ¼ r SI!k!x ð1Þ ¼ 4:023 ¼ 24:937 £ d0 þ 2:222 £ l0 þ r SI!k!x ð2Þ ¼ 6:758 ¼ 239:0 £ d0 þ 6:245 £ l0 þ r Vð0Þ ¼ 10:079 ¼ u

where

Vð1Þ ¼ 17:786 ¼ 2101:586 £ h0 þ 10:079 £ m0 þ u

Yðt þ 1Þ 1i ¼ YðtÞ

Vð2Þ ¼ 28:24 ¼ 2776:458 £ h0 þ 27:865 £ m0 þ u

For any probability distribution, 1 can be estimated by 1=1 ¼ f ðtÞ=Fðt þ 1Þ 2 FðtÞ: For small value of t; every parameter has to be revised after introducing the bias 1i :

a0 ¼ a £ e 21 ;

b0 ¼ b £ e 1 ;

l0 ¼ l £ e 2 ;

h0 ¼ h £ e 23 ; m0 ¼ m £ e 3

a Kmax c¼

¼

a0 1 £ 2; K 0max 11

c0 ; 12

d¼

Xmax ¼ X 0max £ 13 ;

b¼

d0 ¼ d £ e 22 ;

b0 ; 11

Imax ¼ I 0max £ 12 ;

d0 12

e¼

e0 ; 13

f ¼

f0 13

According to Eq. (33), Kmax ¼ 118:583: Then, parameter a is equal to 2 0.804. Since all the parameters appear plausible, SðtÞ and VðtÞ from 1997 to 2004 are shown in Table 8 and Fig. 5. Based on the predictive results, the externalization of enterprise benefits by the QCC core knowledge is expected to reach its climax in 2001. Afterward, swiftly declining tendency will appear. Thus, UPEC has to introduce or develop a substitutional knowledge as soon as possible to maintain its competitiveness, and to prevent from reducing enterprise benefits massively due to knowledge depreciation. Further compared with the situation from 1980 to 1991, the life cycle of knowledge becomes obviously shorter. For enterprises, the growth and use of knowledge can create enormous enterprise benefits in the short-term, but the knowledge will decline quickly and lead to the recession period. From states that 1980 to 1991, the model demonstrates that UPEC still have a 5-year buffer zone

Table 7 The solutions of all the parameters Estimates

Parameters

1=e i

Estimates

Parameters

a0 ¼ 20:0182 b0 ¼ 21:503 d0 ¼ 0:0209 l0 ¼ 0:8570 r ¼ 2:222 h0 ¼ 0:00635 m0 ¼ 0:8287 u ¼ 10:079

a0 =K 0max ¼ 20:0182 b0 ¼ 21:503 I 0max ¼ 43:452 c0 ¼ 0:9081 d0 ¼ 0:0511 X 0max ¼ 141:702 e0 ¼ 0:8998 f 0 ¼ 0:0711

1=11 ¼ 0:6104

a ¼ 20:00678 b ¼ 20:9174 d ¼ 0:0103 l ¼ 0:6009 r ¼ 2:222 h ¼ 0:0031 m ¼ 0:5791 u ¼ 10:079

a=Kmax ¼ 20:00678 b ¼ 20:9174 Imax ¼ 61:971 c ¼ 0:6368 d ¼ 0:0358 Xmax ¼ 202:773 e ¼ 0:6288 f ¼ 0:0497

1=12 ¼ 0:7012

1=13 ¼ 0:6988

V.B. Kreng, C.M. Tsai / Expert Systems with Applications 25 (2003) 177–186 Table 8 The SðtÞ and VðtÞ resulted from the knowledge diffusion model Year

1997 ðt 1998 ðt 1999 ðt 2000 ðt 2001 ðt 2002 ðt 2003 ðt 2004 ðt

¼ 0Þ ¼ 1Þ ¼ 2Þ ¼ 3Þ ¼ 4Þ ¼ 5Þ ¼ 6Þ ¼ 7Þ

SðtÞ (NT million dollars)

SK!X ðtÞ (NT million dollars)

SI!K!X ðtÞ (NT million dollars)

VðtÞ (NT million dollars)

