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Applied Soft Computing
j o u r n a l h o m e p a g e :w w w . e l s e v i e r . c o m / l o c a t e / a s o c
A hybrid ANP model in fuzzy environments for strategic alliance partner
selection in the airline industry
James J.H. Liou
a, Gwo-Hshiung Tzeng
b,c,∗, Chieh-Yuan Tsai
d, Chao-Che Hsu
eaDepartment of Industrial Engineering and Management, National Taipei University of Technology, No. 1, Section 3, Chung-Hsiao East Road, Taipei 106, Taiwan bSchool of Commerce, Kainan University, No. 1, Kainan Road, Luchu, Taoyuan 338, Taiwan
cInstitute of Management of Technology, National Chiao Tung University, 1001 Ta-Hsueh Road, Hsinchu 300, Taiwan
dDepartment of Industrial Engineering and Management, Yuan Ze University, No. 135, Yuantung Road, Chungli City, Taoyuan County 320, Taiwan eDepartment of Transportation Management, Tamkang University, 151 Ying-Chuan Rd., Tamsui, Taipei 251, Taiwan
a r t i c l e i n f o
Article history:
Received 16 September 2009 Received in revised form 9 August 2010 Accepted 17 January 2011
Available online 26 February 2011 Keywords:
Strategic alliance
Fuzzy preference programming Analytic network process (ANP) Airline industry
a b s t r a c t
Strategic airline alliances are an increasingly common strategy for enhancing airline competitiveness and satisfying customer needs, especially in an era characterized by blurring industry boundaries, fast-changing technologies, and global integration. Airlines have been very active in utilizing this form of strategic development. However, the selection of a suitable partner for a strategic alliance is not an easy decision, involving a host of complex considerations by different departments. Furthermore the decision-makers may hold diverse opinions and preferences arising due to incomplete information and knowledge or inherent conflict between various departments. In this study fuzzy preference programming and the analytic network process (ANP) are combined to form a model for the selection of partners for strategic alliances. The effects of uncertainty and disagreement between decision-makers as well as the interde-pendency and feedback that arise from the use of different criteria and alternatives are also addressed. This generic model can be easily extended to fulfill the specific needs of a variety of companies.
© 2011 Published by Elsevier B.V.
1. Introduction
Strategic alliances between airlines are now common in the aviation industry. They are frequently made in response to chang-ing economic and regulatory conditions[1]. Three major alliances established within the last 10 years—Star Alliance, One-world and Sky Team—now account for nearly 70% of passengers and turn-over in the global market[2]. Strategic alliance strategies allow airlines to expand networks, attract more passengers, and take advantage of product complementarities, as well as providing cost-reduction opportunities in passenger service related areas (such as code-sharing, joint baggage handling, joint use of lounges, gates and check-in counters, and exchange of flight attendants)[3]. A good strategic partner can further enhance the quality of their con-necting services by adjusting arrival and departure flights so as to minimize waiting time between flights while providing sufficient time to make connections. On the other hand, ineffective strategic alliances can lead to the loss of core competencies and capabili-ties, exposure to unexpected risk and even business failure. Take for example—the fall of Swissair. Financial statements show that
∗ Corresponding author at: School of Commerce, Kainan University, No. 1, Kainan Road, Luchu, Taoyuan 338, Taiwan.
E-mail address:[email protected](G.-H. Tzeng).
its airline alliance policy and investment strategy were responsible for the majority of its losses from 1997 to 2001[4].
Prior research suggests that the choice of alliance partner is an important variable with significant influence on the performance of the strategic alliance partners[5,6]. An appropriate partner is one that can contribute resources and capabilities that the focal firm lacks. This ultimately determines the viability of the strate-gic alliance. Partner-related selection criteria require consideration to determine whether the corporate cultures of the partners are compatible, and whether trust exists between the partners’ man-agement teams. This ensures that the selected partner and focal firm achieve organizational interdependence. Although the impor-tance of selecting the right partner for forming strategic alliances has been recognized in literature, there have been few empirical studies on how to choose that partner which stress the interrela-tionship between the partners and the focal firm at the same time. The analytic network process (ANP) was proposed by Saaty[7]to overcome the problem of interrelation among criteria or alterna-tives. The ANP is a general form of the analytic hierarchy process (AHP), which releases the restrictions of the hierarchical structure. It has been successfully applied in many multi-criteria decision making (MCDM) problems[8–11]. However, due to problems such as incomplete information and subjective uncertainty, even experts find it difficult to quantify the precise ratio of weights for the dif-ferent criteria. The concept of fuzzy sets has been incorporated into 1568-4946/$ – see front matter © 2011 Published by Elsevier B.V.
AHP to deal with the problem of uncertainty, although ANP has not often been used to address this type of problem in fuzzy environ-ments. A way to cope with uncertain judgments and to incorporate the vagueness that typifies human thinking is to express the prefer-ences as fuzzy sets or fuzzy numbers[12]. Therefore, the objective of this study is to combine fuzzy preference programming and ANP to make a model capable of helping airlines select the best partner for strategic alliances.
The rest of this paper is structured as follows: In Section2, we summarize some of the important previous studies regarding the strategic alliance strategy, and the problem characteristics are described. In Section3, the basic concepts of fuzzy preference pro-gramming and ANP are reviewed. In Section4, a strategic alliance model is developed. The implementation using the proposed fuzzy ANP is presented in Section5. Section6includes discussions and some conclusions.
