The influencing internal and external factors for a company’s future are referred to as strategic factors. In SWOT analysis, these factors are grouped into four parts called SWOT groups: strengths, weaknesses, opportunities, and threats. By applying SWOT in strategic decisions, the purpose is to select or constitute and implement a strategy resulting in a good fit between the internal and external factors (Kangas et al., 2003). Moreover, the chosen strategy has also to be in line with the current and future purposes of the decision makers (Pesonen et al., 2001). SWOT involves systematic thinking and comprehensive diagnosis of factors relating to a new product, technology, management, or planning. SWOT matrix is a commonly used tool for analysing external and internal environments concurrently in order to support for a decision situation (Kurttila et al., 2000; Kangas et al., 2003; Dağdeviren and Yüksel, 2007).

Grey system theory can be used to deal with uncertainty of information (Deng, 1989). The major advantage is that it can generate satisfactory outcomes using a relatively small amount of data or with great variability in factors (Li et al., 1997). Grey system theory provides an approach for analysing and modelling the systems with limited and incomplete information.

Let x denote a closed and bounded set of real numbers. A grey number ⨂ x, is defined as an interval with known upper and lower bounds but unknown distribution information for x (Deng, 1989). That is, ⨂ x = [ x _ , x ‾ ] = [ x , ∈ x ∣ x _ ⩽ x , ⩽ x ‾ ] where x _ and x ‾ are the lower and upper bounds of ⨂ x, respectively.

Some basic grey number mathematical operations are represented by the following relationships (expressions (1)–(4)) (Liu and Lin, 2006): (1) ⨂ x 1 + ⨂ x 2 = [ x _ 1 + x _ 2 , x ‾ 1 + x ‾ 2 ] , (2) ⨂ x 1 − ⨂ x 2 = [ x _ 1 − x ‾ 2 , x ‾ 1 − x _ 2 ] , (3) ⨂ x 1 × ⨂ x 2 = [ min ( x _ 1 x _ 2 , x _ 1 x ‾ 2 , x ‾ 1 x _ 2 , x ‾ 1 x ‾ 2 ) , max ( x _ 1 x _ 2 , x _ 1 x ‾ 2 , x ‾ 1 x _ 2 , x ‾ 1 x ‾ 2 ) ] , (4) ⨂ x 1 ÷ ⨂ x 2 = [ x _ 1 , x ‾ 1 ] × [ 1 x ‾ 2 , 1 x _ 2 ] .

Different methods are proposed to transfer a grey number into crisp equivalent. A variation of the CFCS (Converting Fuzzy data into Crisp Scores) method is applied in this paper. This approach has been deemed to be more effective by researchers for arriving at crisp values (e.g. when compared with the Centroid method) (Opricovic and Tzeng, 2003; Wu and Lee, 2007).

Consider an m × n grey matrix X p = [ ⨂ x i j p ], corresponding to a given decision maker p, whose elements ⨂ x i j p = [ x _ i j p , x ‾ i j p ] are grey numbers.

The modified-CFCS method includes three-step procedure described as follows: 1)

Normalize: (5) x ˜ _ i j p = ( x _ i j p − min i x _ i j p ) Δ min max , (6) x ˜ ‾ i j p = ( x ‾ i j p − min i x ‾ i j p ) Δ min max , where (7) Δ min max = max i x ‾ i j p − min i x _ i j p ;

Decision-making trial and evaluation laboratory (DEMATEL) method was originally developed between 1972 to 1979 by the Science and Human Affairs Program of the Battelle Memorial Institute of Geneva, with the purpose of studying the complex and intertwined problematic group. It has been widely accepted as one of the best tools to solve the cause and effect relationships among the evaluation criteria (Chiu et al., 2006; Liou et al., 2007; Tzeng et al., 2007; Wu and Lee, 2007; Lin and Tzeng, 2009). This method is applied to analyse and form the relationship of cause and effects among evaluation criteria (Yang et al., 2008) or to derive interrelationship among factors (Lin and Tzeng, 2009). DEMATEL incorporates four generic stages:

Step 1. Calculating the direct-influence matrix by scores. Based on experts’ opinions, evaluations are made of the relationships among elements (or variables/attributes) of mutual influence. Using a scale ranging from 0 to 4, with scores representing ‘no influence (0)’, ‘low influence (1)’, ‘medium influence (2)’, ‘high influence (3)’, and ‘very high influence (4)’, respectively.

