- Email: [email protected]
A goal compatibility model for technology transfers
Appl. Math. Lett. Vol. 28, No. 9, pp. 91-103, @ 1998 Elsevier
1998
ScienceLtd. All rights reserved Printed in Great Britain
PII: SO8957177(98)00147-2
0893-9659/98 $19.00 + 0.90
A Goal Compatibility Model for Technology Transfers C. N. MADU Department of Management and Management Science Lubin School of Business, Pace University 1 Pace Plaza, New York, NY 10038, U.S.A. CHINHO LIN Graduate School of Industrial Management National Cheng Kung University Tainan, Taiwan, ROC C.-H. KUEI Department of Management and Management Science Lubin School of Business, Pace University 1 Pace Plaza, New York, NY 10038, U.S.A. (Received September
1996; accepted May 1997)
Abstract-In this paper, we present a minimization approach to goal incompatibility in technology transfers especially to less developed countries. The proposed model is based on a need-capability assessment for alternative technologies for transfer, and then, minimizing the distance between need and capability to achieve goal compatibility. By transferring technologies with minimum deviation between an LDC’s needs and capabilities, appropriate technologies could be transferred. A fuzzy theory is used in this mode to avoid errors which are often made in using subjective judgment. An input-output matrix and budgetary constraints are integrated into the model to determine the allocation of development funds to alternative technologies. A LINDO software is used to solve the problem. @ 1998 EleevierScienceLtd. All rights reserved. Keywords-Technology transfer, Appropriate number, Nonsymmetrical
technology,
Goal compatibility,
Triangular
fuzzy
fuzzy linear programming.
INTRODUCTION In this paper, we present a model to achieve goal compatibility
in the transfer of technology to Less Developed Countries (LDCs). Goal compatibility, in this contest, deals with the transfer of appropriate technologies. Appropriate technology is a transferred technology that helps a LDC to meet its needs, given its capabilities. It is, therefore, necessary to transfer those technologies that show the minimum deviation between an LDC’s needs and its capabilities. Madu and Jacob [l] discussed the issue of goal compatibility between the recipient and the transfer or of technology. They note that it is necessary to achieve reasonable compatibility between them in order to successfully transfer technology. The absence of goal compatibility leads to failures in technology transfers. However, goal incompatibility can exist if a technology that does not meet the needs or the capabilities of an LDC is transferred. Madu [2] presented critical success factors for technology transfers and notes that appropriate technologies should be able to utilize the existing capabilities of the LDCs to satisfy their needs.
%=et 91
by 44-W
92
C. N.
MADIJ et al.
Madu [3] developed a need-capability assessment matrix to identify which technologies an LDC should focus on in achieving its socio-economic development goals. However, knowing that many technologies or industries are mutually dependent on each other, LCDs need a model that should minimize goal incompatibility and allow them to develop a portfolio for technology transfer. In a recent article, Madu and Madu [4] presented a systems model for transferring mutually dependent technologies. However, they did not address the issue of goal incompatibility between the needs and capabilities of an LDC. This paper explicitly models goal incompatibility and considers it in allocating resources to mutually dependent technologies.
RESEARCH
BACKGROUND
The technology transfer literature is rich in conceptual frameworks [2,5,6], but only very few models exist and many of these do not consider planning issues but focus purely on economic modeling [7,8]. Technology transfer studies often address issues such as the inappropriateness of technology transfers [5,9], economic implications [lO,ll], cultural, ethical, and psychological issues (1,12-151. Only recently were planning issues discussed [1,3,4,16]. Yet, there are very few mathematical models to guide the policy making that is involved. The lack of such models is partly due to the fact that technology transfer decisions are not purely objective and, therefore, cannot be easily quantified. However, there exists in the operational research literature, methods to reasonably address some aspects of the technology transfer policy making problems [17]. Madu [2] presented a detailed literature review on technology transfer. Obvious from this review is the need for planning models, especially in deciding which technologies to transfer and the resources to be allocated to them. Ramanujam and Saaty [6] used the analytic hierarchy process to analyze technological choice in less developed countries. However, their model did not deal with resource allocation to mutually dependent technologies. Madu and Madu [4] extended this work by taking a holistic view of technology transfer and integrating technological resource allocation decisions in satisfying the LDC’s socio-economic goals. A linear programming model was formulated and used to solve this problem. Madu [18] identified three main causes of failure in technology transfers, namely, structural, behavioral, and technological. Other works have used cognitive mapping and influence diagramming to analyze potential failures of technology transfers [1,12,15,19]. Notable among these is the work of Madu and Jacob [l], where the Dialectical Materialism Inquiry System (DMIS) was used to analyze the contradictory goals of both the transferor and the recipient df technology. It is noted in this study that conflict exists between the transferor and the receiver of technology, however, productive conflicts support the effective transfer of technologies. While several of these studies have identified and analyzed problems in the transfer process, only the work by Madu and Madu [4] presented an explicit mathematical model to plan the transfer of technologies to LDCs in order to satisfy their socioeconomic goals. Specifically, their paper identified the criteria that influence technology transfer decisions, prioritized them in terms of achieving the socio-economic goals of the LDC, and used the priority indices to normalize an input-output matrix. Consequently, a LP model was developed and solved to determine the allocation of limited resources to mutually dependent technologies. The present paper is significantly different from the work by Madu and Madu [20] in the following ways. (1) The objective of the paper is to minimize the goal incompatibility that exists in the transfer of technology by matching an LDC’s needs to its capabilities. To achieve this, a need-capability assessment matrix is used. The objective in Madu and Madu [20] WBSto maximize an LDC’s social welfare and there was no consideration of goal incompatibility. On the other hand, the aim of the present paper is to provide a method through which appropriate technologies could be transferred by minimizing the deviations between a LDC’s needs and its capabilities.
Goal Compatibility Model
(2) In
order to achieve its stated objective,
93
Madu and Madu [20] used a multicriteria
namely, the Analytic Hierarchy Process (AHP) to develop priorities for the criteria.
model, There
are no criterion explicitly discussed in this paper, but they can be integrated into the needcapability
assessment matrix.
Furthermore,
AHP is not used in this paper.
In the next section we shall introduce the need-capability
NEED-CAPABILITY
ASSESSMENT
assessment matrix.
MATRIX
(NCAM)
The NCAM was developed by Madu [3] to match a LDC’s needs to its capabilities
for a
given technology. Through this matrix, a LDC can position itself in terms of its technological capabilities. The basic concept of this matrix is laid out in Figure 1. This figure is a 3 x 3 matrix with three dimensions for both the needs and the capabilities:
low (L), medium (M),
and high (H). For any given technology, a LDC should position itself on the matrix in order to evaluate the suitability of the technology. It is apparent from this matrix that there are nine possible positions that a LDC may find itself in with regards to a particular technology. The relative importance of these positions is shown using a scale. For example, a scale of 1 shows an undesirable position, while a scale of 9 shows a highly desirable position. A desirability measure for each cell of the matrix is obtained by assuming that the values assigned to both needs and capabilities are multiplicative, thereby allowing for the possibility of synergy. It is, therefore, clear from this matrix that the desirability for a technology goes up as both the needs and capabilities for that technology increase. Prioritization of Need-CapabilityAssessmentMatrix Needs i
Low
Medium
High
Low-
Capabilities Medium
High
Scale 1 2 3 6 9
2
4
6
3
6
9
Statement of Importance Undesirable Least Desirable Desirable Very Desirable Highly Desirable
Figure 1. The arrowsshow the movementof resources from technologieswith lower to those with higher needs. This assumesthat capabilities are transferable. The NCAM matrix can be used in two phases. The first phase will be to identify technologies that have “acceptable” desirability indices, for example, 4, 6, and 9. The second phases will be to use the matrix for resource allocation decisions to the different technologies selected for Phase 1. Figure 2 gives further definitions of the position an LDC can find itself in. Phase 2 is a pragmatic way of assessing the needs and capabilities of LCDs. Many policy making issues involving technology transfers involve multiple players which we refer to a stake-
C. N. MADU
et al.