2. The strategic alliance
While merger activities have slowed significantly since 2000, strategic alliances are increasingly and widely used by airlines. International alliances give airlines access to parts of the world than would otherwise be economical, or where there may lack the authority to operate their own flights[3]. Through alliances, part-ners are able to compete more successfully. Yoshino and Rangan [13] and Gomes-Cassers [14] define the alliance as a coopera-tive venture between firms situated on the continuum between markets and hierarchies. The alliance is distinguished by several characteristics: independent firms; horizontal or vertical relation-ships; relationships which are not solely transactional; partners share resources, risks and benefits but have limited control and incomplete contracts. The types of airline alliance may include reciprocal frequent-flyer program recognition, shared lounges and check-in facilities, code-sharing agreements, marketing arrange-ments, procurement policies, system commonality, and even the interchangers of flight-crew personnel and aircraft[2].
There have been a number of empirical studies on the effective-ness of alliances, including those by Gellman Research Associates [15], Park and Cho [16], Oum et al. [17], Park et al. [18], and Zhang et al.[3]. Results show that alliances improve a carrier’s performance on a number of economic measures, including pro-ductivity, pricing, profitability, and share price. Other studies, such as Dev et al.[19]discussed strategic alliances from a number of theoretical perspectives, including transaction cost economics, net-work relationships, game theory, developmental processes, ethics and firm internationalization. Brueckner[20]analyzed the effects of international airline code-sharing on traffic levels and welfare using specific demand and cost functions. He showed that the beneficial effects of code-sharing outweigh its harmful effects for most parameter values in his theoretical model. Fan et al. [21] examined the forces influencing the consolidation and structure of the airline alliance. They highlighted the following five forces: (i) increased globalization in trade and air transportation; (ii) increased intra-regional interaction, (iii) economic incentives for airline consolidation; (iv) pace of liberalization of international air transport industry, and (v) anti-trust concerns. Holtbrugge et al. [2]investigated human resource management (HRM) after strate-gic alliance. The main focus in all of these alliance studies has been the importance of the strategic alliance or the performance mea-sures after the alliance. Discussion of the issue of strategic partner selection has been relatively rare. The selection of a suitable part-ner for a strategic alliance is not an easy decision, involving many complex considerations. It is essentially a group-decision involving many dimensions and inherent risks, such as inter-partner con-flicts, and potential structural and cultural incompatibilities. The
proposed hybrid fuzzy preference programming and ANP model is able to consider decision-makers’ uncertainty and provides insights into the interrelationship between alliance motivations and part-ner selection criteria in the airline industry, which to the best of our knowledge, has largely been neglected.
3. Proposed hybrid fuzzy preference programming and ANP model
In this section, the concepts of fuzzy preference programming for coping with the uncertain judgments in a group-decision pro-cess are first introduced. The ANP method for determining the best partner for the strategic alliance is then discussed, including con-sideration of the dependence and feedback effects. The combined model can help companies to evaluate a suitable partner and fulfill their specified needs.
3.1. Fuzzy preference programming
Fuzzy preference programming was first proposed by Mikhailov and Singh[22]. It is mainly used to derive priority vectors from a set of comparison judgments or interval comparisons. Let A ={lij, uij}
represent an interval comparison matrix with n components, where lijand uij are the lower and upper bounds of the corresponding
uncertain judgments. Interval judgments are considered consis-tent if there exists a priority vectorw that satisfies the following
inequalities: lij≤
wi
wj ≤ uij
. (1)
Inconsistency in the judgments indicates that no priority vector satisfies all the interval judgments simultaneously. Thus, a suffi-cient solution vector has to satisfy all the interval judgments as much as possible, that is
lij≤˜
wi
wj
˜
≤uij, i= 1, 2, . . . , n − 1; j = 2, 3, . . . , n; j > i, (2)
where ˜≤ denotes the statement “fuzzy less or equal to”.
In order to handle the above inequalities we can represent them as a set of single-sided fuzzy constraints:
wi− wjuij≤0,˜
−wi+ wjlij≤0.˜
(3) The above m fuzzy constrains can be represented in the following matrix form:
Rw ˜≤0, (4)
where the matrixR ∈ m×n; m = n(n− 1).
The kth row of Eq.(4)is a fuzzy linear constraint, which can be defined as a linear membership function of the type:
A˜k(Rkw) =
⎧
⎪
⎨
⎪
⎩
1−Rkw dk , 0 <Rkw ≤ dk, 0, Rkw ≥ dk, 1, Rkw ≤ 0 (5)where dkis tolerance parameter for the kth row, representing the
admissible interval of approximate satisfaction of crisp inequality
Rkw ≤ 0. The membership function of Rkw can be represented as
inFig. 1.
The membership function(5)is equal to zero when the cor-responding crisp constraint Rkw ≤ 0 is strongly violated; it is between zero and one when the crisp constraint is approximately satisfied; and it is equal to one when the constraint is fully satisfied. To solve the fuzzy preference programming, two assumptions are needed. First let A˜k(Rkw), k = 1, 2, . . ., m be the membership functions of the fuzzy constraintsRw ˜≤0 on the n − 1 dimensional
simplex, whereA
kis a fuzzy number of the kth pair-wisecompari-son:
Qn−1= {w = (w1, w2, . . . , wn)|wi> 0, w1+ w2+ . . . + wn= 1}.
