**6. Computational results analysis**

**Fundamental value**

**fi** **Index**

Economic development

—

46.02

54.99

45.8

Training

Culture Tourism Economic development programs

Economic development policies

Infrastructure

38.64

—

45.79

36.6

Roads Lighting Collective transportation

Traffic Policies infrastructure

Administration

10 —

10

10

Administrative control

Staff Safety Patrimony Policies administration

**Table 2.**

Summary of M-MACBETH indicies (applied to city hall of Fortaleza/2013).

0.01

10

10

0.001

0.01

0.01

0.1 0.0788 0.0524 0.0269

31.14

10.01

0.0027

0.0311

0.01

57.59

47.11

0.0052

0.0576

0.0471

84.09

76.18

0.0079

0.0841

0.0762

100

100

0.01

0.1

0.1

0.26 0.1967 0.0386 10

10

0.0149

0.0458

0.0366

67.27

46.83

0.076

0.308

0.1714

83.63

59.11

0.1005

0.3829

0.2163

0.046 0.3864 100

0.3232

91.79

67.29

0.1249

0.4203

0.2463

100

0.1493

0.4579

0.366

10

10

0.0212

0.055

0.0458

0.191

45.99

37.01

0.0879

0.2529

0.1695

**Maximun**

**Minimum**

**Subcriteria**

**si** **Index** 0.4602 100

0.3774 0.3359

81.99

70.76

0.1546

0.4509

0.3241

86.49

73.01

0.1737

0.4756

0.3344

194 Management of Information Systems

100

0.2118

0.5499

0.458

**Maximun**

**Minimum**

**Index**

**Maximun**

**Minimum**

**ki**

The graphs presented in the following figures were constructed based on the computational results generated by the implementation of the proposed model applied to the City Hall of Fortaleza, exercise 2013. In the abscissa, we find the budget allocations x (where i ranges from 1 to 285, number of variables of our Primal problem). In the ordinate, we have the values the values of k. These figures graphically show the sensitivity of the computational results. **Figures 1** and **2** shows, respectively, the ranges. The curves in pink present the maximum value and in yellow the minimum value that k can assume.

Following the model, we must construct the intersection curve of these two graphs. **Figure 3** shows the interval, intersection of the curves shown in the earlier graphs. The curve in pink shows the maximum value and the yellow line the minimum value that k can assume.

We can see that the variation spectrum of k is small, since the curves almost coincide. There is a small gap in which each k can vary without changing the budget distribution.

If we have two methodologies in the proposed model that generate two intervals (e) for variation of k, we must analyze which of the two methodologies contributes to the definition of the maximum limit and the minimum limit of the solution. The pink color curves presented in the graphs (**Figures 2** and **3**) that present the maximum values for k in the intervals (intersection) and (M-MACBETH), respectively, were superposed and are shown in **Figure 4**:

The dotted line in green stands for the maximum values of the M-MACBETH curve and the continuous in pink represents the maximum values of the intersection curve. It is the comparison of the two, in which the curve of the intersection of the maximum value of k coincides with that of M-MACBETH. We can see, then, that the definition of k by the actors (multicriteria method) imposes an upper limit of the values of the budget distribution. Let us therefore evaluate the main contribution of the lower limit. **Figures 5** and **6**, below, show the comparison of the minimum boundary curves of the intervals.

Except for a few points, the curve of the intersection of the minimum value of k coincides with that of LINDO. We conclude that legal and specific constraints (linear programming) impose the lower limit of the values of the budget distribution.

In the case of the City Hall of Fortaleza, participatory management (definition of k) by the actors (community) limits the budget distribution by assigning the maximum values of the

**Figure 1.** Variation of k - LINDO.

**Figure 2.** Variation of k-M-MACBETH.

the values of k. These figures graphically show the sensitivity of the computational results. **Figures 1** and **2** shows, respectively, the ranges. The curves in pink present the maximum

Following the model, we must construct the intersection curve of these two graphs. **Figure 3** shows the interval, intersection of the curves shown in the earlier graphs. The curve in pink

We can see that the variation spectrum of k is small, since the curves almost coincide. There is

If we have two methodologies in the proposed model that generate two intervals (e) for variation of k, we must analyze which of the two methodologies contributes to the definition of the maximum limit and the minimum limit of the solution. The pink color curves presented in the graphs (**Figures 2** and **3**) that present the maximum values for k in the intervals (intersection) and (M-MACBETH), respectively, were superposed and are shown in **Figure 4**:

The dotted line in green stands for the maximum values of the M-MACBETH curve and the continuous in pink represents the maximum values of the intersection curve. It is the comparison of the two, in which the curve of the intersection of the maximum value of k coincides with that of M-MACBETH. We can see, then, that the definition of k by the actors (multicriteria method) imposes an upper limit of the values of the budget distribution. Let us therefore evaluate the main contribution of the lower limit. **Figures 5** and **6**, below, show the

Except for a few points, the curve of the intersection of the minimum value of k coincides with that of LINDO. We conclude that legal and specific constraints (linear programming) impose

In the case of the City Hall of Fortaleza, participatory management (definition of k) by the actors (community) limits the budget distribution by assigning the maximum values of the

shows the maximum value and the yellow line the minimum value that k can assume.

a small gap in which each k can vary without changing the budget distribution.

value and in yellow the minimum value that k can assume.

196 Management of Information Systems

comparison of the minimum boundary curves of the intervals.

the lower limit of the values of the budget distribution.

**Figure 1.** Variation of k - LINDO.

**Figure 3.** Interval (intersection LINDO and M-MACBETH).

**Figure 4.** Comparison of M-MACBETH and intersection - maximum.

**Figure 5.** Minimum curves: intervals β and γ.

**Figure 6.** Minimum curves - intervals θ and γ.

priority grades of the budget activities. It is the legal and specific restrictions of each activity that impose the minimum amounts of amounts of the budget activities. Both seek a balance of budget distribution, reconciling the will of the population and laws.
