3.2.1. Phase 1: *PSUIdi*Calculation

The first phase addresses the calculation of *PSUIdi* . To do this, the aspiration levels for each indicator have to be established. Our proposal follows previous works [5,12,40,41], so that, for positive initial indicators, the aspiration levels were set to the 80% value of the mean for each initial indicator; whereas in the case of negative initial indicators, the reciprocal percentage of the mean was used.

Results obtained are shown in Figure 3 (Water companies are listed following the ranking obtained for the global indicator in the second phase. The numbers associated with the water companies are provided in Table 5). For each water company, a set of three values is represented in different colors which denote each dimension. Note that, following the formulation of the dimensional indicators, the maximum value that a water company can ge<sup>t</sup> for each dimension is 1. Therefore, for the social dimension, it can be seen that five water companies obtain remarkable results in comparison to others: Águas de Cascais, EPAL, SMAS de Sintra, Vimágua and SMSB de Viana do Castelo. According to its location, Águas de Cascais, EPAL, and SMAS de Sintra are located in MA Lisbon region, and Vimágua and SMSB de Viana do Castelo in North region. It can be seen that most of the water companies obtain poor results for this dimension and that just a few of them obtain values greater than 0.5.

Likewise, an analysis within the environmental dimension reveals the good performance of Águas de Gondomar, Indaqua Matosinhos, Infraquinta, and Tavira Verde. Similarly, based on its location, Águas de Gondomar and Indaqua Matosinhos are located in the North region; and Infraquinta and Tavira Verde in the Algarve region. Aguas de Gondomar reaches the best position, since it provides the largest production of energy (IEN2). Note that each of these four better-positioned water companies produces between 14% and 20% of the energy that it uses. In general, most of the water companies obtain poor results in this dimension, too.

Additionally, in both of these dimensions, the values which indicate the certifications obtained for each water company plays an important role in the construction of the dimensional indicators, as determined in [12].

Finally, the results obtained for the economic dimension are ranged between 0.18 and 0.8 for all companies, highlighting Águas de Valongo and Indaqua Santo Tirso/Trofa, which are located in the North region. In particular, these water companies reach values greater than the average for all the initial indicators. In the data obtained, approximately the 56% of the water companies present an operating cost coverage ratio (IEC3) larger than the average.

In general, note that the best dimensional performance of the water companies is located in MA Lisbon, Algarve and North regions, despite the fact that more than a half of the companies (approximately 54%) are located in the other two regions (Alentejo and Centre regions).

In the same way, Table 3 shows the top 20 water companies for each dimension considered. It should be noted that there are four companies that appear among the top 20 in the three dimensions: Águas de Cascais, Águas de Valongo, Águas de Paredes, and Indaqua Matosinhos. Furthermore, 13 other companies stand out for two dimensions.

**Figure 2.** The two-phase approach applied to the case study.

**Figure 3.** Dimensional results obtained for each of the 163 water companies.



Similarly, Table 4 shows the bottom 20 water companies for each dimension. In this case study, most of the companies (33) ge<sup>t</sup> bad results in just one of the three dimensions and only three water companies obtain poor results in the three dimensions: CM de Castelo de Paiva, CM de Arronches, and CM de Aljustrel.


**Table 4.** Bottom 20 water companies for each dimension.

In managerial terms, within the top-20 rankings, those companies that follow the municipal concessionaire managemen<sup>t</sup> model obtain good results in the environmental (13) and economic dimensions (11). Additionally, in the social dimension, the ranking is leaded by a mixture of water companies following di fferent managemen<sup>t</sup> models: municipal or State-owned companies (VIM ÁGUA and EPAL), municipal concessionaire ( Águas de Cascais), or direct managemen<sup>t</sup> (SMAS de Sintra and SMSB de Viana do Castelo).

The results obtained in this section are of grea<sup>t</sup> interest for water regulators. They enable the operators to learn from the best positioned water companies in each dimension and establish operative strategies in the correct direction with the aim of reducing the weaknesses in the mid-term. In general, social and environmental issues are still insu fficiently integrated into managemen<sup>t</sup> processes and there is room to improve these dimensions. Regulators should promote certification programs to encourage water companies to make necessary improvements in order to obtain these certifications.

### 3.2.2. Phase 2: *GSUIa* Calculation

Once the dimensional indicators (*PSUI<sup>d</sup> i* ) are obtained for each water company, the optimization problem (Equation (7)) is applied in order to obtain the Global Sustainability Indicator proposed (*GSUIa*). These solutions will provide the weights for social (S), environmental (EN), and economic (EC) dimension, maximizing the global score for each water company. In this way, this problem provides the weights for social, environmental, and economic dimension, maximizing the global score for each water company. The lower and upper bounds of the constraints are set to 0.001 and + <sup>∞</sup>, respectively. This ensures that each dimension represents, at least, the 0.1% of the global score.

Figure 4 shows the values obtained for *GSUIa*. It can be observed that there are five water companies ( Águas de Cascais, Águas de Gondomar, Águas de Valongo, Indaqua Matosinhos, and Vimágua) that reach a value equal to 1 for the global indicator. EPAL, Indaqua Santo Tirso/Trofa and SMAS de Sintra are, also, very close to achieving a score of 1. It should be noted that 42.95% of the set of water companies obtain a global value greater than 0.70; in particular, 25.15% of water companies obtain a global value greater than 0.80. Then, a large group of water companies obtains good results, as they reach a value close to 1. Additionally, there are no companies obtaining a global value lower than 0.20.