(6) The feasible fuzzy ˜P area on the simplex Qn−1 is a fuzzy set,
described by the membership function: P˜(w) = [min
1(R1w), . . . , m(Rmw
|w1+ . . . + wn= 1], (7)
The feasible fuzzy area is defined as the intersection of all fuzzy constraints on the simplex. The second assumption of the fuzzy preference programming selects a priority vector with the highest degree of membership as follows:
ˇ= max[min{A˜1(R1w), . . . , A˜m(Rmw)}|w1+ . . . + wn= 1], (8) where m=1
2n(n− 1).
Bellman and Zadeh [23] proposed a max-min operator for deriving a maximizing solution for general decision-making prob-lems with fuzzy goals and fuzzy constraints. Zimmermann[24] employed Bellman and Zadeh’s idea to show that the max-min fuzzy linear problem can be transferred into a conventional linear programming:
Maximize ˇ
Subject to dkˇ+ Rkw≤ dk,
w1+ w2+ . . . + wn= 1, wi> 0, i= 1, 2, . . . , n, k = 1, 2, . . . , m.
(9) where ˇ≤ 1 − (Rkw/dk) can now be written as dkˇ+ Rkw ≤ dk.
The details of the max-min operator and its relationship between fuzzy preference programming are illustrated inAppendix A. For comparison, we also added the compromise solutions with multi-ple objectives obtained using the min-max operator, as shown in Appendix B.
The optimal solution for the above linear program is a vector (w∗, ˇ∗), whose first component represents a priority vector which
has the maximum degree of membership in the feasible fuzzy area, and the second component gives us the value of that maximum degree, the so-called consistency index[12]. Please note that for the max-min operator, the maximum ˇ represents the highest degree
of membership in the decision set: D(xmax)= max
x≥0minij {Gi(x), Cj(x)}. (10)
However, in our proposed fuzzy preference programming method, we only apply the fuzzy constraints Cj and do not use the mem-bership function of fuzzy goals Gi(seeAppendix A). Furthermore, the ˇ value is equal to 1, representing the highest consistent level (which is similar to 0 in the AHP consistency ratio ); 0 indicates when the constraints are completely violated.
3.2. Analytic network process
ANP is the generic form of AHP, allowing for more complex inter-dependent relations among elements/criteria[7]. Saaty[25]first developed AHP in 1971, to help establish decision models through a process that contains both qualitative and quantitative compo-nents. Qualitatively, it decomposes a decision problem from the top overall goal to a set of manageable clusters, sub-clusters, and so on, down to the bottom level, which usually contains scenar-ios or alternatives[26]. Although both the AHP and the ANP derive ratio scale priorities by making paired comparisons of elements on a criterion, there are some differences between them. The first dif-ference is that the AHP is a special case of the ANP, because the ANP handles dependence within a cluster (inner dependence) and among different clusters (outer dependence). Second, the ANP is a nonlinear structure, while the AHP is hierarchical and linear, with a goal at the top level and the alternatives on the bottom level[27]. The first step in the ANP is to develop the structure of the designed model. The AHP decision model is always restricted to being hierarchical, containing several levels assumed to have inde-pendent criteria. Only adjusted levels of the ANP are assumed to have dependence/correlation with each other. Therefore, the ANP is a network structure, where the hierarchical restriction is relaxed so that dependence/correlation can be stipulated in any part of the decision model to form the sub-matrices for the so-called super-matrix[7,26]. The second step is to compare the criteria for the whole system to form a supermatrix. This is done through pair-wise comparisons by asking “How much importance does a criterion have compared to another criterion with respect to our interests or preferences?” The relative importance value is determined using a scale of 1–9, representing equal importance to extreme impor-tance, respectively[7,28]. The general form of the supermatrix can be described as follows: 2 1 1 2 1 2n 21 1n 11 11 12 1 1n 2
C C
m m mn m1 mC
e
e
e
e
e
e
e
e
C
e
e
C
C
=
W
2 1m 12 11 21 22 2m 22 21 2n m m1 m2 mm m2 m1 mne
e
e
e
e
⎤
⎡
⎥
⎢
⎥
⎢
⎥
⎢
⎥
⎢
⎥
⎢
⎥
⎢
⎥
⎢
⎥
⎢
⎥
⎢
⎥
⎢
⎥
⎢
⎥
⎢
⎥
⎢
⎥
⎢
⎦
⎣
W
W
W
W
W
W
W
W
W
,
(11)1
0
0
R w
k(
)
k k Aμ
~R w
d
kFig. 1. Illustrated membership function.
where Cmdenotes the mth cluster; emn denotes the nth element
in the mth cluster; and matrixWij is compose of a serial
princi-pal eigenvector of the influence of the elements compared in the jth cluster to the ith cluster. The form of the supermatrix depends on the variety of the structure. For example, if the structure of the system is shown as inFig. 2, the unweighted supermatrixW,
con-taining the local priorities derived from the pair-wise comparisons throughout the network can be illustrated as follows:
3 2 1 13 1 21 2 33 32 3
0
0
0
0
0
C
C
C
W
C
W
C
W
W
C
⎤
⎡
⎥
⎢
=
⎢
⎥
⎥
⎢
⎦
⎣
W
.