Needs Low
Medium What are the potentials of developing the capabilities?
Can appropriate capabilities be developed to satisfy the high demand? Potential problem area. Should be given adequate attention.
What are the potentials of exporting the capabilities? Can internal needs be generated?
Capabilities can be used to satisfy the moderate needs. The existing capabilities are just enough to satisfy existing needs.
Higher needs can be satisfied if capabilities are further developed.
Are there external markets to absorb the excess output? Can internal needs be generated to exploit the high capabilities?
Generate output to satisfy the moderate consumption. If external markets exist ship the excess output. Apply capabilities to other areas if possible.
Highly desirable. Ds mand and capabilities are fully developed.
LOW
Capabilities
Medium
High
High
Undesirable, should not be emphssized.
Figure 2. Need-capability
amassment matrix.
holders. These stakeholders are the active participants in technological decisions [21]. By being active participants, their actions and reactions significantly influence the successful transfer of technology. The stakeholders are charged with identifying the specific needs of the LDC, which, of course, may have internal and external components. They also match these needs to capabilities that will make it easier to implement the technology. Several list of needs and capabilities could be generated. However, through group decision support systems and the application of Delphi-type techniques [2], reasonable decisions on the importance of any need or capability could by reached. In thii paper, we recommend the use of a scale of 0 to 10 to denote the importance of each technology type in relation to the needs and capabilities of the LDC.
SIMPLE
FUZZY
SET THEORY
The first publications in fuzzy set theory is by Zadeh [22]. Zadeh writes: ‘the notion of fuzzy set provides a convenient point of departure for the construction of a conceptual framework which parallels in many respects the framework used in the csse of ordinary sets, but it is more general than the latter and, potentially, may prove to have a much wider scope of applicability, particularly in the fields of pattern classification and information processing”. Essentially, such a framework provides a natural way of dealing with problems in which the source of imprecision is the absence of sharply defined criteria of class membership rather than the presence of random variables. So, fuzzy set theory provides a strict mathematical framework in which vague concep tual phenomena can be precisely and rigorously studied. It can also be considered as a modeling language well suited of situations in which fuzzy relations, criteria, and phenomena exist. Next part, we will introduce some tools about fuzzy set theory we use in this paper. Triangular
Fuzzy
Number
In thii paper, we will make use of the concept of fuzzy set theory. Namely, we will give a fuzzy number to the different views of the stakeholders on different criteria in order to integrate each stakeholder’s opinion precisely.
Goal Compatibility Model
95
Dubois and Prade [23] defined a fuzzy number and describe its meaning and features. A fuzzy number A is a fuzzy set which membership function is PA(Z) : R --t [0, 11,and its character is: (1) p~ (z) is continuous; (2) PA(Z) is a convex fuzzy set; (3) it exists exactly zc E R with PA
= 1.
Triangular fuzzy number PA(Z) = (I, m,u) can conform to the above-mentioned Figure 3), and its membership function is:
I PA(X)=
(x - 1)
terms (see
l
m-l’
(x - ?J)
m
<
x
<
‘1L
--’
m-_21’
(1)
other.
0,
Figure 3. Triangular fuzzy number. DEFINITION. A, = {x 1 PA(Z) 2 u} a E [0,11, that fuzzy number A whose confidence interval A, at a- level can be stated
A, =
M,Gl
(2)
af and a$ mean the upper and lower boundaries of confidence interval. Kaufmann and Gupta [24] use the concept of a-cut and extension principle [22]. If trianguiar fuzzy number A and fi whose confidence interval are A, and B, at a-level, in which A, = [a?, a$], B, = [bp, b$], then the fuzzy number operation are: 1. addition
A,(+)B,
= [a? + br,a$ + b$] ;
(3)
AJ-)Bo
= [a? - bg,a; - by];
(4)
2. subtraction
3. multiplication Aa(.)Ba = [ayby, a:b:] ; 4. division Aa(:
=
[ 1. g,
2
2
1
(5)
(6)
Defussication
Determination of the best crisp value under a fuzzy membership function includes mean-ofmaxima and center-of-area methods. The former is to select a nonfuzzy value which corresponds to the maximum value of the membership function, averaging in some ways when there are many
C. N. MADIJ
96
et al.
values. The latter is to choose a value which equally divides the area under the membership function curve. Furthermore, some a values must be decided by the decision-makers or all members of the decision-making group, and it is not easy to decide such value (see [25]). In this paper, we make use of the triangular fuzzy number to deal with stakeholders’ opinions. The weights after integrating many stakeholders’ opinions are still triangular fuzzy numbers. The defuzzication method we used was developed by Tzeng and Teng [25]. The conception of this method was derived from the center-of-area methods. If there is a triangular fuzzy number whose membership function is (x - 1) l
(x--1,
m
m--‘L1
-
’
-
other.
0, Then the best crisp performance value will be DFi
Ku- 1)+ cm - 01
=
3+1 Nonsymmetrical
Fuzzy
*
(7)
LP
A model in which the objective function is crisp, that is, has to be maximized or minimized and in which the constraints are all or partially fuzzy is no longer symmetrical [26]. The problem we are faced with is the determination of an extremum of a crisp function over a fuzzy domain. So we can’t use the biggest fuzzy membership function value or the intersection of fuzzy objective function and fuzzy constraint. Zimmermann proposed that we can use the following method to solve this kind of problem. If there is a model of linear programming, it can be stated as max
f(x) = cT(x),
s.t.
Ax += b, DxIb, x > 0.
Here += denotes the fuzzified version of 5 and has the linguistic interpretation smaller than or equal”. And its membership function can be stated as if Aix 5 bi, ( 1, bi+pi-Aix
Pi(x)
=
Pi
,
if bi C Aix 5 bi +piy
“essentially
(9)
if Aix > bi + pi.
The membership function of the objective function can be determined by solving the following two LPs: max f(x) = cT(x), s.t.
Ax 5 b, DxIb,
(10)
x >_(I
yielding supRI f = (cTx),+
= fr; and max
f(x) = CT(x),
s-t.
AxIb+P, Dx
yielding sups(k) f = (c~x)~,, = fo.
(11)
Goal Compatibility
Model
97
The membership function of the objective function is therefore, if f0 5 cTx,
1,
/&)
=
1
CTX - fi
fo 0,
if fi < cTx 5 fo,
fl '
if cTz 5 fi.
Then we can get the classical LP to solve nonsymmetrical Max
A,
s.t.
W-0 -
02)
fl)
Xp+Az
-
CT2
I
fuzzy LP problem.