Step 2. Normalizing the direct-influence matrix. Based on the direct-influence of matrix A, the normalized direct-relation matrix D is acquired by using formulas (10) and (11) (10) D = k A where (11) k = Min ( 1 max 1 ⩽ i ⩽ n ∑ j = 1 n | a i j | , 1 max 1 ⩽ j ⩽ n ∑ i = 1 n | a i j | ) , i , j ∈ { 1 , 2 , … , n } .

Step 3. Attaining the total-influence matrix T. Once the normalized direct influence matrix D is obtained, the total-influence matrix T of NRM can be obtained through formula (12), in which I denotes the identity matrix (12) T = D ( I − D ) − 1 .

Step 4. Analysing the results: in this stage, the sum of rows and the sum of columns are separately expressed as vector r and vector c by using formulas (13), (14), and (15). Then, the horizontal axis vector ( r + c ) is made by adding r to c, which exhibits importance of the criterion. Similarly, the vertical axis ( r − c ) is made by deducting r from c, which may separate criteria into a cause group and an affected group. In general, when ( r − c ) is positive, the criterion will be part of the cause group. On the contrary, if the ( r − c ) is negative, the criterion is part of the affected group. Therefore, the causal graph can be achieved by mapping the dataset of the ( r + c , r − c ). (13) T = [ t i j ] n × n , i , j = 1 , 2 , … , n , (14) r = [ ∑ j = 1 n t i j ] n × 1 = [ t i · ] n × 1 , (15) c = [ ∑ i = 1 n . t i j ] 1 × n t = [ t · j ] n × 1 .

The ANP can be used as an MCDM method to systematically select the most suitable alternatives. The ANP is a relatively simple and systematic approach that can be used by decision makers. The ANP is an extension of AHP by Saaty (1996) that helps to overcome the problem of interdependence and feedback among criteria and alternatives.

The Analytic Network Process is a generalization of the Analytic Hierarchy Process. Many decision problems cannot be structured hierarchically because they involve the interaction and dependence of higher level elements in a hierarchy on lower level elements (Saaty and Özdemir, 2005). While the AHP represents a framework with a unidirectional hierarchical relationship, the ANP allows for complex interrelationships among decision levels and attributes (Dağdeviren and Yüksel, 2007).

ANP approach comprises four steps (Saaty, 1996; Chung et al., 2005; Dağdeviren and Yüksel, 2007):

Step 1. Model construction and problem structuring: the problem should be stated clearly and decomposed into a rational system like a network.

Step 2. Pairwise comparisons and priority vectors: in ANP, like AHP, pairs of decision elements at each cluster are compared with respect to their importance towards their control criteria. In addition, interdependencies among criteria of a cluster must also be examined pairwise; the influence of each element on other elements can be represented by an eigenvector. The relative importance values are determined with Saaty’s scale.

Step 3. Super matrix formation: the super matrix concept is similar to the Markov chain process. To obtain global priorities in a system with interdependent influences, the local priority vectors are entered in the appropriate columns of a matrix. As a result, a super matrix is actually a partitioned matrix, where each matrix segment represents a relationship between two clusters in a system.

Step 4. Synthesis of the criteria and alternatives: priorities and selection of the best alternatives. The priority weights of the criteria and alternatives can be found in the normalized super matrix. To achieve these weights, the limiting power of the super matrix should be computed. This concept is parallel to the Markov chain process (Meade and Sarkis, 1998). The limiting power of the super matrix has an equilibrium distribution, as in the Markov chain process. Alternatives in the model can be ordered using limiting priorities obtained from the equilibrium distribution of the super matrix.

According to this research, pairwise comparisons are done based on grey data in pairwise comparison matrix, thus this research needs a method for grey pairwise comparison matrix analysis.