(12)W21is a matrix that represents the weights of cluster 2 with respect
to cluster 1; matrixW32 denotes the weights of cluster 3 with
respect to cluster 2; and matrixW13shows the weights of cluster 1
with respect to cluster 3. In addition, matrixW33is denoted as the
inner dependence and feedback within cluster 3. After forming the supermatrix, the weighted supermatrix is derived by transforming the sum of all columns to exactly unity. This step is very similar in concept to the Markov chain for ensuring that the sum of the prob-abilities of all states equals 1[28]. The weighted supermatrix can then be raised to limiting powers, to calculate the overall priorities that are represented on each row in the converged matrix.
4. Constructing a strategic partnering model for analysis
The model was developed and validated using input from an international airline operating in Taiwan. This airline currently flies to more than 40 destinations around the world, although most are within the Asia Pacific region. The company has sought to join strategic alliances in order to develop a far-reaching service net-work and increase competitive power, to enhance the effectiveness of its global logistics and to provide better service for satisfying cus-tomer needs. The decision is a strategic one, in that the success of the development would have great impact on the competitiveness of the company.
Since partner selection is crucial to success, it is imperative for decision-makers to devise, identify and recognize effective partner selection factors as well as to evaluate questions of compatibility and feasibility prior to joining or developing any strategic alliance. The conceptual model of the strategic partner selection process is first developed based on previous work[10,16,18,26,29]. Then, through the Delphi method we consulted with some senior man-agers of the airline in order to modify the original model. After adding/deleting some elements and modifying the flow graph, the final strategic model used in this study is illustrated inFig. 3. Of
Cluster 1 Cluster 2
Cluster 3
Fig. 2. Illustrated structure of the system (example).
course, the present network was mainly based on the managers’ opinions of the case company; other companies may end up with different networks based on their own operation environment.
The relative factors and alternatives are structured in the form of a hierarchy. The model requires the development of attributes at each level and a definition of their relationship. The ultimate goal is to select the best partner. To do this, it is first necessary to strategically analyze the internal organizational and external envi-ronmental driving forces, which act as the underlying motivation and reasons for alliance formation. Based on the considered driving forces, the alliances’ scope and structure are provided for evalua-tion. There are five major ways to implement strategic alliances, including market, product/service, computer systems, equipment and equipment servicing, and logistics. After the types of strategic alliance are investigated, some choices of appropriate partners for strategic alliance formation are considered. Finally, the evaluation of the alliance is fed back into the analytical phase, to incorporate any changes based upon experience. We are seeking to determine which of several alternatives would best support the realization of the ultimate goal while feedback effects are considered. Details of the procedure are described as follows:
(1) Strategic analysis: The first step is the strategic analysis phase where internal and external driving forces for a strategic alliance are analyzed. The internal drivers include “risk shar-ing,” “economies of scale,” “access to assets, resources and competencies,” and “shaping competition.” Strategic alliances are seen as an attractive mechanism for hedging risk, because neither partner has to bear the full risk or cost of the alliance activities [30]. The economies of scale advantage can be achieved when alliance partners link up their existing networks so that they can provide connecting services for new markets. Marketing costs can be shared between alliance partners, which may have strongly entrenched positions in certain markets[31]. The regulatory framework for “bilateral agreements”, landing rights and congestion at certain airports means that airlines already possessing licenses to operate a route or have slots at congested airports have important and marketable assets that are attractive to alliance partners[29]. Strategic alliances can also be used as a defensive ploy to reduce competition, since an obvious benefit of strategic alliances is converting a competitor into a partner[32]. Alternatively, alliance formation may form part of an offensive strategy, for example by linking with a rival in order to put pressure on the profits and market share of a common competitor[33].
The external drivers include “information revolution,” “eco-nomic restructuring,” and “global competition.” Computer reservations systems (CRS) allow airlines to monitor, manage and control their capacity through yield management and their clients through frequent flyer programs. Undoubtedly, the air-lines that own the CRS will favor their own flights. Joint airline ownership may reduce the chances of CRS being biased in favor of a particular airline, but the dominance of CRS companies gives them considerable market power[31]. Also, consumers often favor their own national airline or its partners to an
Marketing Code-sharing Frequent flyer reciprocity Promotion integrated Promotion separate Product / service Integrated brands Brands remain separate Adopted under license
Strategic Alliance Structure
Computer systems Integrated Shared Separate Equipment and equipment servicing Shared equipment Separate equipment Shared maintenance Separate maintenance Logistics Shared offices Separate offices Shared terminals Separate terminals
Strategic Alliance
Internal Drivers
Risk sharingEconomies of scale, scope & learning Access to assets, resources & competencies Shaping competition
External Drivers
Information revolution Economic restructuring Global competitionMotivations
Choice of Alliance Partners/Alternatives
Capability Compatibility
Commitment
Oneworld
Star Alliance SkyTeam
Control Geographical fit
Fig. 3. Network structure of project partnering.
extraordinary degree. Such a patriotic attitude to purchasing, rarely replicated in other industries, drives airlines to form alliances as the only effective means of market entry [29]. Economic restructuring through the philosophy of economic disengagement by governments, as is currently occurring in many parts of the world, has also had a major impact on airline industry structure. In addition, liberalization, privati-zation, foreign ownership and transnational mergers may also have a major impact upon the future structure of the airline industry, even though many regulatory and ownership barri-ers remain in force worldwide. Since this means that mergbarri-ers and acquisitions are often precluded as viable growth strate-gies for international airlines. Consequently the formation of strategic alliances is, in many cases, the only available form of market entry. Airlines seek to maximize their global reach, in the belief that those that offer a global service will be in the
strongest competitive position. In other words, globalization is an important external drive for alliance formation in today’s highly competitive environment.