22.219 26.818 37.830 51.668 55.883 40.417 17.995 6.546

19.997 22.795 31.072 43.049 45.337 29.597 9.274 1.273

2.222 4.023 6.758 8.619 10.546 10.820 8.721 5.273

10.079 17.786 28.240 32.811 37.061 33.834 23.452 12.091

against knowledge depreciation, which the enterprise benefits created by the knowledge can manage to maintain 50% from the peak of the whole period after 5 years. However, in the prediction from 1997 to 2004, enterprises will only have less than three-year buffer zone to maintain 11.7% of enterprise benefits from its peak of the whole period after 3 years. Such phenomena demonstrate that the speed of knowledge change and diffusion will become faster and faster. Therefore, only if enterprises and individuals can continuously learn and grow, they can still maintain the competitiveness with time. Finally, by means of the knowledge diffusion model proposed, the parameters of UPEC promoting the QCC system from 1980 to 1991 and from 1997 to 1999 are shown in Table 9. For the reason that other enterprises have extensively adopted and practiced the QCC core knowledge, the Kmax and Xmax of the knowledge from 1997 to 2004 is, therefore, lower than those from 1980 to 1991. In order to innovate and develop the nearly mature QCC core knowledge, UPEC have to devote more resources than ever to maintain its competitiveness. The parameters ‘a’ and ‘b’ will become negative from 1997 to 2004, which demonstrates that new knowledge is very difficult to be copied by others. As a result, the new QCC core knowledge won’t suffer depreciation in the beginning, however, it will gradually depreciate because of knowledge diffusion. In addition, the parameters ‘c’ and ‘d’ appear sharp falling tendency from 1997 to 2004, which implicates that the activities of inside knowledge innovation have reached their limits. Without outside assistance, UPEC has to make extraordinary effort to keep pace with the speed of change by vigorously

Fig. 5. The SðtÞ and VðtÞ resulted from the knowledge diffusion model.

185

Table 9 The parameters of UPEC promoting the QCC system from 1980 to 1991 and from 1997 to 2004

Kmax a b Imax c d Xmax e f

1980–1991

1997–2004

138.547 0.47452 0.585225 49.41125 3.14992 0.58125 208.958 0.36944 0.02092

118.583 20.804 20.9174 61.971 0.6368 0.0358 202.773 0.6288 0.0497

introducing new knowledge. At last, contrary to the parameters ‘c’ and ‘d’, ‘e’ and ‘f’ considerably climb from 1997 to 2004, which is mainly beneficial from the abilities to accept and learn new knowledge. Such tendency also demonstrates that UPEC successfully transformed from external knowledge into internal knowledge. Therefore, managers can use parameters ‘e’ and ‘f’ to compare learning abilities of different knowledge during different periods inside enterprises, and further develop an index to measure its abilities.

5. Conclusion In the era of knowledge economy, knowledge assets have become one of the important factors towards enterprise competitiveness. However, the measurement and management of knowledge assets are still limited. This study presents an ABC-based approach combined with the product diffusion model to construct the knowledge diffusion model. By improving the drawbacks of the ABC model only statically demonstrating enterprises knowledge value, the proposed model can assist enterprises to measure and predict the dynamic relationship between enterprise benefits and knowledge values as well. Finally, according to the findings provided by the knowledge diffusion model, a set of effective knowledge management strategies can be developed to enhance competitiveness of enterprise. Since the ABC model measures the value of every knowledge item of enterprises process, the calculation of knowledge value has to, therefore, focus on process. Such measurement over process will also help enterprise decide the policy on process reengineering and to further construct the best business process from the viewpoint of knowledge value. According to the case study of UPEC, the knowledge diffusion model proposed is suitable to describe the dynamic relationship between knowledge value and enterprise benefits because the R2 values of the VðtÞ and SðtÞ are acceptable. Based on the data analysis of UPEC from 1980 to 1991 and from 1997 to 2004, the diffusion rate tends to become faster and faster. For the UPEC, this model can

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effectively predict the life cycle of knowledge changes. Besides, parameters in knowledge diffusion model can also reflect how knowledge works in UPEC, and the change of parameter value in different periods can also demonstrate the performance of executing knowledge management. Finally, the knowledge diffusion model only emphasizes on how a single knowledge can influence the enterprise benefits. However, multiple items of knowledge are normally developed within enterprise at the same time. In addition, there are sometimes mutual multiplication, curtailment, and substitution among them. How to bring those facts into the knowledge diffusion model will be one of directions in the future. Because every parameter in knowledge diffusion model has its own meaning, it’s a tough task to optimize all parameters concurrently. Hence, comparing with various knowledge strategies to find the optimal is necessary to obtain the maximum enterprise benefits.

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