Choosing Best Alliance Partners and Allocating Optimal
Alliance Resources Using the Fuzzy Multi-Objective
Dummy Programming Model
Jih-Jeng Huang1, Gwo-Hshiung Tzeng2,3, and Chorng-Shyong Ong1
1
Department of Information Management, National Taiwan University, Taipei, Taiwan; 2Institute of Management
of Technology, National Chiao Tung Universit, Hsinchu, Taiwan; 3Department of Business Administration, Kainan
University, Taoyuan, Taiwan
Synergy effects are the motives to enter strategic alliances, however due to lack of adequate
preparation or planning, these alliances often fail. It is no doubt that the successful strategic
alliance depends on choosing the correct alliance partners and appropriate resource
allocation. In this paper, the fuzzy multi-objective dummy programming model is proposed
to overcome problems above. Two types of strategic alliances, joint ventures and mergers
and acquisitions (M&A), are demonstrated to choose the best alliance partners and allocate
the optimal alliance resources in a numerical example. Based on the results, our method can
provide the optimal alliance cluster and satisfaction in strategic alliances.
Keywords: fuzzy sets; strategic alliances; De Novo programming; joint ventures; mergers
and acquisitions (M&A)
Introduction
A strategic alliance may be defined as a cooperative arrangement between two or more
independent firms that exchange or share resources for competitive advantage. Since the
1980s, strategic alliances have been widely discussed (Porter & Fuller 1986, Harrigan &
Newman 1990, Auster 1994) and hundreds of papers have been published about this issue.
The essential motives of strategic alliances are “synergy effects”, as represented in the
following equation:
V (∪ Sk ) > ∑V ( Sk ); k = 1,", K
k
(1)
k
where V (⋅) denotes the satisfaction (or value) function and Sk denotes the kth alliance firm.
When Eq. (1) is satisfied, alliance firms can share more satisfaction level than their original
states through strategic alliances.
Since some firms rush into strategic alliances without appropriate preparation or
planning to choose the correct partners and resource allocation, these alliances often fail
(Dacin et al. 1997). It can be seen that the questions above are usually complex and
diversified, i.e. with the different firm’s goals, culture, and resources, the best alliance
partners and resource allocation are dissimilar. This paper proposes a model which can
determine the best partner choice and the optimal resource allocation for strategic alliances.
Although the criteria for choosing correct partners have been widely proposed, such as
complementary strengths, commitment, coordination, and compatible goals (Brouthers
1995, Arino & Abramov 1997, Yoshino & Rangan, 1995, Gerlinger 1991), these papers
seem to ignore the issue of resource allocation. It is clear that only by using these alliance
resources effectively can synergy effects arise. On the other hand, the issue of resource
allocation (Bretthauer & Shetty 1997, Bretthauer & Shetty 1995, Lai & Li 1999, Robinson
et al. 1992) also has been discussed for a long time in operations research and the purposes
of resource allocation is concerned with obtaining the maximum profits for the enterprise
and satisfaction/utility for the customer under limited resources. It is reasonable to
incorporate the both concepts to overcome the problems of choosing alliance partners and
1
resource allocation.
In order to overcome these problems and derive a useful model, several issues should be
considered. First, since the problem of choosing alliance partners is part of the
combinatorial problem, the scaling problem should be considered. Second, these objectives
in a firm and the satisfaction in an alliance should be precisely measured and calculated.
Third, based on the principle of the market mechanism, the unit price of resources should
be incorporated into the model. It is clear that the optimal resource allocation varies with
the different unit price of resources. Finally, because the real-world problems usually have
the restriction of integer type, the integer resource allocation solutions should be supported.
In this paper, we propose the fuzzy multi-objective dummy programming model to
satisfy these claims above and provide the best alliance cluster and the optimal resource
allocation combinations. In addition, two types of strategic alliances, joint ventures and
mergers and acquisitions (M&A), are demonstrated to choose the best alliance partners and
allocate the optimal alliance resources in a numerical example using the proposed method.
On the basis of the numerical results, we can conclude that the proposed method can
provide the optimal alliance cluster and satisfaction for alliance partners.
The rest of this paper is organized as follows. The review of strategic alliances is
discussed in Section 2. De Novo programming is proposed in Section 3. Fuzzy
multi-objective dummy programming is derived in Section 4. In Section 5, a numerical
example is used to illustrate the proposed method by considering joint ventures and M&A.