-f1,
5 b+p, (13)
DX
THE
MODEL
In this model, stakeholders determine three values those are, “possible range” and “the most possible value” for each factors of need or capability. Then the weights assigned by stakeholders are triangular fuzzy numbers. Let )?fijk represent the weight assigned by stakeholder, i, when comparing need, j, to technology, k, and i = 1,2,. . . , N; j = 1,2,. . . , M; and 0 5 FVijk 5 10. Thus, for any given technology k, the total score assigned by N stakeholders based on M needs for the LDC can be obtained as N
p
=
M
2 2 i=l
pTijk.
(14)
j=l
Similarly, if there are L number of capabilities to support that technology, and 1 = 1,2,. . . , L, then T$?) = 2 i=l
kWijk.
(15)
f=l
When fjN) and i?i” are the total scores for technology k given the needs and capabilities of the LDC, respectively. Define a ratio scale for both needs and capabilities as follows ff’J’ -WI _ -ak 1ONM’ -(Cl -(c) _ *k ak
(16)
-iiKE.
Notice that 0 5 iit’ 5 1. Let (qk= &v’ - &c’,
k= 1,2,...,K
(17)
represent the distance between the ratio scores for the needs and the capabilities of the LDC. The next step is to let & defuzzy. We can use model (7) to get a crisp value 8k. The objective in transferring appropriate technology is to satisfy the needs for the LDC, given its capabilities. There is, therefore, a need to transfer a technology that will minimize the difference between the needs and capabilities of the LDC. Suppose we define Xk as the ratio of resources allocated to technology k; Rk as the resources demanded by technology k; and R as the total budget for all
C. N. MADU et al.
98
the technology types, we can then setup a mathematical
(4
programming model of the form:
minimize: k=l
subject to:
0 < Xk 5 %, xk
k=
1,2 ,...,
K,
(18)
1.
=
k=l
However, notice that the use of 1.1 removes directional effect. The objective function could have been restated as K
minimize:
c
6;zk.
(1%
k=l
While the constraints remain the same. It is easy to see that (A) and (B) converge to the same solution. Madu and Madu [20] explicitly considered the mutual dependence between industrial sectors of technology types and integrated it in maximizing the social welfare of an LDC. To consider this in the context of minimization, let square matrix B represent the input-output matrix with size k. Define B(i, j) as the input of technology or industry i to technology or industry j. It is assumed that each industrial sector represents a distinct technology type and (i, j) = 1,2, . . , , K. Then L(i,j) is an opportunity matrix that shows lack of In addition, let B* = max{B(i,j)}. independence between different technology types and can be expressed as L(i,j)
= B’ - B(i,j).
(20)
Let p = lack of dependence vector matrix. The coefficients in the (i,j) position of the L(i,j) matrix is weighted by ]0i] and ]ej] or 0: and 0; and summed over each row to obtain the lack of dependence vector matrix [27]. Prom this the transformed mathematical programming model can be expressed as (C)
minimize
PTz,
subject to:
0 5 Xk 5 %, (21)
K c k=l
k
xk = 1.
Resource Requirement (millions $)
Technology Type
1
Mining
250-275
2
Agriculture
lO&llO
3
Oil Exploration
4
Textile
150-165
Information Processing I
200-220
LI l--IT&al
375-412.5
~
I
1075-1182.5
I
I
The solution to Models (A), (B), or (C) is simple and it is based of a LINDO software. However, in the practical way to make policy that the real resource requirement of each technology is very hard to estimate. The policy making unit just measured it by a estimative value. So we must make use of nonsymmetrical fuzzy LP to drive better solution.
Goal Compatibility Model
99
EXAMPLE The example presented here is partially based on the data presented in [3,4]. Here, five technologies applied in five different industrial sectors are being considered for transfer to a particular LDC. We assumed that the resource requirement of each technology is an interval value. Namely, the upper bound value is the lower bound value added by 10%. These technologies and their resources requirements are listed below. Suppose that a budget of $1 billion has been devoted to technological development projects. These resources have to be allocated in order to minimize the gap between needs and capabilities. An input-output matrix to show the interdependence between the industrial sectors has been established by economists and knowledgeable experts using techniques like the Delphi since economic data is lacking in this LDC. The matrix is presented below.
I Industrial Sector ~~ ~ ~~ I~ M: Mining I
M
T
1
I
~7 1.0570 1 0.105 1 1.980 1
0
1
0
1 0.2234 1 1.108 1 0.495 1
0
1
0
A: Agriculture
A
0
0: Oil Exploration
1.1128
0.758
1.589
0.145
0
T: Textile
0.2580
0.337
0.175
0.149
0.149
I I: Information Processing
1 1
1 0.7560 1 0.890 1 1.156 1 1.085 1 1.085. 1
In order to solve this problem, need-capability assessment matrices must be developed for each industrial sector. A typical hypothetical example for the mining industry technology-type is presented below. Table 1. Technology: mining need assessment. Social-Economic Growth
Revenue Generation
Employment Opportunities
Enhanced Competitiveness
Stakeholder 1
(2 $5, 7)
(1, 4, 6)
(3, 5, 7)
(3, 6, 7)
Stakeholder 2
(1, 1, 1)
(5, 7, 8)
(6, 8, 9)
(7, 9, 9)
Stakeholder 3
(2, 4, 6)
(3, 6, 9)
(5, 7, 8)
(5, 7, 8)
Note: For example, (2, 5, 7) means that when importing the “mining technology”, if the purpose is “social-economic growth “. Stakeholder 1 thinks that the “possible range” is “2-7”and “the most possible value’% “5”.
The identified needs fo the LDC are matched with the different technologies and the specific capabilities needed for that technology are assessed. In this matrix, three stakeholders are used to make all the assessments. A similar matrix for capabilites produces the table below. Table 2. Technology: mining capabilities assessment. Effective Waste Management
Organizational Management
ReeoWCeS Development
supporting Industry
Labor Requirement
Supporting Service
Stakeholder 1
(1, 2, 3)
(2, 3, 5)
(4, 7, 8)
(1, 1, 3)
(5, 7, 7)
(2, 3,5)
Stakeholder 2
(2, 4, 6)
(1, 2, 3)
(3, 8, 9)
(2, 3, 4)
(5, 6, 9)
(1, 2, 3)
Stakeholder 3
(1, 1, 4)
(2, 4, 7)
(4, 6, 8)
(1, 2, 3)
(7, 8, 9)
(4, 5, 6)
100
C. N. MADIJ et al.
F’rom these two matrices and models (14)-(17), T,(,N)
we can get the table below.
[26a + 43, -16a + 851
T,(Z)
[26a + 48, -28a 26a + 43
ait)
+ 1021
-16af85
26a + 48 a\:’ [180’
-28a
I
-1OOa + 159
360
[
+ 102 180
134a - 75 lhl
1
120
[ 120’
360
’
1
This procedure is followed for all the technology types. Suppose that we can get the table below.
Information
(-0.2083,0.0056,0.1056)
Processing
By using model (7), we can get each crisp value which are listed below. lo41
ied
0.0565
0.0324
If331
IhI
lbl
0.1324
0.0296
0.0778
From the input-output matrix presented above, B’ = 1.980, so,
L(Q)
0.9230 1.7566 = i 0.8672 1.7220 1.2240
Let 1, = the entries in matrix L(i,j),
Pi =
Ioil 5
1.875 0.872 1.222 1.643 1.090
0
1.980 1.980 1.835 1.831 0.895
1.485 0.391 1.805 0.854
1.980 1.980 1.980 1.831 0.895
then,
lejlkj,
i=1,2
(...(
K.
j=l
So, ,0 and 0 are 1 x k matrices with the following entries
P =
‘0.0468’
‘0.1324’
0.0163
0.0296
0.0272
,
9=
0.0778
0.0328
0.0565
_0.0110_
,0.0324_
.
