## Abstract

The world is facing a growing water scarcity problem in the most diverse regions. The Rio Grande do Norte (RN), a Brazilian semi-arid region, is facing its severest drought in the last 100 years. Given this context, managing water resources and combating the effects of the drought have become even more important. Decisions made in this context may involve multiple criteria established by more than one decision-maker. To tackle this issue, a multicriteria model for group decisions is proposed in order to rank the municipalities of the region and thus guide the public administration's efforts in tackling the drought and mitigating its effects. The applicability of the model is exemplified by studying the Apodi-Mossoró river basin, for which the PROMETHEE GDSS method was selected and the preferences of three decision-makers were calculated.

## Introduction

Conflicts over the use of water are not inherent to the modern world: they have recurred throughout history. According to Ferguson et al. (2013), water systems in cities around the world are facing environmental and societal pressures such as water scarcity, decaying waterways, floods, changing demographics, and an infrastructure that is aging. Dong et al. (2016) emphasize that rapid urbanization and population growth have resulted in a serious global shortage of water and in the environment deteriorating. The scarcity of fresh water is related to several factors and has become a major concern in various parts of the world. According to Buurman et al. (2016), rationing water and disruptions in its supply can cripple production processes, and communities may incur additional prohibitive costs when seeking alternative sources of water. Boggia & Rocchi (2010) note that because water is scarce and there are different interests and stakeholders involved, this calls for more complex water management due to the presence of legal rights and economic interests that must be considered during the decision-making process.

The situation becomes even more complicated in places that are affected by long periods of drought, such as northeast Brazil. The lack of rainfall means that reservoirs are not regularly replenished with water, thus making it difficult to manage water resources. WMO & GWP (2016) state that droughts are a normal part of the climate and can occur in any climate pattern in the world. Droughts are one of the costliest natural hazards and have significant impacts that affect many economic sectors and people simultaneously. Hong et al. (2016) state that droughts can evolve into a natural disaster depending on the duration and the resulting negative socioeconomic effects.

According to Wilhite et al. (2014), responses to droughts in all parts of the world have generally been reactive and taken a crisis management approach. Pischke & Stefanski (2016) argue that this reactive, or crisis management, approach is untimely, poorly coordinated, and not integrated and, moreover, such an approach provides negative incentives for adapting to a changing climate. Hong et al. (2016) state that to implement effective drought management measures, public authorities need to adopt a holistic and integrated approach.

The Brazilian semi-arid region, which is found in the northeast, is home to approximately 12% of the country's population (about 25 million people) and has natural characteristics that create unfavorable conditions regarding the water balance. High temperatures, low thermal amplitudes, strong insolation, and high evapotranspiration rates as well as low rainfall and infrequent rains result in rivers often having little or no water for use by humans whether domestically or for agricultural or industrial purposes. After four consecutive years of low precipitation, the region is in a critical situation since the rainfall indexes of the last years were insufficient to maintain adequate levels of water in reservoirs (ANA, 2016).

Given that scenario, according to Silva et al. (2010), decision-making that involves water resources management is usually complex due to the need to consider several objectives that also involve environmental, social, and economic impacts. Kalbar et al. (2013) propose that environmental decisions require the participation of multiple stakeholders and have large-scale implications that affect both the local and global environments. According to Vincke (1992), multicriteria support for decision-making aims to support decision-makers (DMs) with tools that enable them to make progress when solving problems. Sikder & Salehin (2015) state that this is about evaluating alternatives in relation to decision-making criteria and that these tools are practical and useful in helping to solve real-life problems that involve conflicting criteria.

Vincke (1992) states that there are three families of multicriteria methods. The first is characterized by aggregating different points of view into a single function. These include Multi-Attribute Utility Theory (MAUT), Simple Multi-Attribute Rating Technique using Swings (SMARTS), Simple Multi-Attribute Rating Technique Exploiting Ranks (SMARTER), and the Analytic Hierarchy Process (AHP). The second involves the construction of an outranking relationship between the alternatives and the exploitation of that relationship, including the elimination and choice translating algorithm (ELECTRE) and the Preference Ranking Method for Evaluation Enrichment (PROMETHEE). The third family, also known as interactive methods, alternates between calculation and dialogue steps. The management of water resources is a very promising research field, where several tools and approaches can be used to focus on different aspects of the problem. This is evidenced by the studies of Tsakiris & Spiliotis (2011), Spiliotis et al. (2015), and Pinto et al. (2017).

