**5. Case study: Fortaleza city hall**

We used as a case study the budget data for the 2013 fiscal year of the City Hall of Fortaleza, approved by the Municipal Council and published in the official gazette.

The City Hall of Fortaleza 2013 Budget is composed of several tables. Among them, we show the Government Programs and the General Summary of Revenue as being of most relevance for the development of this work. We look for the government programs defined as goals to be achieved in 2013 by the City Hall of Fortaleza, and their respective activities; And, from there, we apply the definition proposed in the model. The targets will be achieved through the application of the budget allocations defined for each of the activities planned for the government programs.

#### **5.1. Application of the model**

Initially, we start from the Government Programs table of the 2013 City Hall of Fortaleza budget and classify activities as fundamental values. We call the areas of general interest in society: Education, Infrastructure, Environment, Administration, Health, Economic Development and Social Assistance. For each fundamental value, we define classification sub criteria as presented in **Table 1**.

The areas and their sub criteria were defined based on interviews with several specialists in the areas of planning, education, health, administration, infrastructure, etc. … The proposed method consists in classifying each budget activity as the fundamental value, that is, if that activity refers to Education, Infrastructure, Environment, Administration, Health, Economic Development or Social Assistance; And the sub-criterion presented in the table above. We apply M-MACBETH to compare the attractiveness of fundamental values and their sub criteria and then define the "degree of importance" of each activity group. We understand by activity group the set of budgetary activities that have as fundamental value and subcriterion the same classification. The definition of the attractiveness indices predicted in the


**Table 1.** Fundamental values and their sub criteria.

M-MACBETH method was carried out based on research with some actors from different social levels, selected at random. We defined as "consensus" between the actors the arithmetic mean of their answers in each comparison, calculated from the one-to-one correspondence of the attractiveness, on a scale of 2 to 6 proposed in the model (from 2—Much less important to 6—much more important).

We understand that the choice of actors and the definition of consensus among them should be the object of specific research within a participatory management project. Our aim in this case study was to stand for an interest of a randomly defined community, without scientific research on the representativeness of the community since this research transcends the object of our research. On the other hand, to apply the M-MACBETH software, inserting the result "of this consensus" in steps:

#### **5.2. Definition of the attractively index among the fundamental values**

We present in **Table 2** - Summary of the M-MACBETH Indices, column "f - Index" the result of the comparison of the attractiveness of the fundamental values (Health, Education, Social Assistance, Environment, Economic Development, Infrastructure and Administration) - MACBETH. On the other hand, Health was identified as the most important fundamental value and Management was of the least importance. In the table of values of M-MACBETH we defined with 10 points the lowest value of attractiveness for calculating the individual indexes.

### **5.3. Definition of the attractiveness index among the subcriteria of the fundamental values**

We present in **Table 2** - Summary of the M-MACBETH Indices, column "S - Index" the result of the comparison of the attractiveness of the subcriteria of each fundamental value, using


M-MACBETH method was carried out based on research with some actors from different social levels, selected at random. We defined as "consensus" between the actors the arithmetic mean of their answers in each comparison, calculated from the one-to-one correspondence of the attractiveness, on a scale of 2 to 6 proposed in the model (from 2—Much less important

Health Hospital Basic attention Medication Surveillance Health policies

Education Feeding Fundamental Infant Adults Education

We understand that the choice of actors and the definition of consensus among them should be the object of specific research within a participatory management project. Our aim in this case study was to stand for an interest of a randomly defined community, without scientific research on the representativeness of the community since this research transcends the object of our research. On the other hand, to apply the M-MACBETH software, inserting the result

We present in **Table 2** - Summary of the M-MACBETH Indices, column "f - Index" the result of the comparison of the attractiveness of the fundamental values (Health, Education, Social Assistance, Environment, Economic Development, Infrastructure and Administration) - MACBETH. On the other hand, Health was identified as the most important fundamental value and Management was of the least importance. In the table of values of M-MACBETH we defined with 10 points the lowest value of attractiveness for calculating the individual indexes.

**5.3. Definition of the attractiveness index among the subcriteria of the fundamental** 

We present in **Table 2** - Summary of the M-MACBETH Indices, column "S - Index" the result of the comparison of the attractiveness of the subcriteria of each fundamental value, using

**5.2. Definition of the attractively index among the fundamental values**

to 6—much more important).

**Fundamental value**

192 Management of Information Systems

Economic development **Classification subcriteria**

Training Economic

Social assistance Habilitation Social assistance

Infrastructure Road Collective

**Table 1.** Fundamental values and their sub criteria.

Management Staff Safety Patrimony Administration

programs

development programs

transportation

Environment Oversight Urbanization Preservation Privacy Policy

policies

Policies Tourism Culture

Laser Citizenship Policies social

Lighting Traffic Policies infra

Control

assistance

policies

—

"of this consensus" in steps:

**values**


**Table 2.** Summary of M-MACBETH indicies (applied to city hall of Fortaleza/2013).

the method M-MACBETH. According to the proposed model, the degree of importance k for the government activity whose budget allocation x is bound will be the product of the index established for its fundamental value by the index established for its sub-criterion: k = f × s. **Table 2** presents in the column "k - Index" the product of the columns "f - Index" and "s - Index" for each established subcriteria.

The objective function applied to the case study can be seen in the https://www.dropbox. com/s/ga4flhp61291ro4/Restrictions%20and%20degrees%20of%20attractiveness.pdf?dl=0 through the horizontal reading of the table, by the sum of the product of the fifth column (relation of the k's) by the corresponding x.

#### **5.4. Restrictions**

Each budget activity may be present in more than one constraint. This model applied to the City Hall of Fortaleza in 2013 can be seen in tabular form in the https://www.dropbox.com/s/ ga4flhp61291ro4/Restrictions%20and%20degrees%20of%20attractiveness.pdf?dl=0. The columns 1 and 2 present the budget allocations of government activity x; Columns 3 to 9 show whether the activity is present in restrictions 1 to 7, respectively; And columns 10 and 11 refer to the specific constraints of each activity (minimum and maximum values, if any).

The table reading can be done horizontally, where you can see each model variable, that is, the budget allocation of each activity and the vertical form of columns 3 to 9, the sum of the rows in each column is the composition of A restriction. Columns 10 and 11 shows whether there is a specific constraint, that is, whether there is a restriction on the maximum or minimum value, respectively, for the budget allocation of that activity. The revenues that make up the second term of the restriction can be found in the "General Summary of Revenue" table, in the fiscal year 2013 of the City Hall of Fortaleza, approved by the City Council and published in the official Gazette.

The first lines of the model, that is, the objective function and the first constraints (those imposed by the specific legislation) are formed by many variables. The other constraints of the primal problem are specific to each government activity, and therefore are made up of only one variable.

We applied LINDO/PC, release 6.1 for analysis and solution of the model in linear programming applied to the City Hall of Fortaleza. The software generated the result of the application of the model for budget optimization/City Hall of Fortaleza - 2013, presenting an array of 578 rows and 285 columns.