(2) Strategic development: In determining the methods by which strategic development will take place, organizational man-agement is faced with making a choice between a variety of different alliance structures and scopes, as indicated inFig. 3. The airline will prioritize its strategic development based on previous strategic analysis and its current operational situa-tion. There are many ways to implement a strategic alliance, such as shared airport facilities, synchronized scheduling, reci-procity in frequent flyer programs, freight coordination and joint marketing activities. There are usually inner dependence and feedback effects between these different strategic alliance strategies. Also, due to resource constraints, it may be possi-ble to pursue only some of these options. Once the preference
Table 1
Fuzzy weight comparisons of external drivers.
Market Service/product Computer Equipment Logistic Weights
Market 1 (1, 3) (2, 5) (3, 5) (1, 3) 0.41 Service/Product (1/3, 1) 1 (1/5, 1/3) (3, 7) (1, 3) 0.16 Computer System (1/5, 1/2) (3, 5) 1 (4, 7) (3, 5) 0.24 Equipment (1/5, 1/2) (1/3, 1) (1/7, 1/4) 1 (1/2, 3) 0.08 Logistic (1/3, 1) (1/3, 1) (1/5, 1/3) (1/3, 2) 1 0.11 Consistency index = 0.92.
is made, the airline is committed to pursuing these courses of action.
(3) Strategic partner selection: There are several reasons for the successful implementation of strategic alliances but the impor-tance of partner selection has been emphasized by several writers [34,35]. There are some important factors that need to be considered when choosing appropriate partners. The selected partner should have the capability to carry out its role within the alliance. Partners should also be able to demon-strate equal commitment to an alliance through experiencing commensurate levels of risk. The compatibility of the part-ner and the focal firm, both in cultural and operational terms, is another significant factor. For example, the failure of the “Alcazar” alliance in the early 1990s was due to misunderstand-ings between the various American partners and differently affiliated CRS systems. The success of the strategic alliance also depends on an effective control system and whether partners are likely to contribute to the alliance. Sometimes, a strong focused leadership can be viewed as opportunistic, and a power imbalance lends potential for conflict among the partners. A key question that needs to be addressed in the assessment of alliance control is the extent to which each partner is able to achieve whatever strategic objectives they have set them-selves when entering into the alliance relationship[29]. The geographical fit also needs to be considered when selecting strategic partners. Airlines are careful to avoid forming partner-ships with airlines that have overlapping markets. For example, in the Northwest/KLM alliance, partners have distinctive geo-graphical strengths in the USA and Europe.
(4) Feedback evaluation: After the partners are decided, the selected partners will have some degree of impact or effect on the focal firm, both internal and external. Whether an alliance can improve a carrier’s performance and fulfill the objectives that drove the alliance is an essential factor for long-lasting strate-gic alliances. If the interdependence within the alliance is not strong enough and performance improvement is limited, the alliance will easily collapse. Therefore, the evaluation and feed-back for selected partners as related to the driving forces is included in this model.
5. Implementation of the proposed hybrid model
In this study, the general manager of the airline under study designated a team to develop a strategic partner selection plan. Twenty-five managers from different departments, including planning, operation, maintenance, human resources, information systems, and safety, with at least 15 years experience in the airline and expertise in their own particular fields filled out a survey.
5.1. Pair-wise comparisons and fuzzy preference programming In ANP, like AHP, managers are asked to make pair-wise com-parisons of the elements in each level with respect to their relative importance toward their upper/control criterion. To ensure that no extreme cases exist, the Delphi method is applied to collect the data. Since different experts come from different departments they propound a variety of viewpoints, and his or her judgment will be different. After circulating the questionnaire several times, each pair-wise comparison converges to an acceptable range, with-out extreme cases. As mentioned in Section3.2, a scale of 1–9 is used to compare the two components, with a score of 1 represent-ing no difference between the two components and 9 representrepresent-ing overwhelming dominance of the component under consideration (row component) over the comparison component (column com-ponent). When scoring is conducted for a pair, a reciprocal value is automatically assigned to the reverse comparison within the matrix (i.e., aji= 1/aij). Since many of these values are strategic and
subjec-tive, the comparison ratios are represented as an interval (lij, uij),
with upper and lower bounds. Two separate pair-wise comparison matrices (internal and external drivers) have to be developed in this step. An example of the pair-wise comparison matrix of exter-nal drivers for the strategic alliance is shown inTable 1. Please note that the intervals shown inTable 1indicate a range of answers from 25 managers.
Using the fuzzy preference programming introduced in Section 3.1, the interval of the comparison ratios (Table 1) can be trans-ferred into a linear programming problem as follows (the tolerance parameter dk= 1): maximize ˇ Subject to ˇ+ w1− 3w2≤ 1, ˇ− w1+ w2≤ 1, · · · ˇ+ w4− 3w5≤ 1, ˇ− w4+ 0.5w5≤ 1, w1+ w2· · · + w5= 1.
The above linear programming problem is solved in order to derive the consistency index and the weighted priorities for this matrix, as indicated in the last column ofTable 1. The weighted internal drive priorities can be used for similar procedures to obtain the sub-matrix showing motivation, as illustrated inTable 2. It is obvious that the market (0.41) has the highest priority with respect to external drives, while the computer system (0.43) is considered the most important of internal drives.