According to Lu et al. (2007), group decision-making is defined as a decision situation in which more than one individual is involved. To Silva & Morais (2014), the decision of a group is given by aggregating individuals' preferences. The result may not reflect the opinion of each individual DM, thus implying that there is a high level of divergence among them. There are several tools that can be used to convert individual decisions into group decisions. Among them is the PROMETHEE group decision support system (PROMETHEE GDSS) proposed by Macharis et al. (1998), which is based on the PROMETHEE and GAIA methods. According to Gonçalves & Belderrain (2012), PROMETHEE GDSS belongs to the family of outranking methods and sets out to address the ranking problem. Using group decision-making support methods that can ensure public participation in the decision-making process, Michels (2016) states that public participation has become increasingly important in the water sector, and public engagement is included to improve the quality of decision outcomes, to generate legitimacy in the process, and to solve water-related conflicts.

Given this context, this study proposes a multicriteria model for ranking the municipalities in a semi-arid region to better allocate actions to combat the drought and its effects in a crisis management context. The proposed model is applied in the semi-arid region of the state of Rio Grande do Norte. It seeks to identify which municipalities are in the most critical situation regarding the impacts associated with the drought.

The next section describes the status of the water resources in the semi-arid region of Rio Grande do Norte. Afterwards, the multicriteria model for prioritizing the municipalities is presented. Then, the numerical application of the model is performed using the PROMETHEE GDSS methodology. The results obtained are discussed and final considerations are presented.

## Status of water resources in the Brazilian semi-arid region

Magalhães (2016) states that the northeastern region has the greatest frequency and intensity of droughts. The semi-arid region, also known as ‘Sertão,’ usually suffers from scarcity of water and is strongly affected by periodic droughts. According to Campos & Studart (2008), even though the demographic density is low and there is little anthropogenic degradation, the semi-arid environment does not offer sustainable conditions for agriculture in dry years. However, there is a set of conventional solutions that can be used to address the problem, namely, inter-basin transfer, constructing dams, introducing irrigation, forecasting drought, mounting work fronts, building water tanks, and engaging in new practices in water resources management.

According to Magalhães (2016), 2015 was the fourth consecutive year of drought. This is very serious because, in addition to the loss of agricultural output, small-, medium- and even some large-capacity reservoirs have dried up, and water trucks must bring water from locations that are at even greater distances from where help is needed. The recent situation has been one of the most complicated due to the current length of the drought period in the region, which has persisted since 2012. Consequently, the level of water used for consumption and held in reservoirs has fallen sharply. According to the data from ANA (2016), the levels of water in the reservoirs of the northeastern region fell from 46.3% of total capacity in 2012 to 16.3% in 2016. The situation is similar in the state of Rio Grande do Norte where the decrease was from 52.5% to 15.5% in 2016.

The situation may be worsened by the context of climate change that directly affects the region. According to IPCC (2014), the risk of water supply shortages will increase due to reduced rainfall and increased evapotranspiration rates in the Brazilian northeast region, thereby affecting the water supply, the ability to generate power, and the sustainability of agriculture. To Angelotti et al. (2015), the higher temperatures in the semi-arid area tend to increase its water deficit, thus considerably affecting rain-dependent activities.

Approximately 92% of the territory of the state of Rio Grande do Norte is semi-arid, which makes matters worse. Therefore, due to the prolongation of the drought, the state government, by Decree Number 25,931 of 03/21/2016, renewed the emergency status for 153 of the 167 municipalities in the state, which account for 91.6% of land in the state. Of these municipalities, 21 are in total collapse and therefore water trucks or artesian wells are used to meet their supply needs.

According to SEMARH (2016), the state has 16 river basins, of which the Apodi/Mossoró and Piranhas/Açu basins are the largest. In March 2016, the basins held only 21.85% and 17.25% of their water capacity, respectively. According to data from ANA (2016), the volume of water in the state reservoirs dropped to the 19.9% capacity mark. Given the below-average rainfall forecast for 2016, the trend is for there to be further large-scale depletion of these levels in the region in 2017. In regions with a water deficit, irrigation plays a primordial role in planning agricultural development. Consequently, the drought has a considerable impact on the economy of the regions affected, which are generally characterized by a high dependence on agriculture, specifically small-holder farming.