Section 6 presents a discussion of implementation and conclusions are in the last section.
The review of strategic alliances
A strategic alliance may be defined as a cooperative arrangement between two or more
independent firms that exchange or share resources for competitive advantage. From the
resource-based views (Barney 1991, Grant 1991, Wernerfelt 1984, Barney et al. 2001,
Barney 2001), valuable resources which firms do not own are the motive for strategic
alliances. Many classifications for valuable resources have been proposed (Miller &
Shamsie 1996), and these resources can generally be classified into tangible (e.g. financial
and technological) and intangible (e.g. knowledge-based and managerial) resources.
In order to acquire competitive advantage and the ability to respond quickly in a dynamic
environment, firms should consider how to construct and extend limited resources to
develop a capability for sustainable competitive advantage (Teece et al. 1997). Through
strategic alliances, firms can gain their partners’ complementary resources to enhance or
reshape their internal processing to create synergies and competitive advantage within a
market (Nohria & Garcia-Pont 1991). According to the different degrees of vertical
integration or independence, various forms of strategic alliances can be represented using
the following spectrum (Lorange & Roos 1992):
Hierarchy
M&A
Joint
Ownership
Formal
co-operative
venture
Joint
ventures
Informal
co-operative
venture
Market
Large
Degree of vertical integration
None
High
Degree of independence
Low
Figure 1. Spectrum of strategic alliances
However, the questions arise: “How can we choose the correct partners?” and “How can
we allocate these valuable resources?” It is no doubt that choosing the correct partners is
2
the first step to enter a successful strategic alliance, and this process requires careful
screening, which can be a time-consuming process. Furthermore, it is more important that
firms can gain nothing unless they can use their newly-acquired resources effectively. In
other words, the optimization of resource allocations is the key to whether firms can create
synergies and obtain competitive advantage. In this paper, we demonstrate two types of
strategic alliances, joint ventures and M&A, to choose the best alliance partners and
determine the optimal resource allocation for the alliance.
Joint ventures can be defined as the sharing of assets, risks, profits or investment projects
by more than one firm or an alliance cluster (Kough 1988, Kough 1991, Harrigan 1985).
Joint ventures can be considered as a mechanism to reduce the transaction costs incurred
when acquiring other firms (Hennart & Reddy 1997). Over the time that the concept of
joint ventures has been used in practice, the number of joint ventures in the U.S. grew by
423% over the period 1986-1995 (Hitt et al. 1997). If the strategic alliance is a joint venture,
a firm can share the surplus resources with alliance partners to increase total alliance
satisfaction. We can depict the concepts above in Figure 2 to display the processes of joint
ventures.
Optimize
Alliance member 1
Surplus
resource
sharing
Self-satisfaction
Optimize
Alliance member 2
Self-satisfaction
#
#
Optimize
Alliance member m
Self-satisfaction
Figure 2. The concept of joint ventures
Note that based on the concepts above, it is obvious that the equilibrium of joint ventures is
where all alliance partners have the same satisfaction.
Alliance member 1
Optimize
Alliance member 2
New
enterprise
M&A
#
Alliance member m
Figure 3. The concept of mergers and acquisitions
3
Alliance
satisfaction
On the other hand, M&A is the extreme situation of strategic alliance, where two or more
firms form one enterprise and that enterprise can use all partners’ resources to optimize the
goals of the organization (Whitelock & Rees 1993). This means that the enterprise may
cancel some products in firms for the alliance to optimize the overall alliance satisfaction. A
firm will favor M&A over joint ventures when the assets it needs are not commingled with
other unneeded assets within the firm that holds them, and hence they can be acquired by
buying the form or a part of it (Hennart & Reddy 1997). Using Figure 3, we can present the
processes of M&A to optimize the alliance satisfaction.
The main difference between joint ventures and M&A is that joint ventures emphasize
the sharing of surplus resources to optimize alliance satisfaction (i.e. alliance members still
develop their own products), whereas M&A is concerned only with optimizing the overall
alliance satisfaction. In order to discuss the way to allocate optimal alliance resources in a
market mechanism, De Novo programming is proposed in the next section.
De Novo programming
Traditionally, the resource allocation problem (Hackman & Platzman 1990) can be
considered to maximize the following knapsack problem:
max z = Cx
s.t.