The second step in our pair-wise comparison of different alliance structures is to compare the relative importance of three pro-posed alliances. The three propro-posed alliances have been arrived
Table 2
Weight priorities for motivation.
Weights
Market Service/product Computer system Equipment Logistic
Internal drives 0.21 0.13 0.43 0.16 0.07
Table 3
Fuzzy weight comparisons for marketing.
Star Alliance One-world Sky Team Weights Star Alliance 1 (1, 5) (3, 7) 0.57
One-world (1/5, 1) 1 (1, 3) 0.29
Sky Team (1/7, 1/3) (1/3, 1) 1 0.14
Table 4
Weight priorities under different alliance structures. Weights
Star Alliance One-world Sky Team
Marketing 0.57 0.29 0.14
Service/product 0.46 0.42 0.12
Computer system 0.16 0.62 0.22
Equipment 0.41 0.36 0.23
Logistics 0.21 0.34 0.45
at through discussion with 25 airline managers through the Del-phi method. Five separate pair-wise comparison matrices (market, service/product, computer system, equipment, and logistics) are required to fully describe the relative importance of different alliances with respect to alliance structure. An example of one of these matrices is shown inTable 3. The weight priorities (last col-umn ofTable 3) can be derived by fuzzy preference programming similar to step one. In this case, the “Star Alliance” would have the greatest importance with respect to marketing consideration. The other weight priorities (under different alliance structures) are shown inTable 4. The results indicate that “One-world” is better for their computer system while the “Sky Team” leads on logistics. As described in our model (Fig. 3), the motivations for strategic alliances include both external and internal drivers. Any formulated strategic alliance should fulfill its original motivations. Therefore, we must consider the feed-back effect that will occur if the selected alliance can satisfy its internal and external drives. Using similar procedures to steps one and two, we obtain the weight priori-ties with respect to different alliances as shown inTable 5. In the “Star Alliance” there is probably more emphasis placed on external drives, “One-world” places greater importance on internal drives, while in “Sky Team” internal and external drives are found to be fairly close in importance to each other.
5.2. Sensitive analysis
In our fuzzy preference programming, the tolerance dkwas set
as 1. That is the membership function of pair-wise comparison will decrease monotonically from 1 to 0 over the tolerance interval dk= 1
(Fig. 1). To investigate the influence of the tolerance on the obtained weights, we conducted a sensitivity analysis by setting different dk
values. We tried values ranging from 0.1 to 9, which represented the maximum pair-wise comparison value to the minimum value. These results indicate that the obtained weights were all the same for all the different tolerance setting values, except that the ˇ value increased from 0.189 to 0.991 as the tolerance dkincreased from
0.1 to 9. Since our main purpose is to derive the weights of the criteria, the proposed model is robust with the various tolerances of the membership functions.
Table 5
Weights of internal and external drives under different alliances. Weights
Internal drives External drives
Star Alliance 0.19 0.81
One-world 0.85 0.15
Sky Team 0.54 0.46
Strategic Choice of Motivations Alliance Alliance
13 21 22 32 Structure Partner Motivations
Strategic Alliance Structure Choice of Alliance Partner
0
0
0
0
0
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⎥
⎢
⎥
⎣
⎦
W
W
W
W
Fig. 4. Structure of strategic alliance in the ANP model.
5.3. Super-matrix and limit matrix
Given the interdependent influences, a system that consists of process steps and feedback effects needs to be transformed into a super-matrix. This can be achieved by entering the local prior-ity vectors into the super-matrix, to in turn obtain global priorities. The inner dependence and feedback effects between levels/clusters for the model developed for strategic alliance selection are shown inFig. 3. Inner dependence exists within the alliance structure and feedback effects are related to motivation. A general view of the super-matrix for this study is also shown (Fig. 4), where the pair-wise comparison matrices of the three steps are entered into the correct locations. In a super matrix, these individual matrices are called sub-matrices. For example,W21is the sub-matrix of
motiva-tion, whileW22is the sub-matrix of inner dependence within the
“alliance structures” cluster. The complete un-weighted superma-trix for the ANP model is show inTable 6. Please note that due to inner dependenceW22, the diagonal elements ofW22are first set
to 0.5 while the other elements are set to 0, then the column vec-tors (under the alliance structure) are normalized to sum up to one [28]. The un-weighted super-matrix is then raised to a sufficiently large power until convergence occurs. In this study, convergence occurs at 36 times.Table 7provides the final limit matrix. This limit matrix is a column stochastic and represents the final eigenvector. The alternative with the largest value should be the one selected. As shown inTable 7, the results of the alliance-partner alternatives in the case study point to the selection of “One-world” as the best choice, due to a weight of 0.108, which is larger than that of the other two alternatives.
5.4. Result analyses and discussion
Although ANP has been widely used in various applications, it is hard for decision-makers to quantify precise judgments about cri-teria under conditions of incomplete information and subjective uncertainty. In this paper, we propose a hybrid model combin-ing fuzzy preference programmcombin-ing and ANP, which extends the original ANP by using fuzzy judgments to compare the ratios of weights between criteria. This model can avoid the convergence problems encountered using standard fuzzy arithmetic operations in fuzzy ANP. Since standard fuzzy arithmetic operations are used to multiply and divide fuzzy numbers, the method may result in the convergence and rational problems of fuzzy global weights. We use linear programming to derive the steady-state priority vec-tors, and then use ANP to consider clusters/criteria dependence. The model should be more practical for actual application than ANP, which ignores the uncertain judgments often made in the real world, and conventional fuzzy ANP, which causes convergent problems. Table 8 shows a comparison of the results obtained between our proposed model and the original ANP method. Our model indicates that One-world is the best selection while the original ANP method points to Star Alliance (with a higher weight 0.100 than 0.098 of One-world) as being optimal. However, in our
Table 6
Un-weighted supermatrix.