(22)
Goal Compatibility Model The model is therefore,
min
0.0468~1 + 0.0163~~2+ 0.0272~3 + 0.0328~~ + O.O1lxs,
s.t.
0 5 1000x1 += 250, 0 I 1OOOX~4= 100, 0 5 1OOOX~4= 375, 0 < 1000x4 *=
150,
0 5 1ooox:s += 200, x1 + x2 + x3 + x4 + x5 = 1. Because (1)
min
0.0468~1 + 0.016322 + 0.02’72~3 + 0.032824 + 0.01125,
s.t.
0 < 1OOOxl < 250, 0 5 1000x2 5 100, 0 5 1000x3 < 375, 0 5 1000x4 < 150, 0 5 1OOOX~< 200, x1+x3+x3+x4+x5=1.
The optimal solution fl = 0.02714
(2)
min at.
0.0468~1 + 0.016322 + 0.027223 + 0.032824 + 0.011~5, 0 5 1000x1 < 275, 0 5 1OOOX~5 110, 0 I 1000x3 5 412.5, 0 < 1000x4 5 165, 0 5 1000x5 I 220, x1+x2+x3+x4+x5=1.
The optimal solution fo = 0.02517. Then making use of model (13), we can get max
X
s.t.
0.0468x1+
0.0163x2 + 0.0272~3 + 0.0328x4 + 0.011x5 - 0.00197X 5 -0.02714,
25X + 1000~~ 5 275, 10x + 1000x2 5 110, 37.5X + 1000x3 5 412.5, 15X + 1000x4 5 165, 20x + lOOOx!j5 220, xi 2 0,
i=1,2
,...,
5,
x1 + x2 + x3 + x4 + 26 = 1, O
101
102
C. N. MADU
The solution below.
Converting
to this problem
these solutions
can be easily obtained
et al.
by LINDO software.
Xl
22
x3
x4
25
0.175
0.1
0.375
0.15
0.2
into dollar figures, we have the allocation
The solution
is listed
plan as follows:
CONCLUSION In this paper, we present a nonsymmetrical fuzzy linear programming model to minimize goal incompatibility in the transfer of technology to less developed countries. Goal incompatibility exists when a gap exists between the needs and capabilities of an LDC for a particular technology. The wider this gap is, the less likely that an appropriate technology will be transferred. It is, therefore, necessary to transfer technologies that show more congruity to the needs and capa bilities of an LDC. However, to do this requires that the interdependentce that exists between different technologies be studied and factored into the nonsymmetrical fuzzy LP model. The proposed model uses a need capability assessment matrix which is based on a scoring model to assess the needs and capabilities of a LDC for a particular technology. In order to integrate each stakeholder’s opinion precisely, the concept of fuzzy number is used here. A ratio scale is created and the distance between the ratio scales obtained for the needs and capabilities for a particular technology is used to obtain the lack of dependence vector for the nonsymmetrical fuzzy LP model. It is shown that the solution to the nonsymmetrical fuzzy LP problem is simple since it is based on a LINDO software. The mode presented here is limited by the fact that it is based on the expert knowledge of the stakeholders. However, this limitation cannot be avoided in any policy or decision making situation. Any situation involving a human decision making process cannot be expunged from this problem. Therefore, the quality of the decisions reached depends on the quality of the stakeholders’ assessment of the situation.
REFERENCES 1. C.N. Madu, Strategic planning in technology transfer: A dialectical approach, Technological Forecasting and Social Change 95, 327-287, (1989). 2. C.N. Madu, Transferring technology to developing countries, Long Range Planning 22, 115-124, (1989). 3. C.N. Ma&, Strategic Planning in Technology Transfer to Leas Developed Countries, Quorum Books, Westport, CT, (1992). 4. C.N. Madu and A.N. Ma&, A systems approach to he transfer of mutually dependent technologies, Socioeconomic Planning Sciences 27, 269-287, (1993). 5. S. Derakhshani, Factors affecting sucess in international transfers of technology: A synthesis and text of a new contingency model, Developing Economies 21, 21-45, (1983). 6. V. Baminujam and J.M. Alexander, Technological choices in the less developed countries: An analytic hierarchy approach, Techological Forecasting and Social Change 19, 81-98, (1981). 741-766, (1961). 7. E.I. Mansfield, Technical change and the rate on imitation, Econometrika, 8. R. Vernon, International investment and international trade in the product life cycle, Quarterly Journal Economics, 190-207, (1966). 9. C.N. Madu, Cognitive mapping in technology transfer, Journal of Technology Zknsfer 15, 33-39.
of
Goal Compatibility Model
103
10. C.N. Madu, An economic decision for technology transfer, Engineering Management International 5, 53-62, (1988). 11. R. Vernon, International investment and international trade in the product life cycle, Quarter19 Jouwaal of Economics, 190-207, (1966). 12. N.C. Georgantxae and C.N. Madu, Congnitive proceases in technology management and transfer, Z’echnologicnl Forecasting and Social Change 38, 81-95, (1990). 13. A. Leg&o, Jr., Towards a calculus of development analysis, Technological Forecasting and Social Change 14, 217-230, (1979). 14. C.N. Madu and R. Jacob, Strategic planning in technology transfer: A dialectical approach, Technological Forecasting and Social Change 36, 327-338, (1989). 15. C.N. Madu, Prescriptive framework for the transfer of appropriate technology, R&ures 33, 932-950, (1990). 16. Technology Atlas Team, A framework for technology based national planning, Technological Forecasting and Social Change 32, 5-18, (1987). 17. D. Kernball-Cook and D.J. Wright, The search for appropriate OR: A review of operational research in developing countries, Journal of the Operational Research Society 32, 1021-1032, (1981). 18. C.N. Madu, Cognitive mapping in technology transfer, Journal of Technology ‘Iknafer lb, 33-39, (1990). 19. C.N. Madu and R. Jacob, Multiple perspectives and cognitive mapping to technology tranefer decision, fitures 23, 978-997, (1991). 20. C.N. Madu and A.N. Madu, A systems approach to the transfer of mutually dependent technologies, SocioEconomic Planning Sciences 27 (4), 269-287, (1993). 21. K.J. Radford, Stmgegic Planning: An Analytical Appnmch, Reetom Publishing, Reston, VA, (1980). 22. L.A. Zadeh, Fuzzy set, Information and Control 8 (3), 338-353, (1965). 23. D. Dubois and H. Prade, Operation on fuzzy numbers, International Journal of Systems Science 9,613-626, (1978). 24. A. Kaufmann and M.M. Gupta, Introduction to l&q/ Arithmetic, Van Nostrand Reinhold, New York, (1991). 25. G.H. Tzeng and J.Y. Teng, nansportation investment project selection with fuzzy multiobjectives, tin+ portation Planning and Technology 17, 91-112, (1993). 26. H.J. Zimmermann, F&zl/ Set Theory and Its Applications, Kluwer Academic, Boston, (1991). 27. T.L. Saaty and J.M. Alexander, Thinking With Models, Pergamon Press, Oxford, (1981).
