3.3.1. Regime Method

The regime method is based on two input data: the impact matrix and the weight vector to compare the alternative and to define a ranking of these.

The impact matrix developed for the analyzed case study is illustrated in Table 1, starting from the list of criteria identified in Figure 1.


### **Table 1.** Impact matrix.

As illustrated in Table 1, in order to evaluate the alternatives and to reflect the complexity of the design problem, each criterion uses a different scale of measurement, qualitative or quantitative, due to their nature and the available information. It is important to highlight that each criterion can be considered as a cost or a benefit, and for this reason, they have to be respectively minimized or maximized.

The main scales are nominal, ordinal, binary, and ratio. For simplicity, we refer to the first three as qualitative information and to the last one as a quantitative scale.

In the case of the Ex Ritiro del Carmine, the scale of measurement and the related unit of measurement used are


For each criterion, it is indicated whether the criterion represents a cost or a benefit (c/b).

The system of weights identifies the priority among the evaluation criteria, which is basically a political issue linked to the policy game and anyone involved in the decision-making process.

The weight vector consists of an ordinal assessment of the criteria. This type of evaluation allows for the simplification of the dialogue with the DMs, especially in the early stage.

During the decision-making process, the DM was asked to express his own preferences through the assessment of the set of weights associated with the evaluation criteria. The identified ordinal sets of weights are shown below in Figure 4.

The two sets highlight two different approaches: the first, which refers to the political class, attributes more importance to the social aspects, while the second, which refers to the technical experts, pays close attention to the economic feasibility.

The results obtained with the regime method are shown in Figure 5.

**Figure 4.** Rank order of criteria.

**Figure 5.** Results of the regime method: rank order of alternatives.

Both the rankings presented "Alternative E: Social hub with antiviolence center for women" as the best compromise solution. The other alternatives were in the same order, but they presented different scores.

## 3.3.2. Weighted Summation Method

The sensitivity of the rank order obtained with the regime analysis was then tested using the WSM, evaluating two new sets of weights through a pairwise process and using them to rank the alternatives.

The WSM is based on the impact matrix and a set of weights to compare the alternatives and to define a ranking of these. The set of weights consists of a matrix, in which the quantitative evaluation of the DM's preferences is reported; this type of evaluation allows the improvement of the design of the expressed preference through a quantitative pairwise evaluation process shown below (Table 2).

The application of weighted summation allows for verification of the robustness and stability of the results through a "sensitivity analysis". This process assesses the variation of the previous results through the variation of the weight matrix.

The weight matrix is assessed in a process of pairwise comparison among every possible couple of criteria. The DM is asked to express his preference through a numeric value that goes from 1, when the considered criteria have the same importance, to 9, when a criterion is "extremely more important" than the other one. The matrix is not symmetrical, because if we compare *a* with *b*, then the value of *b*

with respect to *a* represents the reciprocal. For example, in our case, the criterion *a* was more important than *b*, and the value was 1.2. So, the value of *b* with respect to *a* was the reciprocal (1/1.2, or 0.833).

The identified weight matrixes are shown below in Table 2.


**Table 2.** Sets of weight matrix.


The results of the calculation for the above sets of weights are shown in Figure 6. Both the evaluation rankings presented "Alternative E: Social hub with antiviolence center for women" as the best compromise solution, while the other positions were different in each ranking. These two rankings were different from the previous results due to an improved assessment of the sets of weights.

**Figure 6.** Results of the weighted summation method (WSM): rank order of the alternatives.

The results obtained confirmed that the rank order of the alternative is not sensible to the weight vector assessed.

3.3.3. Social Evaluation and Coalition Assessment

Starting from the definition of the main social actors (see Section 3.1), the first step was the identification of their points of view in relation to the project alternatives. The information from each group, identified in the first stage of the process, was collected through an online survey supplied through Google Forms. The questionnaire was structured with close-ended questions; they had a limited number of answers, among which the respondent must choose the one which best matches his/her opinion. The form presented an initial introductory part with the aim of obtaining general information about the respondent; the second part described the case study and presented the project alternatives in simple and familiar language; in the third section, the respondent was asked to evaluate the presented alternatives through a linguistic evaluation. The linguistic assessment was expressed on a nine-level qualitative scale from "perfect" to "extremely bad".

Examples of the questions posed in each part of the questionnaire are here reported.

	- a) Yes, I am
	- b) I usually frequent the city
	- c) No, I am not
	- a) Yes, I do
	- b) I have heard of it
	- c) No, I don't

The collected evaluations were gathered and are displayed in the equity matrix shown in Table 3.