Consider grey pairwise comparison matrix of ⨂ P = [ ⨂ a i j ] , ⨂ a i j = [ l i j , u i j ]. The weight vector is donated as W = ( w 1 , w 2 , … , w n ). Yu et al. (2011) proposed a goal programming based approach for obtaining the weight vector W from grey pairwise matrix ⨂ P. Their model is constructed based on multiplicative normalization condition, i.e. ∏ j = 1 n w j = 1, i = 1 , 2 , … , n − 1, j = i + 1 , i + 2 , … , n, j > ii$]]>. Their proposed goal programming model based on upper triangular judgement (above main diagonal) is formulated as: (16) Min Z = ∑ i = 2 n ∑ j = 1 i − 1 ( p j i + q j i ) , S.T. x i − x j + q i j ⩾ ln l i j , x i − x j − p i j ⩾ ln u i j , x 1 = 0 , p j i ⩾ 0 , q j i ⩾ 0 , i = 2 , 3 , … , n , j = 1 , 2 , … , i − 1 , x i unrestricted . where, x j = ln ( w j ), and p i j and q i j are defined as nonnegative deviation variables. Solving the above model and determining the optimal value of variables x j , j = 1 , 2 , … , n, using converse logarithmic transformation the weights, w j , j = 1 , 2 , … , n, are figured out. Then, the weights are normalized and final weights are calculated. Interested readers can refer to Yu et al. (2011) paper for details of formulating the above model.

Following the guidelines of David (2013) and based on a PESTEL analysis, the main internal factors (including strengths and weaknesses) and external factors (including opportunities and threats) are determined. These SWOT factors are summarized in Table 1.

Using the framework of SWOT analysis (David, 2013), seven strategic alternatives are developed for this study as presented in Table 2.

This study considers 4 experts of company for completing the matrixes. Each expert expresses his/her opinion about the relation among strengths, weakness, opportunities, threats, and strategies, using a grey scale. According to Eqs. (5) to (9), the average matrix of DEMATEL is computed as follows: A = 0.0000 0.4525 0.9167 0.3273 0.6746 0.6846 0.0000 0.8125 0.9030 0.9365 0.7571 0.6425 0.0000 0.3896 0.7619 0.8857 0.9276 0.5500 0.0000 0.5873 0.5000 0.9276 0.6042 0.4424 0.0000 .

Normalizing the matrix, A, initial direct impact matrix, D, is constructed. D = 0.0000 0.1356 0.2747 0.0981 0.2022 0.2052 0.0000 0.2435 0.2706 0.2807 0.2269 0.1926 0.0000 0.1168 0.2283 0.2654 0.2780 0.1648 0.0000 0.1760 0.1499 0.2780 0.1811 0.1326 0.0000 .

Then, using Eq. (12), the completed direct/ indirect matrix, T, is computed. T = 0.6718 0.8199 0.9200 0.6107 0.8857 1.0868 0.9578 1.1446 0.9284 1.1940 0.9061 0.9126 0.7546 0.6677 0.9575 1.0458 1.0842 1.0114 0.6517 1.0374 0.8554 0.9761 0.9079 0.6895 0.7756 .

Using maximum mean de-entropy method of Li and Tzeng (2009), the threshold value is determined equal to 0.8857. Therefore, the network of interrelation among factors is constructed according to Fig. 2.

In the next stage, according to decision network, Fig. 2, the pairwise comparisons are done. In this regard, all the elements of an impacted cluster are pair-wisely compared in regards to the elements of an affecting cluster. Then, the weight vector of each pairwise decision matrix is obtained and the super matrix is constructed by combining these weight vectors.

To normalize the obtained super matrix, the clusters are compared in regards to each other and based on the relationships in the network. For example, since “strengths” cluster has an impact on “opportunities” and “strategies” cluster, the latter two clusters are compared with the first one. Again, the pairwise matrices are distributed among experts and their judgements are combined via geometric mean. The aggregated pairwise matrix is shown as:

To obtain the weight vector of above grey-pairwise matrix, the model in Eq. (16) is formulated as: min p 12 + q 12 , x o − x s t + p 12 ⩾ ln ( 1.34 ) , x o − x s t − q 12 ⩽ ln ( 1.73 ) , x s t = 0 , x o , x s t : unrestricted .

