An improvement of quantitative strategic planning matrix using multiple criteria decision making and fuzzy numbers

Applied Soft Computing 12 (2012) 2246–2253

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Applied Soft Computing journal homepage: www.elsevier.com/locate/asoc

An improvement of quantitative strategic planning matrix using multiple criteria decision making and fuzzy numbers Hasan Hosseini Nasab a,∗ , Abbas S. Milani b a b

School of Engineering, Yazd University, Yazd, Iran School of Engineering, University of British Columbia, Okanagan, Kelowna, Canada

a r t i c l e

i n f o

Article history: Received 20 April 2010 Received in revised form 13 January 2012 Accepted 4 March 2012 Available online 30 March 2012 Keywords: Fuzzy numbers MCDM QSPM Fuzzy QSPM

a b s t r a c t The Quantitative Strategic Planning Matrix (QSPM) is a useful tool to prioritize strategies at any level including corporate, business and functional. The ratings and attractive scores used in QSPM, however, require judgmental decisions and should be based on expert’s opinion to ensure the applicability of chosen strategies. Application of a fuzzy multi-criteria decision making method is proposed in this paper with the goal of improving the output of conventional QSPM by allowing the experts to employ linguistic terms (qualitative data) in their judgments. Namely, a multi-criteria decision making index via the technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is adapted to the fuzzy QSPM in finding the sum total attractive scores of strategies. As a case study, the proposed method has been applied for strategy prioritization in a Tile Company. The results have been verified with expert knowledge and showed an improvement compared to the non-fuzzy QSPM. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Strategic management is the art of managing organizations in maximizing the potential of achieving business objectives. It attempts to organize qualitative and quantitative information, allowing effective decisions to be made under different conditions of uncertainty. It consists of three distinct stages: strategy formulation, strategy implementation, and strategy evaluation. The well-known SWOT (strength, weakness, opportunity and threat) analysis and QSPM (Quantitative Strategic Planning Matrix) fit into the first stage and have been proven to be excellent tools for deciding among feasible alternative strategies [1–7]. In the SWOT analysis, however, deciding on relative importance of various facts, figures, trends, and data among feasible alternative strategies is critical in arriving at solutions that provide major competitive advantages to a given firm. MCDM (Multi-Criteria Decision Making) is one of the known branches of decision science and is commonly used in comparing finite sets of alternatives/scenarios. In management and planning, MCDM has been used to study methods and procedures that can accommodate multiple, often conflicting, decision criteria [8]. While the conventional QSPM has proven to be a useful tool for strategic planning in several organizations, incorporating intuitive (human) judgments with crisp numbers can affect the precision of decision outputs unfavorably. A method of using fuzzy numbers

∗ Corresponding author. Tel.: +1 250 807 9652; fax: +1 250 807 9850. E-mail address: [email protected] (H. Hosseini Nasab). 1568-4946/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.asoc.2012.03.010

instead of crisp numbers in QSPM along with an MCDM technique is proposed in the present article to address the above shortcoming. After presenting a more detailed background on SWOT analysis, MCDM, QSPM and fuzzy numbers (Section 2), the proposed fuzzy methodology is described in Section 3. An illustrative case study is presented in Section 4 and conclusions are included in Section 5. 2. Background 2.1. SWOT analysis SWOT analysis is a tool in strategy formulation by identifying the strengths, weaknesses, opportunities and threats of a given organization. Several studies have employed the SWOT analysis with the goal of improving the classical strategic planning and management methods. Ozcan and Deha [9] examined the application of SWOT analysis to formulate strategies that are related to the safe carriage of bulk liquid chemicals in maritime tankers. A qualitative investigation using SWOT analysis was implemented for ships carrying liquid chemicals in bulk. The authors developed a set of operation plans by means of converting possible threats into opportunities, and changing weaknesses into strengths. Chang and Huang [10] presented a Quantified SWOT analytical method which provided more detailed data for SWOT analysis. They adopted the concept of multiple attribute decision making and presented a multi-layer scheme to simplify complicated decision-makings, and thus were able to perform SWOT analysis in several enterprises simultaneously. Dyson [4] described another application of the SWOT analysis to strategy formulation and its incorporation into the strategic