The management of water resources in the state is carried out under the management of the Secretariat for the Environment and Water Resources (SEMARH). A representative of the Secretariat chairs the State Council of Water Resources, a body of collective deliberation and of normative character. The council's responsibilities include arbitrating conflicts between users, defining criteria for charging for water use, and other matters related to the management of water resources. The council comprises representatives of public bodies, of users, and of civil society; and river basin committees.

Given the economic recession, there is a shortage of financial resources for actions to combat the effects of the drought. Therefore, it is imperative to know how to better allocate what resources there are for the municipalities that are in the most critical situation. Thus, a multicriteria model is proposed to address the problem.

## Group multicriteria model for allocating resources to combat drought in the Brazilian semi-arid region

The proposed model, presented in Figure 1, can be used to support group decision-making on allocating resources to combat the drought.

Fig. 1.

Flowchart of group multicriteria model for allocating resources to combat the drought in the Brazilian semi-arid region.

Fig. 1.

Flowchart of group multicriteria model for allocating resources to combat the drought in the Brazilian semi-arid region.

In the preparation stage, it is important to identify the DMs involved in the problem. In order to minimize the occurrence of conflicts and to consider the different points of view, a representative of each of the various stakeholders should be involved, and not just water resource specialists. Meetings should be held to define the problem and the objectives to be achieved, so that all participants are aware of what is being analyzed. De Carvalho et al. (2017) emphasize that stakeholders when undertaking decision analysis may reveal biases that are myopic, omissive, divisive, and insensitive, specifically in decisions in the water sector. To deal with the problem, they propose using the Delphi technique to obtain reliable information before taking a decision, and thereby identify the non-neutrality of decision analysis and (re)think the stakeholder's participation. In this context, the figure of the supra-decision-maker is very important as the agent in a hierarchical or political position above the other DMs. This agent can act to emphasize the importance of the process, thus ensuring everyone's commitment during the preparation process. At this stage, problem structuring methods can be applied, as presented by Ackermann (2012). Another important process at this stage involves selecting the method to support decision-making. Roy & Slowinski (2013) propose questions to help an analyst choose a method that aids in solving the problem. These include: (1) what type of outcome is expected by applying the model, and whether this should be a numeric value (score or utility), about ranking alternatives, allocating alternatives into classes, etc.; (2) what are the requirements for preference scales, acquiring preference information, handling imperfect knowledge, accepting compensation among criteria, and whether criteria interact with each other; (3) secondary questions, which deal with intelligibility, characterizing axioms, and identifying weaknesses in the methods considered.

The individual evaluation stage begins with identifying a stable set of alternatives that will be considered in the analysis. Alternatives should be grouped according to their geographical location, the presence of a river basin, or other criteria. Next, the criteria to be considered for ranking should be defined. DMs may choose to use criteria common to all, or they may use different criteria structures, depending on their point of view about the problem. Using different criteria does not affect the result of the application since the input considered in the group decision-making stage is the ranking of alternatives and their scores. Each DM then determines weights and other necessary parameters, and as a result draws up their evaluation matrix. The individual evaluation is performed and therefore obtains the rank of the alternatives for each DM, as well as their relative scores. Sensitivity analysis should be performed varying the parameters to verify their impact on the rank obtained.

Once the individual rankings of each DM are obtained, the group decision-making stage begins. Each decision-maker's weights must be defined according to their power of decision-making. Defining these weights at this stage can be achieved by consensus or by a supra-decision-maker. Based on the DM's weights and on the individual rankings, the matrix of the global evaluation of the alternatives should be drawn up. Once the overall assessment of the alternatives has been made, a sensitivity analysis should be performed to evaluate the results obtained, and conflicts surrounding the solution should be discussed. In the discussion stage, the analyst should identify the potential conflict points between the group ranking and the individual rankings and present the key factors that led to this outcome. DMs can also present their opinions about the results obtained. The multicriteria model, in this context, has the role of augmenting the discussion among the DMs by analyzing their preferences objectively.