(2)
Ax ≤ b,
x ≥ 0.
where matrix C and vector x denote given resource parameters, matrix A denotes the
technological coefficient and b denotes the maximum limited resource portfolio. It can be
seen that the key to optimizing objective functions depends on the appropriate resource
parameters and resource portfolio. In practice, however, it is usually hard to achieve
aspiration levels due to the inappropriate resource allocation.
In addition, although it is rational to allocate resources using the equation above in a
hierarchical system, when the resource allocation problem is under market-based systems,
the factor of a resource’s unit price should be considered and the traditional methods are no
longer suitable. In order to achieve the optimal resource allocation, De Novo programming
is proposed to resolve this problem.
De Novo programming was proposed by Zeleny (1981, 1986) to redesign or reshape
given systems to achieve an aspiration/desired level. Later, various issues, such as
considering fuzzy coefficients (Li & Lee 1990), optimum-path ratios (Shi 1995), and 0-1
programming problem (Kim et al. 1993), have been proposed. The original idea of De
Novo programming was that productive resources should not be engaged individually and
separately because resources are not independent. By releasing various constraints, De
Novo programming attempts to break limitations to achieve the aspiration/desired solution.
The procedures of De Novo programming can be described as follows:
1. Find the aspiration level vector ( z u ) according to the following equation:
max z u = Cx
s.t.
(3)
Vx ≤ B ,
x ≥ 0.
where V=pA denote the unit cost vector, p is the resource’s unit price vector and B
denote the total budget.
4
2. Identify the minimum budget B∗ and its corresponding resource allocation ( x ∗ and
b∗ ) with the aspiration level such as
min B = Vx
s.t.
(4)
Cx = z ∗ ,
x ≥ 0.
3. Using the optimum-path ratio ( r ) to obtain the final solution ( z , x and b ).
z = r ⋅ z ∗ , x = r ⋅ x ∗ and b = r ⋅ b∗ .
where r = B / B∗ .
Since De Novo programming deals with the problem of resource allocations in one
system, the problem of the choosing partners and allocating alliance resources still exists.
Next, we propose the fuzzy multi-objective dummy programming model to provide the best
alliance cluster and the optimal resource allocation combinations in the alliance.
Fuzzy multiple objective dummy programming
In this section, we first describe the concepts of fuzzy sets so that the readers can more
easy to understand the proposed method. However, we do not present all the issues about
fuzzy sets and restrict the relative contents to this paper. The concepts of fuzzy sets were
proposed to extend classical crisp set to consider the certain degree in the interval [0,1].
Since the real-world problems usually are partly true and partly false, fuzzy sets are widely
employed to deal with the problems of uncertainty (especially for the problems of
subjective uncertainty).
In order to present the degree of uncertainty, the degree of membership is developed.
Given fuzzy set A of universe Y, the membership function of set A can be defined as
μ A ( y ) : Y → [0,1]
where
μ A ( y ) = 1 if y is totally in A ,
μ A ( y ) = 0 if y is not in A ,
0 < μ A ( y ) < 1 if y is partly in A .
Usually, the fuzzy set A can be represented using the triangular or the trapezoidal fuzzy
number. Consider the following example in Figure 4, three fuzzy sets, Short, Average, and
Tall, are used to present the degree of height. The fuzzy sets of short and tall can be
represented using the trapezoidal fuzzy numbers (140,140,150,165) and (175, 190, 190,
190), respectively. The fuzzy set of Average can be represented using the triangular number
160, 170, 180).
5
μ( y)
1.0
Short
Average
Tall
140 150 160 165170175 180 190
y
Figure 4. The concepts of fuzzy set
Next, in order to measure the satisfaction of strategic alliances, the concept of fuzzy sets
is used. The conventional fuzzy programming problem (Zimmermann 1978) can be
represented as follows:
max Cx > z
s.t. Ax < b.
(5)
where > and < are the fuzzification of ≥ and ≤ , respectively. Then the satisfaction for
each objective aspiration level can be represented using the following linear membership
function
⎧
0
, cq x ≤ zql
⎪
μ ( zq ) = ⎨( zqu − cq x ) / d q , zql ≤ cq x ≤ zqu
⎪
1
, cq x ≥ zqu
⎩
(6)
where zqu and zql are the aspiration level and the minimum level, respectively and d q
denotes the subjective perception of the minimum tolerant constants which usually assume
d q = zqu − zql , and the corresponding relation can also be depicted as shown in Figure 5.