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development process. Their method linked the SWOT analysis to resource-based planning through an iterative process within an overall planning process. Kahraman [5] proposed a method to evaluate different alternative strategies for e-government applications in Turkey. They used the SWOT in conjunction with the analytic hierarchy process (AHP) to prioritize their strategies. 2.2. Multiple criteria decision making (MCDM) MCDM models normally consist of a finite set of alternatives among which a decision-maker (DM) has to rank and decide. In MCDM, often a finite set of criteria need to be weighted according to their relative importance. One main goal of such models is to aid DMs in integrating objective measurements with subjective judgments that are occasionally not based on individuals’ opinion but on collective group ideas [8]. In a typical MCDM model, a decision matrix consisting of ratings of alternatives with respect to each criterion is first established. The evaluation ratings are, then, aggregated by taking into account the weights of criteria, and eventually a global evaluation score for each alternative is found. There are several aggregating methods in MCDM such as simple additive weighting (SAW), multiplicative exponential weighting (MEW), the technique for order preference by similarity to ideal solution (TOPSIS) [11], and the analytic hierarchy process (AHP) [9,12]. Several useful fuzzy MCDM methods have also been developed in the literature [8,13,14]. Using a fuzzy MCDM, assessing the importance of criteria and the ratings of alternatives with respect to each criterion can be estimated according to linguistic terms. Huan-Jyh and Hsu-Shih [15] proposed a hybrid fuzzy MCDM model for strategic vendor selection. In their method, the vendor evaluation problem was formulated by a combined use of MCDM and a five-step hybrid process through the analytic network process (ANP). Dursun and Karsak [16] described a fuzzy MCDM approach for personnel selection where a fuzzy algorithm was developed using the principles of fusion of fuzzy information, a 2-tuple linguistic representation model [17] and the TOPSIS technique [11]. Their proposed method is particularly useful to manage information assessed by both linguistic and numerical scales where multiple information sources are present. The main advantages of TOPSIS, among other basic MCDM methods, in complex decision making problems is that it is “simple to use”, “can take into account all types of criteria (subjective and objective)”, “its logic is rational and understandable for practitioners”, “the computation process is straightforward”, “the concept permits the pursuit of best alternatives criterion depicted in a simple mathematical manner”, and “the importance weights can be incorporated conveniently” [18,19]. 2.3. The QSPM method Strategic management process, as we shown schematically in Fig. 1 is a set of managerial decisions and actions that determines the long-run performance of an organization. It includes environmental analysis (both external and internal), strategy formulation (short- or long-range planning), strategy implementation, evaluation and control. A main stage of the strategy management process is the strategy formulation in which feasible alternatives are generated and evaluated. Based on the work by David [20], techniques of strategy formulation can be integrated into a decision making framework. More specifically, strategies can be identified, evaluated and selected within a framework that includes three stages: (1) input stage, (2) matching stage, and (3) decision stage (Fig. 2). As shown in Fig. 2, Quantitative Strategic Planning Matrix (QSPM) is the last stage of the strategy formulation. QSPM uses input information from Stage 1 to objectively evaluate feasible alternative strategies identified in Stage 2, and eventually it reveals the relative attractiveness of alternative strategies and provides

