A combined evaluation model for encouraging entrepreneurship policies

Abstract

Initiating small and medium enterprises (SMEs) has become a major issue around the globe. There are many governmental factors that could influence entrepreneurship. To create a strong and energetic environment for new businesses, governments need to develop a spirit of business, remove a number of current obstacles, and provide various supports during the start-ups periods. Here, a critical question arises: how can the government effectively evaluate current policies and how much effort must they put into improving these policies in order to achieve the desired level of economic growth? This paper addresses this question by proposing a combined Multi-Criteria Decision-Making (MCDM) model, which integrates the Analytic Network Process (ANP) approach and the VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method. The former approach is used to construct interrelations among criteria and to obtain criteria weights; the latter method allows the decision maker to realize policy gaps and to rank them in order of magnitude so that large gaps can be reduced to an aspired level. Overall, the study findings show at present, every entrepreneurships policy in Taiwan stands in need of improvement. The proposed model cannot only help the government to evaluate the relative effectiveness of their policies, but it also provides worthwhile recommendations toward the constructing of an ideal policy.

Appendices

Appendix A: Brief of the Analytic Network Process (ANP) method

The ANP, developed by Thomas L. Saaty, provides a way to input judgments and measurements to derive ratio scale priorities for the distribution of influence among the factors and groups of factors in the decision (Saaty 2003). According to Saaty (2001), the ANP comprises five main steps (Aragones-Beltran et al. 2008):

Step 1::

Conducting pairwise comparisons on the elements and calculate the relative importance weights (eigenvectors) of each element.

Step 2::

Placing the result of these computations within the supermatrix (unweighted supermatrix).

Step 3::

Conducting pairwise comparisons on the clusters.

Step 4::

Weighting the blocks of the unweighted supermatrix, by the corresponding priorities of the clusters, so that it can be column stochastic (weighted supermatrix).

Step 5::

Raising the weighted supermatrix to limiting powers until the weights converge and remain stable (limit supermatrix).

Figure 3 is a generalized form of a supermatrix to deal with the interdependence characteristics among elements and components. A supermatrix is actually a partitioned matrix, where each matrix segment represents a relationship between two nodes (components or clusters) in a system (Lee and Kim 2000).

Fig. 3

Supermatrix (Lee and Kim 2000)

Figure 4 depicts the structure and corresponding supermatrix in a network. A node represents a component (or cluster) wit h elements inside it; a straight line/or an arc denotes the interactions between two components; and a loop indicates the inner dependence of elements within a component (Chung et al. 2005).

Fig. 4

Nonlinear network (Lee and Kim 2000)

When the elements of a component “Goal” depend on another component “Criteria”, we represent this relation with an arrow from component “Goal” to “Criteria”. The corresponding supermatrix of the hierarchy with four levels of clusters is also shown: where a ₂₁ is a vector that represents the impact of the “Goal” on the “Criteria” (Saaty 2001); a ₃₁ is a matrix that represents the impact of the “Sub-criteria” on each element of the “Alternatives”. a ₂₂ indicates the inner dependence among “Criteria”. Since there usually is interdependence among clusters in a network, the columns of a supermatrix usually sum to more than one. The supermatrix must be transformed first to make it stochastic, that is, each column of the matrix sums to unity. A recommended approach by Saaty is to determine the relative importance of the clusters in the supermatrix with the column cluster (block) as the controlling component, the result is known as the weighted supermatrix. To achieve a convergence on the importance weights, the weighted is raised to the power of 2k+1; where k is an arbitrarily large number, and this new matrix is called the limited supermatrix. By normalizing each block of this supermatrix, the final priorities of all the elements in the matrix can be obtained (Chung et al. 2005).

Appendix B: The modified VIKOR method

The compromise ranking method (VIKOR) had been introduced as an applicable technique to implement within the MCDM (Opricovic and Tzeng 2002). The data matrix of the VIKOR method is expressed in Table 10.

Table 10 Data matrix of weights and performance scores

As shown in Table 10, a _j represented the jth alternative, j=1,2,…,m; c _i represented the ith criterion, i=1,2,…,n; w _i  represented the weight of the ith criterion, i=1,2,…,n, and x _ij was the performance of alternative a _j with respect to the c _i criterion. The large x _nm was better than small one. According to Opricovic and Tzeng (2004) and Ou-Yang et al. (2009), the VIKOR method included the following steps:

Step 1: Determining the best rating $x_{i}^{*}$ and the worst rating $x_{i}^{ -}$ for all the criteria. Table 10 showed that the criterion i represents a benefit, the $x_{i}^{*} = \max_{j} x_{ij}$, $x_{i}^{ -} = \min_{j} x_{ij}$. Naturally, a candidate having scores $(x_{1}^{*},x_{2}^{*},\ldots,x_{n}^{*})$ would be positive-ideal whereas a candidate having scores $(x_{1}^{ -} ,x_{2}^{ -} ,\ldots,x_{n}^{ -} )$ would be an negative-ideal candidate. It was assumed that such an ideal candidate does not exist; otherwise the decision would be trivial.