Motivations Alliance structure Partners
C11 C12 C21 C22 C23 C24 C25 C31 C32 C33 C11 0 0 0 0 0 0 0 0.19 0.85 0.54 C12 0 0 0 0 0 0 0 0.81 0.15 0.46 C21 0.21 0.41 0.50 0 0 0 0 0 0 0 C22 0.13 0.16 0 0.50 0 0 0 0 0 0 C23 0.43 0.24 0 0 0.50 0 0 0 0 0 C24 0.16 0.08 0 0 0 0.50 0 0 0 0 C25 0.07 0.11 0 0 0 0 0.50 0 0 0 C31 0 0 0.28 0.23 0.08 0.20 0.10 0 0 0 C32 0 0 0.14 0.21 0.31 0.18 0.17 0 0 0 C33 0 0 0.08 0.06 0.11 0.12 0.23 0 0 0
Note: C11= internal drive; C12= external drive; C21= marketing; C22= service/product; C23= computer system; C24= equipments; C25= logistic; C31= Star Alliance; C32= One-world; C33= Sky Team.
Table 7
Limit supermatrix.
Motivations Alliance structure Partners
C11 C12 C21 C22 C23 C24 C25 C31 C32 C33 C11 0.137 0.137 0.137 0.137 0.137 0.137 0.137 0.137 0.137 0.137 C12 0.113 0.113 0.113 0.113 0.113 0.113 0.113 0.113 0.113 0.113 C21 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 C22 0.072 0.072 0.072 0.072 0.072 0.072 0.072 0.072 0.072 0.072 C23 0.172 0.172 0.172 0.172 0.172 0.172 0.172 0.172 0.172 0.172 C24 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 C25 0.044 0.044 0.044 0.044 0.044 0.044 0.044 0.044 0.044 0.044 C31 0.089 0.089 0.089 0.089 0.089 0.089 0.089 0.089 0.089 0.089 C32 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 C33 0.053 0.053 0.053 0.053 0.053 0.053 0.053 0.053 0.053 0.053
proposed model, we considered decision-maker uncertainty when they make a decision, which could make this model more realis-tic than the original method. Furthermore, we divided the experts into two groups, technical (operational, maintenance and safety departments) and non-technical (financial, marketing and service departments). The opinion of the technical group was that One-world was the best alliance, but the result for the non-technical group gave Star Alliance the highest weight. These results might be because Star Alliance has a higher marketing share, and non-technical groups deemed marketing and service to be the important criteria. On the other hand, One-World was chosen by technical groups due to the experts thinking that One-world offered more reliable technical operation. Again, this is the advantage of our model that it can integrate different opinions to come up with an optimal solution.
The empirical results indicate that “One-world” is the best selec-tion from the airline’s viewpoint. However whether to join an alliance or not is not only dependent on the company’s “willing-ness”, but also on “acceptance” of the alliance. Here we provide a tool to help airlines select an optimized strategic alliance given their own requirements. It is also worth noting that different air-lines may end up with different results, based on their own specific needs. Although the present model has proven valuable, there are still some areas that need further discussion. It is acknowledged that the decision levels and criteria involved in any particular implementation may differ depending on the airlines/enterprises involved. In fact, this is one of the strengths of ANP, which can be
used to construct various structures considering inner dependence and feedback effects. A set of criteria should be designed for each application, depending upon what is deemed important for that application. Decision criteria or dependence within/between clus-ters that a company considers to be crucial can be easily added to the generic model. Also, the weighting given each component in the model is dependent on the decision-makers evaluation of the component. This helps facilitate tailoring of the model to the com-pany in question. For example, an airline that stresses enlarging markets would likely select criteria and weightings different from an airline seeking to provide better services/products.
On the other hand, not all possible criteria and interactions are considered. Again, decision factors could be added, depending on the decision environment. Possible extensions in this area currently being explored include risk analysis of strategic alliances and dif-ferent interactions between clusters. For instance, currently, only a one-way influence between motivations, alliance structures and partners is included in the model. The interactions could be mod-eled as two-way interactions. Perhaps a more interesting and useful extension of the model would be to include interactions within alliance structures and alternatives (partners).
One of the limitations of the original ANP is its dependency on the decision-makers. The weightings obtained are based on the decision makers’ subjective opinions and many of these values are strategic, therefore, additional strategic group decision-making tools are needed. Although we can use scenario planning or the Del-phi approach, these are still time-consuming and it is sometimes
Table 8
Comparison between fuzzy preference programming with ANP and original ANP.
Motivations Alliance structure Partners
C11 C12 C21 C22 C23 C24 C25 C31 C32 C33
FPP + ANP 0.137 0.113 0.150 0.072 0.172 0.060 0.044 0.089 0.108 0.053
( )
if x
−f
i*( )
x
( )
if x
( )
i gx
μ
1
Fig. A1. Membership function of fuzzy goals.
hard to reach a consensus. In this study, the uncertainty of judgment is removed by expressing the comparison ratios as an interval, to incorporate the vagueness inherent in human thinking. The pro-posed model has some further advantages. It provides opportunity for solving prioritization problems with mixed types of comparison judgments, such as intervals or crisp numbers. Also, the prioritiza-tion problem is treated as a linear program, which can easily be solved.