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objective basis for selecting best strategies. Principally, the basic components of QSPM are: (1) key factor statements, (2) strategies to be evaluated, (3) ratings, (4) attractive scores, (5) total attractive scores and (6) sum total attractive scores. Conceptually, the QSPM determines the relative attractive of various strategies based on key internal and external factors. The relative attractive of each strategy is computed by determining the cumulative impact of each key internal and external factor. Any number of alternative strategies can be included in QSPM. To develop a QSPM matrix for a given firm, one would need to perform six steps as follows. 1. Make a list of the firm’s key external opportunities/threats and internal strengths/weaknesses (these will be located in the left column of the matrix). 2. Assign weights to each key external and internal factor. 3. Examine the Stage 2 (matching) matrices, and identify alternative strategies that the organization should consider implementing. 4. Determine the attractiveness scores (1 = not attractive, 2 = somewhat attractive, 3 = reasonably attractive, highly attractive) for components of each strategy. 5. Compare the total attractiveness scores; and 6. compute the sum total attractiveness score for the alternatives. Nouri et al. [21] applied QSPM for the evaluation of environmental management of coastal regions in Caspian Sea. They developed 27 strategies using SWOT analysis and ranked them using QSPM. Wang et al. [22] analyzed a set of strengths and weaknesses during a regional planning with and without the Hebei Province. They developed 8 feasible strategic projects and using QSPM selected the top strategic projects. They concluded that Hebei Province would make more contribution for the adjustment of economic structure and cooperation within Beijing, Tianjin and Hebei regions. Rafee et al. [23] discussed the development of strategic management for earthquake debris in big cities. They used the SWOT analysis to assess actual and potential debris management capacities. Results revealed that the most important strategies included an accurate estimation of volume, weight and type of earthquake debris; reinforcement of the present structures; proper design of structures under construction; utilization of experience from other earthquake instances; recycling and reuse of debris and construction wastes; and the identification of temporary debris depot sites within the city. 2.4. Fuzzy methods Real-world decision makings often take place in fuzzy environments/under judgmental uncertainties. Fuzzy sets were introduced by Zadeh [24] as an extension of the classical notion of sets. Since then, fuzzy decision methods have been used in a wide range of domains where input data are incomplete or imprecise. Mahapatra and Roy [6] applied a fuzzy method for single and multi container maintenance planning under a limited time interval of interest. They solved their fuzzy model by a geometric programming technique, which was implemented through three different operators: maximin, max-average mean, and max-geometric mean. Eventually, these operators were applied in the single-container maintenance model in the fuzzy environment. Lee et al. [25] presented a mechanism of integrating fuzzy cognitive map knowledge within strategic planning simulations, where the fuzzy cognitive maps (FCMs) helped the decision maker understand complex dynamics between certain strategic goals and related environmental factors. Lee and Lin [13] proposed a fuzzy SWOT method to evaluate the competitive environment of different transshipment locations as international distribution centers (IDC) in the

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Environmenta l

Internal and External

Scanning

Feedback

Strategy Formulation

MissionObjectives Strategies Policies

Feedback Strategy Implementatio n

ProgramsBudgets Procedures

Feedback

Methods Performanc e

Monitoring and Control

Fig. 1. Schematic of a strategic management process.

Pacific-Asian region. Their work showed that the fuzzy method could identify more competitive locations in comparison to some other non-fuzzy methods.

3. Proposed methodology: fuzzy QSPM with MCDM Priority setting of business strategies is perhaps most critical when resources are scarce or limited for a company. Resources may be limited in financial, manpower, production, transportation, distribution, etc. As mentioned in the background section, different methods have been developed to help decision makers prioritize the business strategies [2–6]. Although the QSPM is a high-level strategic management approach for evaluating possible strategies, it still needs improvements. Particularly, in practice its rating method and obtaining total attractive scores are based on judgmental decisions, and thus they should not be quantified based on crisp/exact values as in the conventional QSPM. In order to accommodate this need, this section discusses a method of Fuzzy Quantitative Strategic Planning Matrix (FQSPM) where fuzzy numbers are used to calculate total attractive scores instead of crisp numbers. In addition, an MCDM method is employed to aid the DMs in integrating objective measurements with their subjective judgments that are normally based on collective group ideas. Steps of the proposed methodology are as follows.

3- Performing SWOT analysis and developing company’s strategies (alternatives). 4- Aggregating expert opinions using fuzzy numbers. 5- Determining criteria weights. 6- Calculating the total score of alternatives in the SWOT matrix using fuzzy MCDM (the weighted sum method, or TOPSIS); and 7- ranking and justifying the alternatives. Formulating strategies begins with the development of a clear vision and mission, followed by internal and external assessments, which leads to establishing long term objectives, and finally generating and deciding among specific strategies. Strategies are generated using SWOT and should be prioritized via MCDM. In the MCDM model, with m alternatives, n criteria and k decision makers, the decision problem may be expressed as

A1

F=

A2

...

11

12

…

1n

21

…

…

2n

…

Cn

...

m2

…

m1

…

Am

C2

…

...

1- Determining company’s vision and mission. 2- Evaluating company’s external and internal factors.

C1

mn

(1)

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STAGE 1: THE INPUT STAGE

External factor evaluation (EFE) Matrix

Internal Factor Evaluation (IFE)) Matrix

Competitive Profile Matrix

STAGE 2: THE MATCHING STAGE

Strengths

Weaknesses, Opportunities Threats(SWOT) Matrix

Strategic position and Action Evaluation (SPACE) matrix

Boston Consulting Group (BCG) Matrix

Internal External (IE) Matrix

Grand Strategy Matrix

STAGE 3: THE DECISION STAGE

Quantitative Strategic Planning Matrix (QSPM)

Fig. 2. A strategy-formulation framework [20].

where, F represents the fuzzy decision matrix with alternatives Ai (i = 1,2, . . ., m) and the criteria Cj , (j = 1,2, . . ., n). Aggregated judgments xij are calculated as follows:

1

xij =

k

(xij1 + xij2 . . . + xijk )

µ Ni

(2)

a1

Where xijk is the fuzzy judgment of expert #k and can be represented using a triangular fuzzy numbers as: xijk = (akij , bkij , cijk )

(3)

Next, a normalization of data can be performed using Eqs. (4) and (5).