μ ( zq )
1
μ ( zq )
0
μ ( zq )
cq x
zqu
zq
Figure 5. The membership function for zq
Note that the minimum (maximum) level zql ( zqu ) can be obtain by solving each single
objective mathematical programming model. For example of the two-objective
mathematical programming problem, the first minimum (maximum) level z1l ( z1u ) can be
obtained by solving the following model:
min (max) z1 = c1 x
(7)
6
s.t.
Ax ≤ b .
By letting μ ( z ) = min{μ ( zq ) | q = 1,", Q} denotes the overall satisfaction level, while
u = 1 − μ ( z ) denotes the overall regret level. We can model two strategic alliance types,
joint ventures and M&A, as follows. Without loss of generalization, in the maximum
problem, if there are I firms in an alliance cluster and J firms are candidates to be chosen to
enter the alliance. Then, according to the concept of joint ventures, we can propose the joint
venture model as follows:
<Joint ventures Model>
min u + e
s.t. Ai xi ≤ bi ,
(8)
S j ⋅ ( A j x j ) ≤ b j where S j ∈ {0,1},
Ci xi + ni − pi = ziu ,
S j (C j x j ) + n j − p j = S j ( z uj ),
⎫⎪
⎬ indicate the equilibrium of joint ventures
u ≥ S j ⋅ n j /( z uj − z lj ), ⎪⎭
m
m
⎫
V ( xi + ∑ S j ⋅ x j ) + e = Bi + ∑ S j ⋅ B j , ⎪
j=1
j=1
⎪
⎬ consider market mechanism
m
m
p (bi + ∑ S j ⋅ b j ) = V ( xi + ∑ S j ⋅ x j ), ⎪
⎪⎭
j =1
j=1
ni ≥ 0; pi ≥ 0; ni ⋅ pi = 0; n j ≥ 0; p j ≥ 0; n j ⋅ p j = 0,
u ≥ ni /( ziu − zil ),
x ≥ 0; b ≥ 0, where x = [ xi , x j ]; b = [bi , b j ], i = 1,", I ; j = 1,", J ,
x, b ∈ Integer (where products and resources are undividable conditions),
where ni , n j and pi , p j denote slack and surplus variables in alliance cluster and
candidate partners, respectively, Sj denotes the dummy variable in the jth firm where 1
indicates to enter strategic alliance, e denotes the unused budget which can be ignored in
resource dividable system but can not be ignored in the resource undividable system. Note
that in the minimum problem, we can substitute u ≥ ni /( ziu − zil ) and u ≥ S j ⋅ n j /( z uj − z lj )
with u ≥ pi /( ziu − zil ) and u ≥ S j ⋅ p j /( z uj − z lj ) i.e. we can ignore pi and p j when
dealing with the maximum problem.
On the other hand, the M&A model can also be derived based on Figure 3 in Section 2 to
obtain the optimal alliance satisfaction as follows:
<M&A Model>
min u + e
s.t. Ai xi ≤ bi ,
(9)
S j ⋅ ( A j x j ) ≤ b j where S j ∈ {0,1},
7
m
m
Ci xi + ∑ S j (C j x j ) +ni − pi = ziu + ∑ S j ( z uj ),
j =1
j =1
m
u ≥ ni /[( ziu − zil ) + ∑ S j ⋅ ( z uj − z lj )], indicates to maximize M&A satisfaction
j =1
m
m
⎫
V ( xi + ∑ S j ⋅ x j ) + e = Bi + ∑ S j ⋅ B j , ⎪
j=1
j=1
⎪
⎬ consider market mechanism
m
m
p (bi + ∑ S j ⋅ b j ) = V ( xi + ∑ S j ⋅ x j ), ⎪
⎪⎭
j =1
j=1
ni ≥ 0; pi ≥ 0; ni ⋅ pi = 0,
x ≥ 0; b ≥ 0, where x = [ xi , x j ]; b = [bi , b j ], i = 1,", I ; j = 1,", J ,
x, b ∈ Integer (where products and resources are undividable conditions).
On the basis of the two models above, we can conclude the advantages of the proposed
method as follows. First, we can easily choose the correct alliances partners by setting a
dummy variable, S, using the conventional mathematical programming methods or other
heuristic algorithms such as genetic algorithms or simulated annealing. Second, using the
concept of fuzzy sets, we can easily measure the alliance satisfaction. Next, by
incorporating the concept of De Novo programming, the unit price of the resources can be
considered in the proposed models.