Solving the above model, the result obtained is x o ∗ = 0, x s t ∗ = 0.2939, since w i = e x p ( x i ), then w o ∗ = 1, and w s t ∗ = 1.34. Normalizing these values, the final weight vector will be w o ∗ = 0.427, and w s t ∗ = 0.573. Similarly, other weights are calculated. Table 3 summarizes the weights of cluster in regards to each other.

Then to obtain the weighted super matrix or stochastic super matrix, the entries of initial super matrix are multiplied by the elements of their corresponding cluster weight in Table 3. This weighted super matrix then rose to limiting powers. After 19th iteration (19th power), the limited super matrix is obtained as is shown in Table 4.

Each column of Table 4 determines the final ratio scale priority of elements in network. In this table, the cluster’s ratio scale priority is equal to sum of its elements’ ratio scale priority. The ratio scale priorities of the elements within their clusters (last column) are calculated by normalizing their ratio scale priority in the related cluster.

Table 4 indicates that among SWOT clusters, the most important one is “opportunities”, and then strengths, weaknesses, and threats are in the second to fourth rank of importance. Also, in each cluster all factors are ranked. The most important strategy is “Holding the training courses in order to enhance the ability of employees”. The 2nd and 3rd strategies are “Establishing human resource management (recruitment, training, promotion and retention)”, and “Identifying, documenting and improving company business processes”, respectively. Therefore, if the considered organization has a limited budget for performing its strategic plan, it must allocate this budget according to the obtained ranking of strategies.

In ANP method, priority of the strategies is determined by using different criteria of SWOT. On the basis of these criteria, organization has a list of prioritized strategies for implementing. In this organization, there are not huge amount of financial resources and budget for performing the strategies. According to the past studies, one of the main reasons in failure of strategies is lack of budgeting and lack of financial resource allocation. Therefore, considering the financial aspect to select strategies is very important.

For solving this problem, a zero/one model is formulated by considering the budget constraints. This model is formulated as: (18) Max Z = ∑ i = 1 k u i x i , S.T. ∑ i = 1 k h i x i ⩽ B , ( x 1 , x 2 , … , x k ) ∈ Δ , x i ∈ ( 0 , 1 ) , i = 1 , 2 , … , k .

The objective function of above model is seeking to maximize the utility of selected strategies. The first limitation shows that total needed budget for implementing the strategies couldn’t be more than total budget. The second limitation indicates the establishment of the organization’s limitations to select strategies. Finally, the last limitation shows the nature zero/one of variable of model.

Zero/one Integer Programming can be solved with lots of methods like direct counting method, implicit counting method and branch and bound methods. In this research, Lingo software is used to solve the model.

According to the surveys, researcher predicts some projects for implementing each of the strategies. Each project has an estimated budget. Table 5 shows anticipated budget for each strategy, their utilities and corresponding decision variables.

Also company defined some restrictions about selecting the strategies as below:

According to the above information, strategy selection model based on budget constraints is formulated as follows: max 0.1501 x 1 + 0.1168 x 2 + 0.1234 x 3 + 0.1074 x 4 + 0.1172 x 5 + 0.1045 x 6 + 0.2805 x 7 , S.T. 200 x 1 + 150 x 2 + 350 x 3 + 200 x 4 + 150 x 5 + 300 x 6 + 200 x 7 ⩽ 1000 , x 1 + x 2 + x 3 + x 4 + x 5 + x 6 + x 7 ⩽ 3 , x 2 = 1 , x 1 + x 3 ⩽ 1 , x 2 − x 4 ⩽ 0 , x 4 − x 6 = 0 , x 4 + x 7 ⩽ 1 , x i ∈ 0 , 1 , i = 1 , 2 , … , 7 .

Lingo Software is used to solve the above model. After solving the model, the optimal solution is determined as follows: x 2 ∗ = x 4 ∗ = x 6 ∗ = 1 .

These outputs indicate that the second, fourth and sixth strategies should be done for the first year.

After implementing the above strategies, the model must specify other strategies for the other year. Therefore, other strategies will be remodelled after removing the accomplished strategies and updating the budget parameters and inserting them in the model. Table 6 illustrates priority of strategies for different years.