6. Concluding remarks
The purpose of this paper is to describe a method for strate-gic alliance selection that allows for consideration of important interactions among decision levels and criteria. We use a hybrid model combining fuzzy preference programming and ANP method-ology that considers uncertainty in group decisions, and both inner dependence and feedback effects for this evaluation. We develop a model for the strategic alliance partner selection process based on the literature and adapted for an airline in Taiwan. The airline acts as a case study for validation of the model approach. This work should be valuable to practitioners because it provides a generic model for partner selection. This strategic decision-making tool can assist an airline in comparing proposed alliance partners with respect to dif-ferent process stages and alliance structures. The model suggests that the “One-world” alliance is the best option for this particular airline. The case study helps to verify that the proposed model is an effective and efficient decision-making tool which can be easily extended.
Appendix A. The max-min operator
A.1. Fuzzy goal and fuzzy constraint programming
In fuzzy goal and fuzzy constraint programming problems, it can mathematically be represented as
max [˜f1(x), ˜f2(x), · · ·, ˜fk(x)]
s.t. Ax ≤ ˜b˜ x ≥ 0
(A1)
wherex is the vector of variables and ˜b is the vector for the fuzzy
right hand side.
First, we can define the membership function of fuzzy goals and fuzzy constraints as follows (seeFigs. A1 and A2):
gi(x) =
⎧
⎪
⎨
⎪
⎩
1, fi(x) > fi∗(x) 1− fi∗(x) − fi(x) fi∗(x) − f− i (x) , fi−(x) ≤ fi(x) ≤ fi∗(x) 0, fi(x) < fi−(x) (A2) jb
b p
j+
j(Ax)
j( )
j Cx
μ
1
(
Ax)
jFig. A2. Membership function of fuzzy constraints.
Cj(x) =
⎧
⎪
⎨
⎪
⎩
1, (Ax)j< bj 1−(Ax)j− bj pj , bj≤ (Ax)j≤ bj+ pj 0, (Ax)j> bj+ pj (A3)The membership function(A2)of the fuzzy objective function i should be 0 for fi(x) levels equal to less than lower bound, 1 for
fi(x) equal to or greater than the upper bounds, and monotonically
increasing from 0 to 1. The membership function(3)of the fuzzy set representing constraint j should be 0 if the constraint is strongly violated (if it exceeds bj+ pj), 1 if it is satisfied in the crisp sense (if
equal to or less than bj), and should decrease monotonically from
1 to 0 over the tolerance interval (bj, bj+ pj).
The membership function of the decision set, D(x), is given by
D(x)= min
ij {Gi(x), Cj(x)}. (A4)
The min-operator is used to model the intersection of the fuzzy sets of objectives and constraints. Since the decision maker wants to have a crisp decision proposal, the maximizing decision will correspond to the value of x, xmax, that has the highest degree of
membership in the decision set: D(xmax)= max
x≥0minij {Gi(x), Cj(x)}. (A5)
In this case, we can transfer Eq.(A1)to ˇ expression method as follows: max x ˇ s.t. ˇ≤ 1 − fi∗(x) − fi(x) fi∗(x) − fi−(x) , i= 1, 2, . . . , k ˇ≤ 1 −(Ax)j− bj pj , j= 1, 2, . . . , m x ≥ 0 . (A6)
In our proposed fuzzy preference programming, we only apply the fuzzy constraint programming (cj) (Eq.(A3)) with the bjequal to 0, (Ax)jequal to (Rw)korRkw and pjequal to dk(Figs. 1 and A2).
Appendix B. The min-max operator
A multi-objective programming (MOP) problem can be mathe-matically represented as follows:
max [f1(x), f2(x), . . . fk(x)]
s.t. Ax ≤ b
x ≤ 0
. (B1)
The compromise solution method was originally proposed by Yu[36]in 1973. The basic idea is to find the minimum distance
f
2(x)
f
1(x)
* 1( ) f x 1 ( ) f− x * 2( ) f x 2( ) f− x Ideal pointNegative ideal point
d
pFig. B1. Euclidean distances to the ideal solution (aspired levels) and negative-ideal
solutions (worst values) in two dimensions.
(dp) between feasible solutions and ideal point (Fig. B1). The dpis
defined as in Eq.(B2). dp=
k i wpi
fi∗(x)− fi(x) fi∗(x)− fi−(x)
p
1/p . (B2)
When the p =∞, Eq.(B2)can be expressed as follows: dp=1= k
i=1 wpifi∗(x) − fi(x) fi∗(x) − f− i (x)
, (B3) dp=∞= max wi
fi∗(x)− fi(x) fi∗(x)− f− i (x)
i= 1, 2, ..., k . (B4)
Using the definition for dp distance as Eqs.(B3)and(B4), the
multi-objective programming Eq.(B1)can be transferred as fol-lows: min x d s.t. Ax ≤ b f1∗(x) − f1(x) f1∗(x) − f− 1(x) ≤ d, i = 1, 2, ..., k x ≥ 0 or min x maxi d s.t. Ax ≤ b x ≥ 0 (B5) References
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