⎡

R11 . N = ⎣ .. Rn1

··· ··· ···

⎤

R1m .. ⎦ . Rnm

(4)



a 3 b1

b2

b3

x

Fig. 3. Schematic of two triangular fuzzy numbers.

Considering wj as the weight of criterion j, the weighted normalized fuzzy decision numbers Pij can be calculated as: Pij = Rij × wj

(6)

The next step is to define a formula for the distance of alternatives. The distance, S, between two triangular fuzzy numbers Ni (a1 , a2 , a3 ) and Nj (b1 , b2 , b3 ) as shown in Fig. 3 may be calculated as: S(Ni , Nj ) =

1 [SL (Ni , Nj ) + SR (Ni , Nj )] 2

(7)

Where sL (Ni ,Nj ) and sR (Ni ,Nj ) are defined as:

Where Rij =

a2

Nj

aij

m,

cj

bij

cij , m a bm j j

; cjm = Max(cij ); bm = Max(bij ); am j j

= Max(aij ), i = 1, 2 . . . m

(5)

sL (Ni , Nj ) = sL (Ni , 0) − sL (Nj , 0) =

a1 + a2 b1 + b2 − 2 2

(8)

sR (Ni , Nj ) = sR (Ni , 0) − sR (Nj , 0) =

a2 + a3 b2 + b3 − 2 2

(9)

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Table 1 Chosen strategies for the Tile Company. Strategies

Definition

Motives

A: Improving the existing production line

•Improving the current process or an existing product •What is the current technical problem to be solved, what process to be improved and why? •What are the technologies the company believes could be suitable? •E.g. Lawrence and KM company, September 2007 •Adding a product to the production line •Changing processing methods or recipes for existing products; adding new services •E.g. Mongo’s New product line •Vertical forward integration occurs when a firm combines with another firm in a later stage of production •E.g. A garment factory integrates forwards when it combines with a boutique, since garment selling follows garment production. •Vertical backward integration occurs when a firm combines with another firm in its preceding stage of production. •E.g. a garment factory integrates backwards when it combines with a weaving factory, because weaving proceeds garment-making in clothes production. •E.g. Cheung Kong (Holdings) Ltd integrated with Anderson Asia (Holdings) Ltd to ensure a steady supply of building materials. It takes place when firms producing the same product or at the same stage of production combine together. •E.g. Hong Kong Bank took over Hang Seng Bank in 1964. •E.g. In 1998, British Petroleum acquired AMOCO. IT occurs when firms producing related products combine together. •E.g. The publication of the Apple Daily by the Next Magazine Publishing LTD •E.g. Ah Yee Leng Tong was taken over by Café de Coral at HK$14 million in May 1990.

Improving productivity and increasing efficiency

B: Adding a new production line

C: Forward integration

D: Backward integration

E: Horizontal Integration

F: Concentric diversification

Hence, the distance between Ni and Nj follows: S(Ni , Nj ) = =

 a + a 1 2 3 2

2

1 a1 + 2a2 + a3 2

2

−

−

  a + a b2 + b3 1 2 +

2

 b1 + 2b2 + b3

2

−

 b1 + b2 2

(10)

Note that S (Ni ,Nj ) is defined as the algebraic distance from Ni to Nj which can be positive, negative or zero. Finally to rank each alternative, a fuzzy TOPSIS (MCDM) perormance index can be adapted as follows. TOPSIS total attractive scorei =

si+

si−

+ si−

, i = 1, 2 . . . m.