1998
ScienceLtd. All rights reserved Printed in Great Britain
PII: SO8957177(98)00147-2
0893-9659/98 $19.00 + 0.90
A Goal Compatibility Model for Technology Transfers C. N. MADU Department of Management and Management Science Lubin School of Business, Pace University 1 Pace Plaza, New York, NY 10038, U.S.A. CHINHO LIN Graduate School of Industrial Management National Cheng Kung University Tainan, Taiwan, ROC C.-H. KUEI Department of Management and Management Science Lubin School of Business, Pace University 1 Pace Plaza, New York, NY 10038, U.S.A. (Received September
1996; accepted May 1997)
Abstract-In this paper, we present a minimization approach to goal incompatibility in technology transfers especially to less developed countries. The proposed model is based on a need-capability assessment for alternative technologies for transfer, and then, minimizing the distance between need and capability to achieve goal compatibility. By transferring technologies with minimum deviation between an LDC’s needs and capabilities, appropriate technologies could be transferred. A fuzzy theory is used in this mode to avoid errors which are often made in using subjective judgment. An input-output matrix and budgetary constraints are integrated into the model to determine the allocation of development funds to alternative technologies. A LINDO software is used to solve the problem. @ 1998 EleevierScienceLtd. All rights reserved. Keywords-Technology transfer, Appropriate number, Nonsymmetrical
technology,
Goal compatibility,
Triangular
fuzzy
fuzzy linear programming.
INTRODUCTION In this paper, we present a model to achieve goal compatibility
in the transfer of technology to Less Developed Countries (LDCs). Goal compatibility, in this contest, deals with the transfer of appropriate technologies. Appropriate technology is a transferred technology that helps a LDC to meet its needs, given its capabilities. It is, therefore, necessary to transfer those technologies that show the minimum deviation between an LDC’s needs and its capabilities. Madu and Jacob [l] discussed the issue of goal compatibility between the recipient and the transfer or of technology. They note that it is necessary to achieve reasonable compatibility between them in order to successfully transfer technology. The absence of goal compatibility leads to failures in technology transfers. However, goal incompatibility can exist if a technology that does not meet the needs or the capabilities of an LDC is transferred. Madu [2] presented critical success factors for technology transfers and notes that appropriate technologies should be able to utilize the existing capabilities of the LDCs to satisfy their needs.
%=et 91
by 44-W
92
C. N.
MADIJ et al.
Madu [3] developed a need-capability assessment matrix to identify which technologies an LDC should focus on in achieving its socio-economic development goals. However, knowing that many technologies or industries are mutually dependent on each other, LCDs need a model that should minimize goal incompatibility and allow them to develop a portfolio for technology transfer. In a recent article, Madu and Madu [4] presented a systems model for transferring mutually dependent technologies. However, they did not address the issue of goal incompatibility between the needs and capabilities of an LDC. This paper explicitly models goal incompatibility and considers it in allocating resources to mutually dependent technologies.
RESEARCH
BACKGROUND
The technology transfer literature is rich in conceptual frameworks [2,5,6], but only very few models exist and many of these do not consider planning issues but focus purely on economic modeling [7,8]. Technology transfer studies often address issues such as the inappropriateness of technology transfers [5,9], economic implications [lO,ll], cultural, ethical, and psychological issues (1,12-151. Only recently were planning issues discussed [1,3,4,16]. Yet, there are very few mathematical models to guide the policy making that is involved. The lack of such models is partly due to the fact that technology transfer decisions are not purely objective and, therefore, cannot be easily quantified. However, there exists in the operational research literature, methods to reasonably address some aspects of the technology transfer policy making problems [17]. Madu [2] presented a detailed literature review on technology transfer. Obvious from this review is the need for planning models, especially in deciding which technologies to transfer and the resources to be allocated to them. Ramanujam and Saaty [6] used the analytic hierarchy process to analyze technological choice in less developed countries. However, their model did not deal with resource allocation to mutually dependent technologies. Madu and Madu [4] extended this work by taking a holistic view of technology transfer and integrating technological resource allocation decisions in satisfying the LDC’s socio-economic goals. A linear programming model was formulated and used to solve this problem. Madu [18] identified three main causes of failure in technology transfers, namely, structural, behavioral, and technological. Other works have used cognitive mapping and influence diagramming to analyze potential failures of technology transfers [1,12,15,19]. Notable among these is the work of Madu and Jacob [l], where the Dialectical Materialism Inquiry System (DMIS) was used to analyze the contradictory goals of both the transferor and the recipient df technology. It is noted in this study that conflict exists between the transferor and the receiver of technology, however, productive conflicts support the effective transfer of technologies. While several of these studies have identified and analyzed problems in the transfer process, only the work by Madu and Madu [4] presented an explicit mathematical model to plan the transfer of technologies to LDCs in order to satisfy their socioeconomic goals. Specifically, their paper identified the criteria that influence technology transfer decisions, prioritized them in terms of achieving the socio-economic goals of the LDC, and used the priority indices to normalize an input-output matrix. Consequently, a LP model was developed and solved to determine the allocation of limited resources to mutually dependent technologies. The present paper is significantly different from the work by Madu and Madu [20] in the following ways. (1) The objective of the paper is to minimize the goal incompatibility that exists in the transfer of technology by matching an LDC’s needs to its capabilities. To achieve this, a need-capability assessment matrix is used. The objective in Madu and Madu [20] WBSto maximize an LDC’s social welfare and there was no consideration of goal incompatibility. On the other hand, the aim of the present paper is to provide a method through which appropriate technologies could be transferred by minimizing the deviations between a LDC’s needs and its capabilities.
Goal Compatibility Model
(2) In
order to achieve its stated objective,
93
Madu and Madu [20] used a multicriteria
namely, the Analytic Hierarchy Process (AHP) to develop priorities for the criteria.
model, There
are no criterion explicitly discussed in this paper, but they can be integrated into the needcapability
assessment matrix.
Furthermore,
AHP is not used in this paper.
In the next section we shall introduce the need-capability
NEED-CAPABILITY
ASSESSMENT
assessment matrix.
MATRIX
(NCAM)
The NCAM was developed by Madu [3] to match a LDC’s needs to its capabilities
for a
given technology. Through this matrix, a LDC can position itself in terms of its technological capabilities. The basic concept of this matrix is laid out in Figure 1. This figure is a 3 x 3 matrix with three dimensions for both the needs and the capabilities:
low (L), medium (M),
and high (H). For any given technology, a LDC should position itself on the matrix in order to evaluate the suitability of the technology. It is apparent from this matrix that there are nine possible positions that a LDC may find itself in with regards to a particular technology. The relative importance of these positions is shown using a scale. For example, a scale of 1 shows an undesirable position, while a scale of 9 shows a highly desirable position. A desirability measure for each cell of the matrix is obtained by assuming that the values assigned to both needs and capabilities are multiplicative, thereby allowing for the possibility of synergy. It is, therefore, clear from this matrix that the desirability for a technology goes up as both the needs and capabilities for that technology increase. Prioritization of Need-CapabilityAssessmentMatrix Needs i
Low
Medium
High
Low-
Capabilities Medium
High
Scale 1 2 3 6 9
2
4
6
3
6
9
Statement of Importance Undesirable Least Desirable Desirable Very Desirable Highly Desirable
Figure 1. The arrowsshow the movementof resources from technologieswith lower to those with higher needs. This assumesthat capabilities are transferable. The NCAM matrix can be used in two phases. The first phase will be to identify technologies that have “acceptable” desirability indices, for example, 4, 6, and 9. The second phases will be to use the matrix for resource allocation decisions to the different technologies selected for Phase 1. Figure 2 gives further definitions of the position an LDC can find itself in. Phase 2 is a pragmatic way of assessing the needs and capabilities of LCDs. Many policy making issues involving technology transfers involve multiple players which we refer to a stake-
C. N. MADU
et al.