As to the questions proposed by Roy & Slowinski (2013) and the character of group decision-making, the PROMETHEE GDSS method, proposed by Macharis et al. (1998), was selected to operationalize the methodology of the model. Initially, given the type of result expected, the method ranks the alternatives. As the analysis is generally carried out within a closed set of alternatives (municipalities of the river basin or geographic region), it is not necessary to obtain an index to identify municipalities, but only to order them. The method also succeeds in processing both numeric and verbal preference scales, thereby facilitating the elicitation process. Another important factor is the non-compensatory character of the methodology. Thus, all the information available in the evaluation matrix is considered in the application, and there is no direct compensation between the performances in the different criteria. In addition, the use of preference functions facilitates how the DMs' preferences are judged, since the DMs' hesitation can be seen by using preference and indifference thresholds. Furthermore, the PROMETHEE GDSS uses similar methodological structures both in evaluating individual performances and those made by group decision. This facilitates understanding the evaluation and its acceptance. In addition, if it is in the group's interest and if there are many biases among the stakeholders, the method allows each DM to use his/her own preference structure independently. Therefore, it is not necessary to reach consensus on the criteria, weights, and other parameters in the individual stage. The method presents a significant problem by using pairwise comparisons between alternatives, which can generate rank reversal. This factor is minimized when considering the application for closed sets of alternatives, with no inclusion or exclusion of municipalities in the areas under analysis.

Regarding the individual evaluation stage, Macharis et al. (1998) propose using the PROMETHEE II methodology for each DM involved. The method, according to Brans et al. (1998), given that there are weights to represent the degree of importance for each criterion, computes the outranking degree in accordance with Equation (1):
(1)
where is a number between 0 and 1 that increases when increases and is equal to zero, if . To find the value of the function , the DM can choose, for each criterion, one of the six functions according to the values of preference (p) and indifference (q) thresholds, as shown in Figure 2.
Fig. 2.

Preference functions for the PROMETHEE methodology, adapted from Brans et al. (1986).

Fig. 2.

Preference functions for the PROMETHEE methodology, adapted from Brans et al. (1986).

According to Figure 2, the DM must choose from the following six functions: (1) a usual function, when there is no parameter to be defined; (2) a U-shape function, for which the parameter q is defined; (3) a V-shape function by setting the parameter p; (4) a level function, considering the parameters q and p; (5) a linear function, which also considers the parameters q and p; and (6) the Gaussian criterion, in which the standard deviation must be fixed.

Once the values of are obtained, two complete preorders can be obtained; the first preorder is represented by an order of actions following the descending order of the numbers , as shown in Equation (2):
(2)
The second preorder follows the increasing order of the numbers , as shown in Equation (3):
(3)
The intersection of these two flows generates the partial preorder result of applying the PROMETHEE I method. The PROMETHEE II method consists of ordering the actions following the flow as defined in Equation (4). Thus, a single complete preorder is obtained.
(4)

Next, the opinions of the group of DMs should be evaluated, as proposed by Macharis et al. (1998). The evaluation matrix is set up using the net flows generated from the application of the PROMETHEE II for each DM. Thus, each DM can be assigned a weight by setting the decision-making power of each DM. The PROMETHEE II methodology is applied to generate the rank of the alternatives based on the positions that each DM expresses. According to Macharis et al. (1998), there is no general rule that can be used to address the conflicts and therefore they recommend tackling the conflicts by returning to previous steps.

The model was evaluated by applying it in order to prioritize the municipalities of Rio Grande do Norte, and took the water resource managers' points of view into account.

## Numerical application

For the numerical application of the model, three DMs (D1, D2, and D3) acting at SEMARH were considered. The objective of applying it was to test its implementation prior to doing so at the State Council of Water Resources. The sector where DMs act is responsible for planning and executing public policies related to water management, including directing actions to combat the drought. Initially, contact was made with the person in charge of the sector, who was characterized as being the supra-decision-maker. He highlighted the impact that the financial crisis is having on the State of Rio Grande do Norte. This prevents the needs of all municipalities that require support from being met. He also emphasized that the current decision-making process lacks a firm structure and does not use any support tool. He indicated the three agents who should participate in the preliminary decision-making process. Decision-maker D1 is responsible for the Water Resources Planning and Management sector; D2 works in the infrastructure sector and is responsible for conducting studies, and managing projects and construction works; D3 is a member of the environment and sanitation sector.

As to the proposed model, there was discussion about the criteria that should be considered. The DMs decided to use the same criteria to analyze the problem, with the justification that this facilitates discussing the results when the application is concluded. Table 1 lists the criteria that the DMs consider are important.

Table 1.

Criteria considered in the prioritization process.