Besides, if both the technological coefficients and resource portfolio are undividable, the
programming can be easily rewritten as the form of the integer programming problem.
Since several algorithms, such as branch and bound algorithm (Bretthauer & Shetty 1995),
linear knapsack method (Mathur et al. 1986, Hochbaum 1995), and dynamic programming
algorithm (Glvoer 1975), can be used to solve this integer fuzzy multi-objective dummy
programming problem, it is more suitable for dealing with the real-world alliance problems.
In order to demonstrate the advantages of the proposed method, a numerical example is
employed to display the satisfaction results in both the joint ventures and the M&A cases.
Numerical example
Strategic alliances are widely adopted by firms to increase competitive advantage in
practice. By exchanging or sharing alliance resources, each alliance firm can obtain more
satisfaction level than their original satisfaction level. However, since every firm has its
own products, objective functions, constraints, and capital, it is hard for firms to consider
the best alliance partners. In this section, the joint ventures and the M&A strategies are
considered here to provide the sound solutions using the proposed method.
Assume Enterprise considers entering strategic alliances with other five candidate firms.
For simplicity, these six firms all produce two products ( x and y ) and have the same
objectives, revenue (R), quality (Q) and satisfaction (S), and production constraints,
material (M), channel (C), promotion (P) and expert (E). Extra information, including
technology coefficients, and capitals in all six firms can be described as shown in Table 1.
Table 1. Objective and production information about six firms
Objectives
Constraints
Products
R
Q
S
M
C
P
E
x
78
4.25
3.52
7
2
7
2
Enterprise
y
125
2.74
4.86
6
8
5
3
8
Capital
4,800
Firm1
Firm2
Firm3
Firm4
Firm5
x1
165
5.78
2.28
3
6
7
2
y1
100
3.03
2.84
5
4
5
3
x2
85
4.97
4.21
2
3
7
2
y2
140
2.77
7.42
5
2
5
3
x3
70
5.99
7.54
8
6
7
2
y3
120
3.93
3.44
6
6
5
3
x4
75
5.57
4.98
8
2
7
2
y4
125
2.36
7.48
8
6
5
3
x5
80
4.38
3.24
4
8
7
2
y5
130
3.69
2.87
6
20
6
15
5
30
3
10
Unit price
3,600
6,400
5,200
4,200
5,400
For Enterprise, the aspiration level can be described to solve the following equations:
max 78 x + 125 y
max 4.25 x + 2.74 y
max 3.52 x + 4.86 y
s.t.
7 x + 6 y ≤ be1 ,
2 x + 8 y ≤ be 2 ,
7 x + 5 y ≤ be 3 ,
2 x + 3 y ≤ be 4 ,
x, y ≥ 0,
be1 , be 2 , be3 , be 4 ≥ 0,
Be = 4800.
In order to increase the enterprise’s objective values, the joint ventures strategy is
considered to choose the best alliance partners. In addition, the corresponding resource
allocation also should be determined. Using Eq. (8), we can obtain the best alliance cluster
and the optimal resource allocation for the case of joint ventures as shown in Table 2.
Table 2. The alliance partners and resource allocation in joint ventures
Alliances
Firm 3
Enterprise
Resource Allocation
x
11.93
6.15
5.78
y
11.74
6.21
5.53
9
b1
b2
b3
b4
159.74
129.85
142.22
59.09
80.33
61.99
74.12
30.94
79.41
67.86
68.10
28.15
Revenue
Quality index
Satisfaction index
μ (z)
2324.57
99.51
114.42
1256.20
43.17
51.84
1068.37
56.34
62.58
0.570
10,000
0.570
0.570
5,069.45
4,930.55
B
By removing the factor of alliance partners, we can obtain the optimal resource
allocation in Enterprise and Firm 3 using the fuzzy multi-objective dummy programming
model as shown in Tables 3 and 4.