Needs Low
Medium What are the potentials of developing the capabilities?
Can appropriate capabilities be developed to satisfy the high demand? Potential problem area. Should be given adequate attention.
What are the potentials of exporting the capabilities? Can internal needs be generated?
Capabilities can be used to satisfy the moderate needs. The existing capabilities are just enough to satisfy existing needs.
Higher needs can be satisfied if capabilities are further developed.
Are there external markets to absorb the excess output? Can internal needs be generated to exploit the high capabilities?
Generate output to satisfy the moderate consumption. If external markets exist ship the excess output. Apply capabilities to other areas if possible.
Highly desirable. Ds mand and capabilities are fully developed.
LOW
Capabilities
Medium
High
High
Undesirable, should not be emphssized.
Figure 2. Need-capability
amassment matrix.
holders. These stakeholders are the active participants in technological decisions [21]. By being active participants, their actions and reactions significantly influence the successful transfer of technology. The stakeholders are charged with identifying the specific needs of the LDC, which, of course, may have internal and external components. They also match these needs to capabilities that will make it easier to implement the technology. Several list of needs and capabilities could be generated. However, through group decision support systems and the application of Delphi-type techniques [2], reasonable decisions on the importance of any need or capability could by reached. In thii paper, we recommend the use of a scale of 0 to 10 to denote the importance of each technology type in relation to the needs and capabilities of the LDC.
SIMPLE
FUZZY
SET THEORY
The first publications in fuzzy set theory is by Zadeh [22]. Zadeh writes: ‘the notion of fuzzy set provides a convenient point of departure for the construction of a conceptual framework which parallels in many respects the framework used in the csse of ordinary sets, but it is more general than the latter and, potentially, may prove to have a much wider scope of applicability, particularly in the fields of pattern classification and information processing”. Essentially, such a framework provides a natural way of dealing with problems in which the source of imprecision is the absence of sharply defined criteria of class membership rather than the presence of random variables. So, fuzzy set theory provides a strict mathematical framework in which vague concep tual phenomena can be precisely and rigorously studied. It can also be considered as a modeling language well suited of situations in which fuzzy relations, criteria, and phenomena exist. Next part, we will introduce some tools about fuzzy set theory we use in this paper. Triangular
Fuzzy
Number
In thii paper, we will make use of the concept of fuzzy set theory. Namely, we will give a fuzzy number to the different views of the stakeholders on different criteria in order to integrate each stakeholder’s opinion precisely.
Goal Compatibility Model
95
Dubois and Prade [23] defined a fuzzy number and describe its meaning and features. A fuzzy number A is a fuzzy set which membership function is PA(Z) : R --t [0, 11,and its character is: (1) p~ (z) is continuous; (2) PA(Z) is a convex fuzzy set; (3) it exists exactly zc E R with PA
= 1.
Triangular fuzzy number PA(Z) = (I, m,u) can conform to the above-mentioned Figure 3), and its membership function is:
I PA(X)=
(x - 1)
terms (see
l
m-l’
(x - ?J)
m
<
x
<
‘1L
--’
m-_21’
(1)
other.
0,
Figure 3. Triangular fuzzy number. DEFINITION. A, = {x 1 PA(Z) 2 u} a E [0,11, that fuzzy number A whose confidence interval A, at a- level can be stated
A, =
M,Gl
(2)
af and a$ mean the upper and lower boundaries of confidence interval. Kaufmann and Gupta [24] use the concept of a-cut and extension principle [22]. If trianguiar fuzzy number A and fi whose confidence interval are A, and B, at a-level, in which A, = [a?, a$], B, = [bp, b$], then the fuzzy number operation are: 1. addition
A,(+)B,
= [a? + br,a$ + b$] ;
(3)
AJ-)Bo
= [a? - bg,a; - by];
(4)
2. subtraction
3. multiplication Aa(.)Ba = [ayby, a:b:] ; 4. division Aa(:
=
[ 1. g,
2
2
1
(5)
(6)
Defussication
Determination of the best crisp value under a fuzzy membership function includes mean-ofmaxima and center-of-area methods. The former is to select a nonfuzzy value which corresponds to the maximum value of the membership function, averaging in some ways when there are many
C. N. MADIJ
96
et al.
values. The latter is to choose a value which equally divides the area under the membership function curve. Furthermore, some a values must be decided by the decision-makers or all members of the decision-making group, and it is not easy to decide such value (see [25]). In this paper, we make use of the triangular fuzzy number to deal with stakeholders’ opinions. The weights after integrating many stakeholders’ opinions are still triangular fuzzy numbers. The defuzzication method we used was developed by Tzeng and Teng [25]. The conception of this method was derived from the center-of-area methods. If there is a triangular fuzzy number whose membership function is (x - 1) l
(x--1,
m
m--‘L1
-
’
-
other.
0, Then the best crisp performance value will be DFi
Ku- 1)+ cm - 01
=
3+1 Nonsymmetrical
Fuzzy
*
(7)
LP
A model in which the objective function is crisp, that is, has to be maximized or minimized and in which the constraints are all or partially fuzzy is no longer symmetrical [26]. The problem we are faced with is the determination of an extremum of a crisp function over a fuzzy domain. So we can’t use the biggest fuzzy membership function value or the intersection of fuzzy objective function and fuzzy constraint. Zimmermann proposed that we can use the following method to solve this kind of problem. If there is a model of linear programming, it can be stated as max
f(x) = cT(x),
s.t.
Ax += b, DxIb, x > 0.
Here += denotes the fuzzified version of 5 and has the linguistic interpretation smaller than or equal”. And its membership function can be stated as if Aix 5 bi, ( 1, bi+pi-Aix
Pi(x)
=
Pi
,
if bi C Aix 5 bi +piy
“essentially
(9)
if Aix > bi + pi.
The membership function of the objective function can be determined by solving the following two LPs: max f(x) = cT(x), s.t.
Ax 5 b, DxIb,
(10)
x >_(I
yielding supRI f = (cTx),+
= fr; and max
f(x) = CT(x),
s-t.
AxIb+P, Dx
yielding sups(k) f = (c~x)~,, = fo.
(11)
Goal Compatibility
Model
97
The membership function of the objective function is therefore, if f0 5 cTx,
1,
/&)
=
1
CTX - fi
fo 0,
if fi < cTx 5 fo,
fl '
if cTz 5 fi.
Then we can get the classical LP to solve nonsymmetrical Max
A,
s.t.
W-0 -
02)
fl)
Xp+Az
-
CT2
I
fuzzy LP problem.