**Figure 4.** Global results obtained for each of the 163 water companies.

Table 5 lists all the water companies (163) according to the values obtained for the global indicator, *GSUIa*. On the one hand, regarding the best results, four companies that belong to the top-20 for every dimension also appear within the best global indicator values. Moreover, between the companies ranked better, based on *GSUI*, there are 11 water companies whose *PSUI* value leads them to the top-20 in two different dimensions. On the other hand, there are three companies that were part of the bottom ranking for all the dimensions and, also, for the global indicator value. In particular, between the 20 worst positioned water companies, based on the global indicator *GSUI*, there are four water companies that also appeared among the worst results for two dimensions. The other 13 water companies included in this bottom 20 ranking obtained poor results in the economic dimension.

An analysis about the correlation between all the rankings is shown in Table 6 using a Kendall tau test. Correlations are significant at 1% level and values obtained show a high correlation between the economic dimension ranking and the global ranking (0.925). The rest of the correlations are similar and positives, and they are ranged between 0.26 and 0.40.

The proportional contribution differences can be explained by the particular profile characterizing each company. A global analysis reveals some influence of the location of the water companies in these lists. On the one hand, note that 12 of the top-20 water companies are located in the North region, three water companies are located in MA Lisbon, three water companies are located in the Centre region, and two water companies are located in the Algarve region. No one of the top-20 water companies is located in Alentejo region. Additionally, the geographical distribution of these water companies with the best performance on GPSUI might be grouped into two main locations along the Portuguese coast: those companies that are placed close to Oporto (for example: Águas de Valongo, Indaqua Matosinhos, Águas de Gondomar, Indaqua Santo Tirso/Trofa, Águas de Paredes, Indaqua Feira, Águas do Porto), and the ones close to the capital (Águas de Cascais, SMAS de Sintra, EPAL). On the other hand, within the bottom-20 water companies, none of them is located in the MA Lisbon or in Algarve region. Nevertheless, most of them are located in the North region (11), five water companies are located in the Alentejo region, and four water companies are located in the Centre region.




**Table 5.** *Cont.*

### **Table 6.** Kendall tau test.


\*\*: significance level at 1%.

In relation to the weights obtained by solving Equation (7), Table 7 summarizes the maximum and minimum values for the virtual outputs obtained, as well as their mean and standard deviation for each dimension. The economic dimension, in general, is the one with the largest virtual outputs in the global aggregation. As the reader may observe in Figure 3, almost all water companies obtain similar (good) values in this dimension. On the contrary, the social and the environmental dimensions lose importance in the global weighting. The results show how some companies obtained very good results in these dimensions but, at the same time, a larger proportion of the companies obtained relatively poor results.

**Table 7.** Statistical information for weights calculated.


Figure 5 shows the percentage contribution of each partial indicator to the value of the global composite indicator, for the top-20 water companies. Di fferences in percentage contribution can be explained by the particular profile characterizing each company. Despite the good performance of those 11 companies within the top-20 at each dimension, in the global score there is no company that displays a balanced contribution among the three dimensions. Then, if a balance between dimensions is searched, the best water companies of the global indicator are not a good reference for the others, in this context. In general, water companies should seek to improve their results in the dimension in which they obtained the worst results in the first phase, without neglecting the maintenance of good performance in those dimensions in which they obtained good results. Moreover, focusing on the companies that have a value equal to 1 in the global indicator, Águas de Cascais and VIMÁGUA exhibit a greater contribution of the social dimension, while Indaqua Matosinhos and Águas de Gondomar prioritize environmental dimension. However, Águas de Valongo stands out for the percentage contribution of the economic dimension, while a minor importance of the others. In the rest of companies, among those with a value of the global indicator close to 1, it is worth mentioning that Indaqua Feira and Águas de Alenquer present a similar performance with an analogous contribution of each dimension, around 8% for the social dimension, 9% for the environmental dimension, and 83% for the economic one. In general, a trade-off between the economic dimension and the others can be observed jointly.

In managerial terms, within the top-20 ranking, ten companies that follows municipal concessionaire managemen<sup>t</sup> model obtain good results the global indicator. The other ten companies present a fair distribution between the other two managemen<sup>t</sup> models. Additionally, note that all water companies belonging to the bottom-20, use the municipal direct managemen<sup>t</sup> model.

Then, the proposed approach allows evaluating the strengths and weaknesses of each water company in a particular dimension and, at the same time, provides information about the contribution of the dimensions to the sustainability overall score. These are the main advantages in comparison to the previous methodology. In fact, if the initial indicators are directly aggregated using the methodology based on goal programming, the results obtained regarding the best and the worst global performance of the water companies are similar to those obtained with the proposed two-phase approach. In particular, the top-13 using the previous methodology is formed by water companies that appear in our global top-20. Nevertheless, using the previous methodology, the advantages named above disappear because dimensional results are not obtained and, therefore, the contribution of them to the global indicator is missing.

Consequently, in light of the results obtained, it is necessary to perform some transformations towards sustainability with a balanced percentage contribution of each dimension. Implementing appropriate programs that highlight social and environmental aspects is required to address global sustainability in an adequate manner. Nevertheless, the proposed approach allows a better observation of the differences among the water companies, dimensional and globally. It eases identifying strengths and weaknesses of the companies, helping the decision-maker to set strategies to improve the mediumand long-term sustainability of such companies.