C1 Population served (no. of inhabitants) Number of inhabitants living in the municipality Max Quantitative
C2 No. of hospitals and basic health units Number of hospitals and basic health units (BHU) located in the municipality Max Quantitative
C3 No. of educational institutions Number of educational units located in the municipality Max Quantitative
C4 Human development index (HDI) Human development index attributed to the municipality Min Quantitative
C5 Income per capita (in R$) Monthly per capita income Min Quantitative C6 Gross domestic product of the agricultural sector (in thousands of R$) GDP added from the municipality's agricultural sector Max Quantitative
C7 Gross domestic product of the industrial sector (in thousands of R$) GDP added from the municipality's industrial sector Max Quantitative C8 Current status of local reservoirs (%) Consider the current availability of water in the reservoirs that serve the municipality Min Quantitative CodeCriteriaDescriptionMax/MinScale C1 Population served (no. of inhabitants) Number of inhabitants living in the municipality Max Quantitative C2 No. of hospitals and basic health units Number of hospitals and basic health units (BHU) located in the municipality Max Quantitative C3 No. of educational institutions Number of educational units located in the municipality Max Quantitative C4 Human development index (HDI) Human development index attributed to the municipality Min Quantitative C5 Income per capita (in R$) Monthly per capita income Min Quantitative
C6 Gross domestic product of the agricultural sector (in thousands of R$) GDP added from the municipality's agricultural sector Max Quantitative C7 Gross domestic product of the industrial sector (in thousands of R$) GDP added from the municipality's industrial sector Max Quantitative
C8 Current status of local reservoirs (%) Consider the current availability of water in the reservoirs that serve the municipality Min Quantitative

As shown in Table 1, criteria C1, C2, and C3 were used to measure the direct impact of the lack of water on the local population. C1 refers to the total population of each municipality, and represents the total number of people who would be affected in the event of the lack of water. C2 is used to measure the number of public or private health facilities that are critically affected when problems occur in the water supply. C3 is used to consider the number of educational units, where supply problems can disrupt teaching in schools and colleges. In this context, for the three criteria, the higher their value, the more critical the lack of water is for the sustainability of the municipalities. Criteria C4 and C5 seek to represent the local population's socioeconomic characteristics. It was decided to use HDI (C4) so as to represent the degree of human development of the locality, the focus being on economic development and quality of life. Thus, the lower the HDI, and the less developed the municipality, the greater the attention that should be paid to the inhabitant's basic needs. Similarly, per capita income (C5) was defined as an indicator of the population's income, which may impact the possibility of investing in other sources of water supply. Criteria C6 and C7 were defined to identify the profile of the local economy. To this end, the DMs decided to use the GDP of the agricultural (C6) and industrial (C7) sectors, and thereby to represent the gross added values these GDPs add to the local economy. It is observed that the profile of the agricultural sector of the region consists predominantly of small-holdings, with small- to medium-sized fields and plantations, often oriented towards providing subsistence to the family working the land. The industrial sector is evaluated as underdeveloped in the region and is concentrated in the largest towns. Therefore, the impacts generated by problems in the water supply cause different impacts, depending on the prevailing economic profile in the municipalities and, thus, it is important to evaluate these aspects separately. While in the industrial sector there can be large-scale unemployment and companies going out of business, in the agricultural sector, the lack of water can jeopardize subsistence farming and lead to an exodus from rural areas. Finally, in criterion C8, the current status of the water reservoirs that supply each municipality was considered. It should be noted that, for this criterion, the reservoir was considered the main source of water supply for each municipality. However, in a municipality, there may be villages that use different reservoirs for their water supply.

Based on the criteria considered, each DM sets up their own evaluation matrix, while considering the weights of the most adequate criteria, evaluating the alternatives, and defining the other parameters. For the numerical application, the hydrographic basin of the Apodi and Mossoró rivers was selected. It consists of 51 municipalities. To simplify the evaluation of this study, the municipalities that form the following areas were analyzed.

• Lower section, comprising the municipalities of Areia Branca (A1), Baraúna (A2), Grossos (A3), Mossoró (A4), Serra do Mel (A5), and Tibau (A6).

• Medium inferior section, comprising the municipalities of Governador Dix Sept Rosado (A7), Apodi (A8), Felipe Guerra (A9), Caraúbas (A10), Upanema (A11), Campo Grande (A12), and Janduís (A13).

The reference values for criteria C1, C2, C3, C4, C6, and C7 were obtained from data provided by the Brazilian Institute of Geography and Statistics (IBGE) on their website. The values for criterion C5 were obtained from data from the United Nations Development Program (UNDP) in 2010. The data for criterion C8 were obtained from the Water and Sewage Company of Rio Grande do Norte (CAERN). For this criterion, a score of 100% was attributed to municipalities that have the option of sourcing their water supply from large artesian wells. Municipality (A4) stands out because it has a mixed water supply (wells and pipeline). Table 2 presents the parameters considered by the DMs and the evaluation matrix for the situation considered.