-f1,
5 b+p, (13)
DX
THE
MODEL
In this model, stakeholders determine three values those are, “possible range” and “the most possible value” for each factors of need or capability. Then the weights assigned by stakeholders are triangular fuzzy numbers. Let )?fijk represent the weight assigned by stakeholder, i, when comparing need, j, to technology, k, and i = 1,2,. . . , N; j = 1,2,. . . , M; and 0 5 FVijk 5 10. Thus, for any given technology k, the total score assigned by N stakeholders based on M needs for the LDC can be obtained as N
p
=
M
2 2 i=l
pTijk.
(14)
j=l
Similarly, if there are L number of capabilities to support that technology, and 1 = 1,2,. . . , L, then T$?) = 2 i=l
kWijk.
(15)
f=l
When fjN) and i?i” are the total scores for technology k given the needs and capabilities of the LDC, respectively. Define a ratio scale for both needs and capabilities as follows ff’J’ -WI _ -ak 1ONM’ -(Cl -(c) _ *k ak
(16)
-iiKE.
Notice that 0 5 iit’ 5 1. Let (qk= &v’ - &c’,
k= 1,2,...,K
(17)
represent the distance between the ratio scores for the needs and the capabilities of the LDC. The next step is to let & defuzzy. We can use model (7) to get a crisp value 8k. The objective in transferring appropriate technology is to satisfy the needs for the LDC, given its capabilities. There is, therefore, a need to transfer a technology that will minimize the difference between the needs and capabilities of the LDC. Suppose we define Xk as the ratio of resources allocated to technology k; Rk as the resources demanded by technology k; and R as the total budget for all
C. N. MADU et al.
98
the technology types, we can then setup a mathematical
(4
programming model of the form:
minimize: k=l
subject to:
0 < Xk 5 %, xk
k=
1,2 ,...,
K,
(18)
1.
=
k=l
However, notice that the use of 1.1 removes directional effect. The objective function could have been restated as K
minimize:
c
6;zk.
(1%
k=l
While the constraints remain the same. It is easy to see that (A) and (B) converge to the same solution. Madu and Madu [20] explicitly considered the mutual dependence between industrial sectors of technology types and integrated it in maximizing the social welfare of an LDC. To consider this in the context of minimization, let square matrix B represent the input-output matrix with size k. Define B(i, j) as the input of technology or industry i to technology or industry j. It is assumed that each industrial sector represents a distinct technology type and (i, j) = 1,2, . . , , K. Then L(i,j) is an opportunity matrix that shows lack of In addition, let B* = max{B(i,j)}. independence between different technology types and can be expressed as L(i,j)
= B’ - B(i,j).
(20)
Let p = lack of dependence vector matrix. The coefficients in the (i,j) position of the L(i,j) matrix is weighted by ]0i] and ]ej] or 0: and 0; and summed over each row to obtain the lack of dependence vector matrix [27]. Prom this the transformed mathematical programming model can be expressed as (C)
minimize
PTz,
subject to:
0 5 Xk 5 %, (21)
K c k=l
k
xk = 1.
Resource Requirement (millions $)
Technology Type
1
Mining
250-275
2
Agriculture
lO&llO
3
Oil Exploration
4
Textile
150-165
Information Processing I
200-220
LI l--IT&al
375-412.5
~
I
1075-1182.5
I
I
The solution to Models (A), (B), or (C) is simple and it is based of a LINDO software. However, in the practical way to make policy that the real resource requirement of each technology is very hard to estimate. The policy making unit just measured it by a estimative value. So we must make use of nonsymmetrical fuzzy LP to drive better solution.
Goal Compatibility Model
99
EXAMPLE The example presented here is partially based on the data presented in [3,4]. Here, five technologies applied in five different industrial sectors are being considered for transfer to a particular LDC. We assumed that the resource requirement of each technology is an interval value. Namely, the upper bound value is the lower bound value added by 10%. These technologies and their resources requirements are listed below. Suppose that a budget of $1 billion has been devoted to technological development projects. These resources have to be allocated in order to minimize the gap between needs and capabilities. An input-output matrix to show the interdependence between the industrial sectors has been established by economists and knowledgeable experts using techniques like the Delphi since economic data is lacking in this LDC. The matrix is presented below.
I Industrial Sector ~~ ~ ~~ I~ M: Mining I
M
T
1
I
~7 1.0570 1 0.105 1 1.980 1
0
1
0
1 0.2234 1 1.108 1 0.495 1
0
1
0
A: Agriculture
A
0
0: Oil Exploration
1.1128
0.758
1.589
0.145
0
T: Textile
0.2580
0.337
0.175
0.149
0.149
I I: Information Processing
1 1
1 0.7560 1 0.890 1 1.156 1 1.085 1 1.085. 1
In order to solve this problem, need-capability assessment matrices must be developed for each industrial sector. A typical hypothetical example for the mining industry technology-type is presented below. Table 1. Technology: mining need assessment. Social-Economic Growth
Revenue Generation
Employment Opportunities
Enhanced Competitiveness
Stakeholder 1
(2 $5, 7)
(1, 4, 6)
(3, 5, 7)
(3, 6, 7)
Stakeholder 2
(1, 1, 1)
(5, 7, 8)
(6, 8, 9)
(7, 9, 9)
Stakeholder 3
(2, 4, 6)
(3, 6, 9)
(5, 7, 8)
(5, 7, 8)
Note: For example, (2, 5, 7) means that when importing the “mining technology”, if the purpose is “social-economic growth “. Stakeholder 1 thinks that the “possible range” is “2-7”and “the most possible value’% “5”.
The identified needs fo the LDC are matched with the different technologies and the specific capabilities needed for that technology are assessed. In this matrix, three stakeholders are used to make all the assessments. A similar matrix for capabilites produces the table below. Table 2. Technology: mining capabilities assessment. Effective Waste Management
Organizational Management
ReeoWCeS Development
supporting Industry
Labor Requirement
Supporting Service
Stakeholder 1
(1, 2, 3)
(2, 3, 5)
(4, 7, 8)
(1, 1, 3)
(5, 7, 7)
(2, 3,5)
Stakeholder 2
(2, 4, 6)
(1, 2, 3)
(3, 8, 9)
(2, 3, 4)
(5, 6, 9)
(1, 2, 3)
Stakeholder 3
(1, 1, 4)
(2, 4, 7)
(4, 6, 8)
(1, 2, 3)
(7, 8, 9)
(4, 5, 6)
100
C. N. MADIJ et al.
F’rom these two matrices and models (14)-(17), T,(,N)
we can get the table below.
[26a + 43, -16a + 851
T,(Z)
[26a + 48, -28a 26a + 43
ait)
+ 1021
-16af85
26a + 48 a\:’ [180’
-28a
I
-1OOa + 159
360
[
+ 102 180
134a - 75 lhl
1
120
[ 120’
360
’
1
This procedure is followed for all the technology types. Suppose that we can get the table below.
Information
(-0.2083,0.0056,0.1056)
Processing
By using model (7), we can get each crisp value which are listed below. lo41
ied
0.0565
0.0324
If331
IhI
lbl
0.1324
0.0296
0.0778
From the input-output matrix presented above, B’ = 1.980, so,
L(Q)
0.9230 1.7566 = i 0.8672 1.7220 1.2240
Let 1, = the entries in matrix L(i,j),
Pi =
Ioil 5
1.875 0.872 1.222 1.643 1.090
0
1.980 1.980 1.835 1.831 0.895
1.485 0.391 1.805 0.854
1.980 1.980 1.980 1.831 0.895
then,
lejlkj,
i=1,2
(...(
K.
j=l
So, ,0 and 0 are 1 x k matrices with the following entries
P =
‘0.0468’
‘0.1324’
0.0163
0.0296
0.0272
,
9=
0.0778
0.0328
0.0565
_0.0110_
,0.0324_
.