(11)

Where Si+ = Si− =

n j=1

S(Pij , Pj+ ), i = 1, 2, . . . m

(12)

j=1

S(Pij , Pj− ), i = 1, 2, . . . m

(13)

n

Pj+ = (1, 1, 1)&Pj− = (0, 0, 0)

Ensuring adequate market outlets

Ensuring a steady supply of raw materials

Turning competitors into partners

Diversify production and reduce risk

ideal solutions are defined in the absolute form as shown in Eq. (14). 4. Illustrative example

2

(a1 + 2a2 + a3 ) − (b1 + 2b2 + b3 ) = 4

Providing economic and social benefits

(14)

Remark. Steps of the conventional TOPSIS method is briefly presented in Appendix A; see [11] for more information. Here the goal is to adapt the final index of the conventional TOPSIS method (Ci∗ in the Appendix A, Eq. (A5) as the sum total attractive score in the QSPM method (Eq. (11)). Also it should be noted that in the original TOPSIS, the positive ideal and negative ideal solutions are calculated relative to the best and least performing values of the given decision matrix. Here, the fuzzy positive ideal and fuzzy negative

To examine the applicability of the described method in Section 3, priority determinations of strategies for a Tile Company were conducted using both the conventional QSPM and the proposed FQSPM. Tile Company began operation in 1979, producing three classes of tiles. The vision and mission of the company were defined as follows: Vision: “To be the first Tile Company that realizes the need to thrive in an extremely competitive marketplace, we plan to continue our growth by focusing on our customer satisfaction.” Mission: “To become the first name in commercial and institutional interiors, our focus is on product and service through constant emphasis on process quality and engineering, which we combine with careful attention to our customers’ needs so as always to deliver superior value to them, and thereby maximizing all stakeholders’ satisfaction.” The potential strategies for the company were developed by a group of experts as shown in Table 1. 4.1. Conventional QSPM Details of the conventional QSPM for strategies A and B for the Tile Company is shown in Table 2 using the SWOT analysis, where the weights and attractive scores (1, 2, 3 or 4) are assigned by a group of five experts at the company. An attractive score of 4 represents the best and 1 the least value. The QSPM sum total attractive score of 3.13 for strategy A versus 3.46 for strategy B indicates

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Table 2 Tile Company’s QSPM. Strategies

SWOT

Affective factors (criteria)

Weight

Attractive score

Weighted/total attractive score

A: Improving the existing production line

Strengths

c1

0.05

3

0.15

Reputation for innovative design c2 Experience in exporting to other countries c3 c4 Insufficient cash flow Weaknesses Problems with on-time delivery c5 Relatively high costs of labor c6 Opportunities c7 Demand increasing by 10% c8 luxurious products c9 Easier access to markets in accession c10 Increased competition of producers Threats From countries with lower costs of labor c11 Recession in many countries markets c12 Sum total attractive score for strategy A Strengths c1 Consistent and high product quality

0.07 0.12 0.08 0.07 0.15 0.09 0.11 0.03 0.12 0.07 0.04

4 2 1 4 4 2 4 4 3 4 3

0.05

4

0.28 0.24 0.08 0.28 0.60 0.18 0.44 0.12 0.36 0.28 0.12 3.13 0.20

c2 Reputation for innovative design c3 Experience in exporting to other countries c4 Insufficient cash flow Weaknesses Problems with on-time delivery c5 Relatively high costs of labor c6 Demand increasing by 10% Opportunities c7 c8 luxurious products c9 Easier access to markets in accession Threats c10 Increased competition of producers From countries with lower costs of labor c11 Recession in many countries markets c12 Sum total attractive score for strategy B

0.07 0.12 0.08 0.07 0.15 0.09 0.11 0.03 0.12 0.07 0.04

2 4 2 4 3 4 4 1 4 4 4

B: Adding a new production line

Consistent and high product quality

0.14 0.48 0.16 0.28 0.45 0.36 0.44 0.03 0.48 0.28 0.16 3.46

Table 3 Priorities of the strategies for the Tile Company based on the sum total attractive scores and the conventional QSPM (ranking result: B > D > A > C > F > E). Criteria

c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11 c12 Total

Affective Factors

Weight

Consistent and high product quality Reputation for innovative design experience in exporting to other countries Insufficient cash flow Problems with on-time delivery Relatively high costs of labor Demand increasing by 10% luxurious products Easier access to markets in accession Increased competition of producers From countries with lower costs of labor Recession in many countries markets

