Article A Two‐Phase Method to Assess the Sustainability of Water Companies Fátima Pérez *, Laura Delgado‐Antequera and Trinidad Gómez Departamento de Economía Aplicada, Universidad de Málaga, 29016 Málaga, Spain * Correspondence: [email protected] Received: 29 May 2019; Accepted: 5 July 2019; Published: 9 July 2019 Abstract: Composite indicators are becoming more relevant for evaluating the performance of water companies from a holistic perspective. Some of them are related with economic aspects, and others focus on social and environmental features. Consequently, a multidimensional evaluation is necessary for handling the great amount of information provided by multiple single indicators of a different nature. This paper presents a two‐phase approach to evaluate the sustainability of water companies. First, a partial composite indicator for each dimension (social, environmental, economic) is obtained using multi‐criteria decision making (MCDM). Then, a global indicator is obtained, in terms of the values reached in the previous stage for every partial indicator, by means an optimization problem rooted in data envelopment analysis (DEA). Our proposal offers the possibility of analyzing the performance of each water company under each dimension that characterizes the concept of sustainability, as well as a joint assessment including all the dimensions, facilitating the decision‐making process. We apply it to evaluate the sustainability of 163 Portuguese water companies. The results show the strengths and weaknesses of each unit and serve as a guideline to decision‐makers on the aspects for improving the performance of water utilities. Keywords: composite indicator; sustainability; water utilities management; data envelopment analysis; multi‐criteria decision making (MCDM) 1. Introduction The evolution of water management is a key issue for the human development. An effective performance of such service is a challenge for the community. Designing a good management system requires considering different factors. In countries such as England and Wales, Portugal, Chile, or the Netherlands, the water industry exists as a monopoly, so that companies and administrations invest their efforts on comparing the different processes within the industry. In general, benchmarking is widely considered a good strategy to control and supervise the performance of this service. Ref. [1] provide a rigorous evaluation of the growing number of benchmarking studies dealing with performance scores based on production or cost estimates. At the same time, the literature reveals frequent use of performance indicators (PIs) when dealing with benchmarking, because of the multiple benefits it brings to the administrations, for instance, to contrast the regulatory conditions, compare, and/or evaluate the quality of the service and establish fair tariff policies. So, in order to control these values, water utilities‐following industry regulations‐ provide systematic reports on different PIs to the government or administrators. The information delivered within this data includes management, environmental, financial and, more recently, social aspects related to water operations. However, different reasons make this set of indicators difficult to interpret because they do not offer a holistic view, as they do not reflect a measure of general performance. To overcome this difficulty, a common approach is to aggregate the PIs into a unique indicator, named a composite indicator (CI). Although the literature offers a wide range of techniques to create a CI, most of them use methodologies from multi‐criteria decision analysis (MCDA). They have been Energies 2019, 12, 2638; doi:10.3390/en12132638 www.mdpi.com/journal/energies Energies 2019, 12, 2638 2 of 20 used to develop CIs applied to diverse sectors of services, activities, or processes [2–4]. In particular, methodologies based on goal programming (GP) are of great interest for the construction of CIs and they have been successfully applied to diverse fields as tourism [5,6], manufacturing [7], human sustainable development [8–10], or environmental sustainability [11,12]. The main advantages of using GP to develop CIs are: it is not necessary to normalize the initial set of PIs; the CI uses the complete information included in the initial set of PIs; and it does not require a large number of units in comparison with the number of initial indicators. Usually, another technique used to create CIs is data envelopment analysis (DEA) [13]. DEA is a linear programming tool for evaluating the performance of a set of peer entities that use one or more inputs to produce one or more outputs. As pointed out by [14], the main advantages of using DEA to construct CIs are: it provides a measure of performance based on real data; DEA models do not require the normalization of the initial data; and DEA respects the individual characteristics of the units and their own particular value systems. Techniques based on DEA have been developed to create CIs in [6,15–17]. Since the 1990s, governments of many countries and organizations have emphasized the importance of the concept of sustainability [18]. There is no consensus on the definition of this concept, although it is widely agreed that it must incorporate social, environmental, and economic factors which are interconnected ([19,20]). The water industry has not ignored this trend and, currently, it has extensively recognized its important role in establishing and operating sustainable water supplies and wastewater treatment systems [2,21]. There is clearly a need for a paradigm shift in the water companies, considering social and environmental aspects in the decision making process, not just economic issues [22,23]. In the framework of evaluating the sustainability of water companies, most of the literature focuses on evaluating the sustainability of physical and engineering aspects [24–26], from an environmental perspective [27] or economic sustainability [28,29]. However, there is a lack interest on assessing the sustainability of water companies themselves. In particular, only a few papers apply different techniques from MCDA to assess the sustainability of water companies from a multidimensional perspective. For instance, Ref. [30] construct an index by aggregating the PIs as a linear combination of their normalized values. Also, the MACBETH (Measuring Attractiveness by a Categorical Based Evaluation Technique [31]) method is used to evaluate the sustainability of water supply systems [24]. Another example, Ref. [19], applies the ELECTRE TRI‐Nc (Elimination and Choice Expressing Reality [32]) method as a tool to integrate the dimensions of a quality of service index. Additionally, Ref. [12] combines the PIs using an index based on distance‐principal components and another based on GP. In view of the above, in this work, a method to assess the sustainability of the water companies is conducted, using the traditional approach of sustainability, which considers three dimensions into this concept: social, environmental, and economic. Then, a two‐phase method combining GP and DEA is proposed, in order to take advantage of both methodologies. A similar two‐phase method is proposed in [6] to evaluate the sustainability of Cuban nature‐based tourism destinations. Nevertheless, in that work, the distance‐principal component (DPC) composite indicator developed by [33] is used to sum up the initial PIs into the dimensions established (social, economic and patrimonial (Although it is usual to use “environmental dimension”, in [6] it is replaced by “patrimonial dimension”.) instead of GP. Choosing a technique based on GP comes from their good properties, as previously mentioned. Then, in the first phase, a technique based on GP [5] is used to obtain the dimensional or partial CIs. In the field of water treatments, there is a lack of consensus on the appropriate criteria to select, in order to determine which PIs are involved in evaluating the status of water sustainability. Then, to overcome this difficulty, as suggested by [34], our proposal groups the initial indicators into the dimensions that characterize the concept of sustainability: social, economic, and environmental dimensions. In this way, when the first phase is applied, three‐dimensional composite indicators (social, environmental, and economic) are obtained for each water company. This allows for independently analyzing the performance of each water company among these three dimensions. Energies 2019, 12, 2638 3 of 20 Later, in the second phase, the dimensional indicators have to be aggregated in order to design a global composite indicator for evaluating the water companies’ sustainability. At this point, a controversial question is the assignment of weights to each dimensional indicator. On the one hand, under some circumstances, it is not easy to obtain information from specialists to determine these weights. On the other hand, the assignation of the same weighting values for all the water companies could be complicated, as each of them might have their own particularities in terms of preferences. To overcome these issues, we have chosen, in the second phase, a DEA‐based model known as “Benefit‐of‐the‐Doubts” [32]. To do this, the values obtained in the previous stage are used as outputs of this “Benefit‐of‐the‐Doubt” approach. This two‐phase approach offers the possibility of considering the strengths and weaknesses of each water company, as well as providing the decision‐makers with useful information. The hypothesis