(22)
Goal Compatibility Model The model is therefore,
min
0.0468~1 + 0.0163~~2+ 0.0272~3 + 0.0328~~ + O.O1lxs,
s.t.
0 5 1000x1 += 250, 0 I 1OOOX~4= 100, 0 5 1OOOX~4= 375, 0 < 1000x4 *=
150,
0 5 1ooox:s += 200, x1 + x2 + x3 + x4 + x5 = 1. Because (1)
min
0.0468~1 + 0.016322 + 0.02’72~3 + 0.032824 + 0.01125,
s.t.
0 < 1OOOxl < 250, 0 5 1000x2 5 100, 0 5 1000x3 < 375, 0 5 1000x4 < 150, 0 5 1OOOX~< 200, x1+x3+x3+x4+x5=1.
The optimal solution fl = 0.02714
(2)
min at.
0.0468~1 + 0.016322 + 0.027223 + 0.032824 + 0.011~5, 0 5 1000x1 < 275, 0 5 1OOOX~5 110, 0 I 1000x3 5 412.5, 0 < 1000x4 5 165, 0 5 1000x5 I 220, x1+x2+x3+x4+x5=1.
The optimal solution fo = 0.02517. Then making use of model (13), we can get max
X
s.t.
0.0468x1+
0.0163x2 + 0.0272~3 + 0.0328x4 + 0.011x5 - 0.00197X 5 -0.02714,
25X + 1000~~ 5 275, 10x + 1000x2 5 110, 37.5X + 1000x3 5 412.5, 15X + 1000x4 5 165, 20x + lOOOx!j5 220, xi 2 0,
i=1,2
,...,
5,
x1 + x2 + x3 + x4 + 26 = 1, O
101
102
C. N. MADU
The solution below.
Converting
to this problem
these solutions
can be easily obtained
et al.
by LINDO software.
Xl
22
x3
x4
25
0.175
0.1
0.375
0.15
0.2
into dollar figures, we have the allocation
The solution
is listed
plan as follows:
CONCLUSION In this paper, we present a nonsymmetrical fuzzy linear programming model to minimize goal incompatibility in the transfer of technology to less developed countries. Goal incompatibility exists when a gap exists between the needs and capabilities of an LDC for a particular technology. The wider this gap is, the less likely that an appropriate technology will be transferred. It is, therefore, necessary to transfer technologies that show more congruity to the needs and capa bilities of an LDC. However, to do this requires that the interdependentce that exists between different technologies be studied and factored into the nonsymmetrical fuzzy LP model. The proposed model uses a need capability assessment matrix which is based on a scoring model to assess the needs and capabilities of a LDC for a particular technology. In order to integrate each stakeholder’s opinion precisely, the concept of fuzzy number is used here. A ratio scale is created and the distance between the ratio scales obtained for the needs and capabilities for a particular technology is used to obtain the lack of dependence vector for the nonsymmetrical fuzzy LP model. It is shown that the solution to the nonsymmetrical fuzzy LP problem is simple since it is based on a LINDO software. The mode presented here is limited by the fact that it is based on the expert knowledge of the stakeholders. However, this limitation cannot be avoided in any policy or decision making situation. Any situation involving a human decision making process cannot be expunged from this problem. Therefore, the quality of the decisions reached depends on the quality of the stakeholders’ assessment of the situation.
REFERENCES 1. C.N. Madu, Strategic planning in technology transfer: A dialectical approach, Technological Forecasting and Social Change 95, 327-287, (1989). 2. C.N. Madu, Transferring technology to developing countries, Long Range Planning 22, 115-124, (1989). 3. C.N. Ma&, Strategic Planning in Technology Transfer to Leas Developed Countries, Quorum Books, Westport, CT, (1992). 4. C.N. Madu and A.N. Ma&, A systems approach to he transfer of mutually dependent technologies, Socioeconomic Planning Sciences 27, 269-287, (1993). 5. S. Derakhshani, Factors affecting sucess in international transfers of technology: A synthesis and text of a new contingency model, Developing Economies 21, 21-45, (1983). 6. V. Baminujam and J.M. Alexander, Technological choices in the less developed countries: An analytic hierarchy approach, Techological Forecasting and Social Change 19, 81-98, (1981). 741-766, (1961). 7. E.I. Mansfield, Technical change and the rate on imitation, Econometrika, 8. R. Vernon, International investment and international trade in the product life cycle, Quarterly Journal Economics, 190-207, (1966). 9. C.N. Madu, Cognitive mapping in technology transfer, Journal of Technology Zknsfer 15, 33-39.
of
Goal Compatibility Model
103
10. C.N. Madu, An economic decision for technology transfer, Engineering Management International 5, 53-62, (1988). 11. R. Vernon, International investment and international trade in the product life cycle, Quarter19 Jouwaal of Economics, 190-207, (1966). 12. N.C. Georgantxae and C.N. Madu, Congnitive proceases in technology management and transfer, Z’echnologicnl Forecasting and Social Change 38, 81-95, (1990). 13. A. Leg&o, Jr., Towards a calculus of development analysis, Technological Forecasting and Social Change 14, 217-230, (1979). 14. C.N. Madu and R. Jacob, Strategic planning in technology transfer: A dialectical approach, Technological Forecasting and Social Change 36, 327-338, (1989). 15. C.N. Madu, Prescriptive framework for the transfer of appropriate technology, R&ures 33, 932-950, (1990). 16. Technology Atlas Team, A framework for technology based national planning, Technological Forecasting and Social Change 32, 5-18, (1987). 17. D. Kernball-Cook and D.J. Wright, The search for appropriate OR: A review of operational research in developing countries, Journal of the Operational Research Society 32, 1021-1032, (1981). 18. C.N. Madu, Cognitive mapping in technology transfer, Journal of Technology ‘Iknafer lb, 33-39, (1990). 19. C.N. Madu and R. Jacob, Multiple perspectives and cognitive mapping to technology tranefer decision, fitures 23, 978-997, (1991). 20. C.N. Madu and A.N. Madu, A systems approach to the transfer of mutually dependent technologies, SocioEconomic Planning Sciences 27 (4), 269-287, (1993). 21. K.J. Radford, Stmgegic Planning: An Analytical Appnmch, Reetom Publishing, Reston, VA, (1980). 22. L.A. Zadeh, Fuzzy set, Information and Control 8 (3), 338-353, (1965). 23. D. Dubois and H. Prade, Operation on fuzzy numbers, International Journal of Systems Science 9,613-626, (1978). 24. A. Kaufmann and M.M. Gupta, Introduction to l&q/ Arithmetic, Van Nostrand Reinhold, New York, (1991). 25. G.H. Tzeng and J.Y. Teng, nansportation investment project selection with fuzzy multiobjectives, tin+ portation Planning and Technology 17, 91-112, (1993). 26. H.J. Zimmermann, F&zl/ Set Theory and Its Applications, Kluwer Academic, Boston, (1991). 27. T.L. Saaty and J.M. Alexander, Thinking With Models, Pergamon Press, Oxford, (1981).