0.05 0.07 0.12 0.08 0.07 0.15 0.09 0.11 0.03 0.12 0.07 0.04 1

Strategies weighted attractive score A

B

C

D

E

F

0.15 0.28 0.24 0.08 0.28 0.60 0.18 0.44 0.12 0.36 0.28 0.12 3.13

0.20 0.14 0.48 0.16 0.28 0.45 0.36 0.44 0.03 0.48 0.28 0.16 3.46

0.10 0.21 0.48 0.42 0.16 0.28 0.09 0.11 0.09 0.48 0.16 0.12 2.70

0.60 0.07 0.42 0.32 0.14 0.36 0.16 0.12 0.16 0.12 0.60 0.12 3.19

0.10 0.36 0.06 0.18 0.48 0.36 0.39 0.02 0.20 0.02 0.08 0.04 2.29

0.08 0.07 0.09 0.10 0.36 0.06 0.18 0.48 0.36 0.39 0.02 0.20 2.39

Table 4 A six-level fuzzy scoring definition. Condition

Very poor (VP)

Poor (P)

Fair (F)

Good (G)

Very good (VG)

Excellent (E)

Fuzzy scale

(0,0.05,0.1)

(0.1,0.25,0.3)

(0.3,0.45,0.5)

(0.5,0.65,0.7)

(0.7,0.85,0.9)

(0.9,1,1)

that adding a new production line would have a higher priority over improving the existing production line in the company. The sum total attractive scores for all the six strategies based on the weighted values are also summarized in Table 3 (the higher the score, the higher the priority). The magnitude of difference between the two sum total attractive scores gives an indication of the relative attractiveness of one strategy over another. Such differences can be useful for the management to choose a final strategy. 4.2. FQSPM with MCDM Tile Company’s fuzzy scores and criteria weights were determined by the same group of experts in the field according to company’s internal and external factors. A six-level fuzzy scale used

to assess the alternatives (Table 4). Using this scale, expert judgments were aggregated (Table 5) and weighted information for each alternative was calculated (Table 6). Using the ensuing decision matrix in Table 6, the FQSPM total attractive scores (i.e., similar to the weighted sum method in MCDM) were obtained as shown in Table 7, from which the priorities of strategies were extracted. Comparison of results in Tables 3 and 7 indicates that using the fuzzy method could change the priorities of the developed strategies. Furthermore, using Eq. (11) for calculating the total attractive scores based on the TOPSIS index shows the same priorities as FQSPM (Table 8). Finally, to validate the results, a total of fifteen experts contributed to ranking the six developed strategies of the company based on their experience and the prioritization worksheet templates shown in Appendix B. Twelve criteria were used

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Table 5 Sample strategic evaluations performed by one of the company’s expert. Criterion Strategies

C1

C2

C3

C4

C5

C6

C7

C8

C9

C10

C11

C12

Strategy A Strategy B Strategy C Strategy D Strategy E Strategy F

G VG P VG VP P

VG F G VP G VP

F VG VG G G G

P F G VG P P

VG VG P P VG G

VG G VG VG VP G

F VG VP P G P

VG VG VP VP G VG

VG P G VP VP VG

G VG VG G VG G

VG VG P VG G P

G VG G VP G VP

Table 6 Fuzzy evaluation of strategies for the Tile Company (the values shown are (a1 + 2a2 + a3 /2) for each representative fuzzy number such as (a1 , a2 , a3 ); also they are based on the final criteria scores obtained from the group of experts). Criteria

C1

C2

C3

C4

C5

C6

C7

C8

C9

0.07 0.725 0.829 0.391 0.108 0.421 0.071

0.12 0.324 0.100 0.845 0.397 0.387 0.401

0.08 0.158 0.202 0.299 0.672 0.211 0.106

0.07 0.769 0.642 0.089 0.112 0.639 0.490

0.15 0.431 0.139 0.789 0.777 0.012 0.400

0.09 0.396 0.218 0.149 0.202 0.689 0.116

0.11 0.332 0.207 0.110 0.099 0.376 0.962

0.03 0.627 0.461 0.287 0.197 0.104 0.794

C10

C11

C12

0.07 0.651 0.767 0.218 0.801 0.444 0.233

0.04 0.291 0.609 0.509 0.076 0.497 0.148

Weights Strategy A Strategy B Strategy C Strategy D Strategy E Strategy F

0.05 0.854 0.290 0.232 0.745 0.011 0.124

Table 7 Priorities of the strategies for the Tile Company using FQSPM. Strategies (sorted by the scores)

Sum total attractive score

Priority

(C) Forward integration (D) Backward integration (A) Improving the existing production line (F) Concentric diversification (B) Adding a new production line (E) Horizontal integration