**Table 3.** Equity matrix.

The equity matrix provided the linguist indication of the interest group judgments for each alternative. Semantic distance was also used in this case to calculate the similarity indexes among interest groups. A similarity matrix was then computed starting from the equity matrix. The similarity matrix provided an index, for each pair of interest groups i,j, of the similarity of judgement over the

proposed alternatives. This index sij was calculated as sij = 1/(1 + dij), where dij is the Minkovsky distance between groups i and j, which was calculated as follows:

$$dij = \sqrt[P]{\sum\_{k=1}^{N} \left(S\_k \left(i, j\right)\right)^P}$$

where *S(i,j)* is the semantic distance between groups i and j in the judgement of alternative *k, N* is the number of alternatives, and *p* > 0 is the parameter of the Minkovsky distance. Lastly, through a sequence of mathematical reductions, the dendrogram of coalition formation was built. It shows possible coalition formation for decreasing values of the similarity index and the degree of conflict among interest groups.

For the case study, we used the NAIADE software for the calculations. This software allowed for comparison of the preferences expressed and analysis of the similarity between the interests of each group. Furthermore, it supplied a graphic representation of the potential coalitions between the parties in the form of a dendrogram. Each meeting point has an associated numeric value, named "similarity index", which shows the similarity of the coalition, with values between 0 and 1.

In the case of the Ex Ritiro del Carmine, the dendrogram (Figure 7) highlights good results in terms of agreement among the stakeholders.

**Figure 7.** Dendrogram of the coalitions.

The first coalition, between G1 and G6 (public administration and social and cultural association), had a similarity index value of 0.8545. The second coalition, between G4 and G7 (freelance professionals and students), had a the similarity index value of 0.8171. The third coalition, between G8 (the employed) and the previous coalition (G4–G7), had a value of 0.8058. The coalition between the two abovementioned groups (G1–G6 and G4–G7–G8) had a value of 0.7954.

In Table 4, the possible coalitions referring to different rankings of the alternatives are shown. It is possible to note that for the ranking (E, C, D, A, B), all the groups were in agreement, having a similarity index of 0.7382, which is really high considering that the maximum value of similarity (total agreement) is 1.


**Table 4.** Possible coalitions on the ranking of the alternatives.

So, the results of the calculation underline that the favorite solution is the "Alternative E: Social hub with antiviolence center for women".

### 3.3.4. Results Comparisons

In the previous sections, we established the rankings for each phase of the proposed framework with different methods. The obtained results supplied the same preference in every stage of the process (Table 5), so that the best compromise solution may be "Alternative E: Social Hub with antiviolence center for women".


**Table 5.** Comparison between different rankings.

P.A.—public administration; T.E.—technical experts; NAIADE—Novel Approach to Imprecise Assessment and Decision Environments.

In the next subsection, we evaluate the financial sustainability of the alternative chosen from the stakeholders involved in the decision-making process.

### *3.4. Definition of a Project Strategy*

Nowadays, the lack of public resources complicates the financing of the redevelopment process. Therefore, public administrations have to assess the public expenditure in order to guarantee economic sustainability throughout the life of a project. Financial analysis allows the evaluation of both the construction cost and the cash flow and calculates the necessary public economic resources to effectively run a reused building [52,53].

Once the new function is defined, it is possible to evaluate the construction cost of the project. This is composed of several rates [50], in particular, technical construction cost (TCC), taxes (corresponding to 21% of TCC), professional costs, preliminary studies and surveys, tender notice, and accidents (corresponding to 5% of TCC).

The values of technical costs used here referred to the official "Listino Tipologico" published by DEI, (Tipografia del Genio Civile) in 2017.

For the Ex Ritiro del Carmine, each rate is shown in Table 6


**Table 6.** Construction cost.

While the cost of construction concerns the early years of the process, the management of the building spans a greater amount of time. Management costs and incomes are evaluated during a time period, which depends on the type and size of the project. For public projects, this is often a period of 20 years [54].

This evaluation requires the formulation of a mode of operation: for each new function, a management hypothesis is made between the "direct management", by the municipality, and the "indirect management", through private rent. Indirect management consists of the renting of the spaces to private companies for each specific activity.

For the monastery, the above hypotheses are reported for each function in Table 7.


**Table 7.** Management model.

The costs and the incomes for each function were evaluated through a market analysis and referring to official list prices. The evaluation used both the comparison between historical data, when available, and an indirect approach, when there were no historical data [50].

The evaluated costs were the following:


The evaluated incomes were the following:


The comparison between the costs and the incomes (Table 8) showed that the costs are greater than the incomes. Therefore, it is necessary to find new funds from public capital. These, which are reported in Table 8, derive from participation in public invitations to tender for single activities.


**Table 8.** Costs, incomes, and funds.

O—ordinary management; SM—staff management; OM—ordinary maintenance; EM—extraordinary maintenance; IT—insurance and taxes; RI—rate income; NRI—nonrate income.

The cash flow is represented on a time line, which relates costs, incomes, and funds to each period of time (Table 9).

The comparison between the costs, incomes, and funds highlights the lack of resources for the management of the Ex Ritiro del Carmine. While the cost of construction is provided by public funds, the incomes do not entirely cover the costs. Therefore, the municipality has to cover the gap with its own resources.

The public financial statement is divided into "missions". The redevelopment of the monastery embraces three different missions, for which €3.3 million are allocated. Therefore, the Ex Ritiro requires at least 1.5% of the stated budget available.



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