Step 2: Computing the values of “concordance” (S _j ) and “discordance” (R _j ). They represented the group utility and the individual regret measures for the alternative a _j , respectively, with the relations

(B.1)

(B.2)

where the weights of the criteria (w _i ) were introduced to express the relative importance of the criteria computed by the ANP method. $D_{j}^{p = 1}$ represented a maximum “group utility” of the “majority”. $D_{j}^{p = \infty}$ represented a minimum individual regret of the “opponent”. According to (B.1) and (B.2), the VIKOR result stands only for the given set of alternatives. Inclusion (or exclusion) of an alternative could affect the VIKOR ranking of the new set of alternatives. This effect could be avoided by fixing an ideal solution (Opricovic and Tzeng 2007). Thus, this study adopted a fixed ideal solution (i.e. the best $x_{i}^{*}$ value = 100 and the worst $x_{i}^{ -}$ value = 0).

Step 3: Computing the aggregate value (Q _j ). Its formula is:

$$Q_{j} = v[ ( S_{j} - S^{*} )/( S^{ -} - S^{*} ) ] + (1 - v)[ ( R_{j} -R^{*} )/( R^{ -} - R^{*} ) ],\quad \mbox{for}\ j = 1,\ldots,m $$

(B.3)

where S ^∗=min _j S _j , S ⁻=max _j S _j and R ^∗=min _j R _j , R ⁻=max _j R _j ; and v was the weight of the decision-making strategy “the majority of criteria” (or “the maximum group utility”), whereas 1−v was the weight of the individual regret. The compromise can be selected with “voting by majority” (v>0.5), with “consensus” (v=0.5), or with “veto” (v<0.5). Then, the VIKOR index (Q _j ) was obtained by weighting the utility and regret measures of each alternative.

Step 4: Ranking the alternatives by sorting each S,R and Q values in an increasing order. The result was a set of three ranking lists denoted as S[.],R[.] and Q[.].

Step 5: Proposing the alternative a ⁽¹⁾ corresponding to Q[1] (the smallest among Q _j values) as a compromise solution. It must satisfy two conditions as follows.

• C1. The alternative a ⁽¹⁾ has an acceptable advantage; in other words, Q[2]−Q[1]≥DQ where DQ=1/(m−1) and m is the number of alternatives (DQ=0.25 if m≤4).

• C2. The alternative a ⁽¹⁾ is stable within the decision-making process; in other words, it is also the best ranked in S[.] or/and R[.].

If one of the above conditions is not satisfied, then a set of compromise solutions is proposed, which consists of:

• Alternatives a ⁽¹⁾ and a ⁽²⁾ if only the condition C2 is not satisfied, or

• Alternatives a ⁽¹⁾,a ⁽²⁾,…,a ^(k) if the condition C1 is not satisfied; and a ^(k) is determined by the relation Q[k]−Q[1]≤DQ (the positions of these alternatives are “in closeness”).

The best alternative, ranking by Q _j , was one with the minimum value of Q _j . The compromise solution could be accepted by the decision-makers because it provided a maximum “group utility” of the “majority” (with measure S _j , representing “concordance”), and a minimum of individual regret of the “opponents” (with measure R _j , representing “discordance”).

In the original VIKOR method, the values of S ^∗, S ⁻, R ^∗ and R ⁻ came from the candidate alternatives, they were not real positive-ideal or negative-ideal values for all criteria. In fact, the positive-ideal point should be represented as a score of 100 and the negative-ideal point should be represented as a score of 0; therefore, the positive-ideal value (S ^∗) would be zero; the negative-ideal value (S ⁻) would be equal to one; the positive-ideal value (R ^∗) would be zero, and the negative-ideal value (R ⁻) would be equal to one. Besides, the weight (w _i ) included in the equation of R _j was not necessary. To improve the measurement of the VIKOR index, we proposed the modified VIKOR method which had been presented by Ou-Yang et al. (2009). The weights (w _i ) were removed from the equation of R _j , so the modified $R_{j}^{\mathit{mod}}$ index and $Q_{j}^{\mathit{mod}}$ were as follows:

(B.4)

(B.5)

Then, $Q_{j}^{\mathit{mod}}$ was simplified as follows.

$$Q_{j}^{\mathit{mod}} = vS_{j} + ( 1 - v )R_{j}^{\mathit{mod}} $$

(B.6)

In the original VIKOR method, the value of Q _j of the best alternative was zero or close to zero and the value of Q _j of the worst alternative was one or close to one. The Q _j cannot indicate how many variances between Q _j and an aspired level, but the modified $Q_{j}^{\mathit{mod}}$ index can overcome this drawback. It was worth noting that the value of DQ should be changed to $DQ^{\mathit{mod}}= (\max_{j} Q_{j}^{\mathit{mod}} - \min_{j}Q_{j}^{\mathit{mod}})/( m - 1 )$ in the modified VIKOR method, other conditions were the same as the conditions of the original VIKOR method.