Table 3. The optimal resource allocation in Enterprise
Resource allocation
x
y
be1
be 2
be 3
be 4
Value
5.73
5.97
75.94
59.23
69.97
29.34
Resource allocation
Revenue
Quality index
Satisfaction index
μ ( ze )
Be
Value
1,193.39
40.71
49.19
0.43
4,800
Table 4. The optimal resource allocation in Firm 3
Resource allocation
x
y
b31
b32
b33
b34
Value
6.24
5.65
83.84
71.36
71.95
29.43
Resource allocation
Revenue
Quality index
Satisfaction index
μ ( z3 )
B3
Value
1,114.99
59.60
66.51
0.65
5,200
Compared with Tables 2-4, Firm 3 shares redundant resource with Enterprise to increase
the alliance satisfaction. It is clear that the alliance satisfaction is larger than the average
satisfaction, i.e. satisfying the following equation:
1
1
μ ( z ) > [ μ ( ze ) + μ ( z3 )] (i.e. 0.57 > (0.43 + 0.65) = 0.54 )
2
2
indicates that due to the emergence of synergy effects, the firms have motives to enter joint
ventures. Next, we use the integer M&A model (i.e. Eq. (9)) to obtain the best alliance
partners and the optimal resource allocation for the case of M&A as shown in Table 5.
Table 5. The alliance partners and resource allocation in M&A
Alliances
Firm 2
Firm 3
Enterprise
Resource Allocation
x
26
12
8
6
y
20
0
20
0
10
b1
b2
b3
b4
248
124
282
112
84
24
84
24
116
64
156
76
48
36
42
12
Revenue
Quality index
4836
182.1
936
51
3480
95.16
420
35.94
Satisfaction index
269.56
42.24
182.08
45.24
μ ( z)
0.60
0.60
0.60
0.60
B
16,400
4,800
8,720
2,880
On the basis of Table 5, it can be seen that the best alliance cluster in M&A is different
with joint ventures. However, the synergy effects can also be found using the same above
method to motivate the development of the M&A strategy. Next, we provide the depth
discussions according to the implementations.
Discussions
Strategic alliances are widely used in business to obtain synergy effects. These synergy
effects may come from economies of scale, economies of scope, learning effects, etc.
However, many firms fail in strategic alliances without the sound planning or screening for
choosing the correct partners and resource allocations. In this paper, we provide a new
method to overcome these problems above.
Two types of strategic alliances, joint ventures and M&A, are demonstrated here to
present the proposed method. From the numerical examples, it can be seen that in joint
ventures, the surplus resources of Firm 3 (i.e. 5,200 − 4,930.55 =269.45) are shared with
Enterprise to increase the alliance satisfaction (from 0.54 to 0.57). This is the reason why
Enterprise has motives to consider the joint venture strategy. The same situation can also be
found in the M&A case.
From our implementation, the M&A strategy seems provide the better satisfaction level
than the joint venture strategy. However, this is not necessarily true in practice. Since in our
case we do not consider the alliance costs such as coordination cost, control cost, and risk
cost, the optimal alliance strategy cannot be determined. The alliance costs between joint
ventures and M&A can be described as Figure 6.
M&A
Joint
ventures
Low
Coordination cost
High
Control cost
Low
High
Risk cost
Low
High
#
Figure 6. Alliance costs in joint ventures and M&A
Since the alliance costs for joint ventures and for M&A are much different, we can not
11
ignore the effect of alliance costs. It is clear that with considering the different cost
functions, the best alliance strategy could be different.
In addition, the most important thing to facilitate strategy alliances may be the issue how
to set the fair sharing criteria. For the joint ventures case, the satisfaction of Firm 3
decreases from 0.65 to 0.57. However, it is impossible for Firm 3 to enter alliances if its
satisfaction level in the alliance is lower than its original level. Therefore, the rational way
to assign synergy effects in our joint ventures case can be restricted such that μ ( ze∗ ) ≥ 0.43
and μ ( z3∗ ) ≥ 0.65, where μ ( ze∗ ) and μ ( z3∗ ) denote the true satisfaction level for
Enterprise and Firm 3, respectively, after joint ventures. The same way can be used to set
the appropriate sharing mechanism for M&A. More discussions about setting the fair
sharing criteria can refer to our paper (Huang et al. 2005).
Conclusions
The goal of strategic alliances is to create and share the maximum synergy effects among
alliance partners. In order to achieve this goal, the correct alliance partners and the
appropriate resource allocation are critical. In this paper, the fuzzy multi-objective dummy
programming model is proposed to overcome the problems above. On the basis of the
numerical results, we can conclude that both the joint ventures and the M&A model can
provide the best alliance cluster, the maximum synergy effects, and the optimal alliance
satisfaction.
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