0.442 0.425

1 2

0.424

3

0.396

4

0.393

5

0.389

6

0.12 0.111 0.845 0.699 0.504 0.767 0.605

strategies is obtained. As a result, the success of QSPM necessitates careful judgments by experts in assigning attractive ratings. If crisp numbers are used instead of linguistic terms, the obtained total attractive scores may be too idealistic and the difference between strategies can be difficult to distinguish. A method for improving QSPM was proposed using fuzzy numbers as the input information and also the TOPSIS MCDM index was adapted in calculating the total attractive scores of strategies. The results showed improvements in prioritization of strategies for a Tile Company. Similar to other strategic planning tools, the fuzzy QSPM should not dictate final decisions; rather it should be used as a decision aid tool. As a potential future work, the proposed methodology may be examined for its robustness as compared to other fuzzy methods. In particular, different fuzzy scales with balanced or unbalanced membership distributions [26] may be examined and compared in the given case study.

Table 8 Ranking the alternatives in FQSPM using the TOPSIS index. Strategies

TOPSIS total attractive score

Priority

(C) Forward integration (D) Backward integration (A) Improving existing production line (F) Concentric diversification (B) Adding new production line (E) Horizontal integration

0.217 0.183 0.131

1 2 3

0.129

4

0.128

5

0.105

6

for the evaluation of strategies based on the company’s external and internal factors (i.e., the same criteria applied for the QSPM analysis in Table 2). All fifteen experts returned the prioritization worksheets which agreed with the result of FQSPM in Table 8.

Appendix A. Steps in the conventional TOPSIS The Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is based on the concept that the chosen alternative should have the shortest distance from the positive ideal solution and longest distance from negative ideal solution [11]. A TOPSIS solution is obtained according to the following steps. Step 1- Normalization – Since each attribute may be measured/rated in different scale, normalization is required. Pij is the normalized value for each criterion value (xij ). Pij =

x

ij

m x k=1 ij

(A1)

Step 2- Weighted normalization – the chosen weights are multiplied by the normalized matrix as:

5. Conclusion

vij = wj Rij i = 1, . . . , 8; j = 1, 2

The QSPM method has proven to be a useful strategic planning tool for several types of organizations; large, small, profit, and nonprofit firms. A limitation of QSPM, however, is that it can only be as reliable as the provided information and the chosen method to compute total attractive scores, based on which the ranking of

Where wj is the weight of the jth criterion. Step 3- Positive ideal and negative ideal solutions – The positiveideal solution is the composite of all best criteria ratings. If all chosen criteria are of the benefit-type (similar to the case study in this article), the positive ideal solution takes the largest value of

(A2)

H. Hosseini Nasab, A.S. Milani / Applied Soft Computing 12 (2012) 2246–2253

Item No.

Requirement(s)

The company chosen

Type(s)/motive(s)

Recording and commenting integration with other groups

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Reason(s) for your comments

Mark(s)

1 2 3 4

each criterion column and denoted by (P+). Similarly, the negativeideal solution (P− ) is the composite of all worst criteria ratings. Step 4- Calculation of separation measures: The separation or distance of each alternative from the positive-ideal solution P+ is given by the n-dimensional Euclidean distance:

   n + (vij − v∗ )2 S = i

j

(A3)

j=1

Similarly, the separation from the negative-ideal solution P− is given by:

   n 2 − (vij − v− ) S = i

j

(A4)

j=1

Step 5- Finally, the similarity to positive-ideal solution, for alternative i, or Ci∗ , is given by: Ci∗ =

Si−

Si−

+ Si∗

(A5)

Appendix B. Sample factsheet template used for the collection of expert data for the Tile Company Scale for marking/rewards: • 2 points for each case of correct integration • 2 points for each reasonable motive for integration. • 1 point for recording and commenting integration with other groups. References [1] C. Chin, C. Klein, An efficient approach to solving fuzzy MADM problems, Fuzzy Sets and Systems 88 (1997) 51–67. [2] S. Zanakis, A. Solomon, N. Wishart, S. Dublish, Multi-attribute decision-making: a simulation comparison of select methods, European Journal of Operational Research 107 (1998) 507–529. [3] G. Liang, Fuzzy MCDM based on ideal and anti-ideal concepts, European Journal of Operational Research 112 (1999) 682–691. [4] R.G. Dyson, Strategic development and SWOT analysis at the University of Warwick, European, Journal of Operational Research 152 (2004) 631–640.

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