Table 2.

Parameters and evaluation matrix of the alternatives.

D1Criteria
C1C2C3C4C5C6C7C8
Weights 0.2222 0.0556 0.0556 0.0278 0.0556 0.0833 0.0556 0.4444
Preference function U-shape Usual U-shape U-shape U-shape U-shape U-shape Usual
5,000 – 0.01 20 5,000 5,000 –
D2C1C2C3C4C5C6C7C8
Weights 0.1739 0.0435 0.0435 0.0870 0.0435 0.1304 0.2174 0.2609
Preference function U-shape Usual U-shape U-shape U-shape U-shape U-shape Usual
3,000 – 0.02 30 4,000 4,000 –
D3C1C2C3C4C5C6C7C8
Weights 0.2909 0.0727 0.0364 0.0545 0.0545 0.0727 0.0545 0.3636
Preference function U-shape Usual U-shape U-shape U-shape U-shape U-shape Usual
6,000 – 0.01 20 6,000 5,000 –
MunicipalitiesC1C2C3C4C5C6C7C8
A. Branca (A1) 25,315 10 49 0.682 449.02 10,307 500,072 100
Baraúna (A2) 24,182 67 0.574 263.68 85,003 191,568 100
Grossos (A3) 9,393 18 0.664 410.84 2,618 60,512 100
Mossoró (A4) 259,815 115 340 0.72 600.28 141,413 1,998,062 19.81
S. do Mel (A5) 10,287 22 47 0.614 284.48 11,100 27,935 100
Tibau (A6) 3,687 13 0.635 396.51 2,137 12,917 100
Dix Sept (A7) 12,374 28 0.592 267.12 4,337 144,123 100
Apodi (A8) 34,763 12 86 0.639 358.66 28,216 207,992 100
F Guerra (A9) 5,734 19 0.636 298.60 2.431 62,967 100
Caraubas (A10) 19,576 11 53 0.638 321.99 11,537 103,224 100
Upanema (A11) 12,992 22 0.596 233.97 6,384 54,826 100
C Grande (A12) 9,289 27 0.621 – 5,368 16,892 19.81
Janduis (A13) 5,345 10 0.615 272.39 2,510 2,921 19.81
D1Criteria
C1C2C3C4C5C6C7C8
Weights 0.2222 0.0556 0.0556 0.0278 0.0556 0.0833 0.0556 0.4444
Preference function U-shape Usual U-shape U-shape U-shape U-shape U-shape Usual
5,000 – 0.01 20 5,000 5,000 –
D2C1C2C3C4C5C6C7C8
Weights 0.1739 0.0435 0.0435 0.0870 0.0435 0.1304 0.2174 0.2609
Preference function U-shape Usual U-shape U-shape U-shape U-shape U-shape Usual
3,000 – 0.02 30 4,000 4,000 –
D3C1C2C3C4C5C6C7C8
Weights 0.2909 0.0727 0.0364 0.0545 0.0545 0.0727 0.0545 0.3636
Preference function U-shape Usual U-shape U-shape U-shape U-shape U-shape Usual
6,000 – 0.01 20 6,000 5,000 –
MunicipalitiesC1C2C3C4C5C6C7C8
A. Branca (A1) 25,315 10 49 0.682 449.02 10,307 500,072 100
Baraúna (A2) 24,182 67 0.574 263.68 85,003 191,568 100
Grossos (A3) 9,393 18 0.664 410.84 2,618 60,512 100
Mossoró (A4) 259,815 115 340 0.72 600.28 141,413 1,998,062 19.81
S. do Mel (A5) 10,287 22 47 0.614 284.48 11,100 27,935 100
Tibau (A6) 3,687 13 0.635 396.51 2,137 12,917 100
Dix Sept (A7) 12,374 28 0.592 267.12 4,337 144,123 100
Apodi (A8) 34,763 12 86 0.639 358.66 28,216 207,992 100
F Guerra (A9) 5,734 19 0.636 298.60 2.431 62,967 100
Caraubas (A10) 19,576 11 53 0.638 321.99 11,537 103,224 100
Upanema (A11) 12,992 22 0.596 233.97 6,384 54,826 100
C Grande (A12) 9,289 27 0.621 – 5,368 16,892 19.81
Janduis (A13) 5,345 10 0.615 272.39 2,510 2,921 19.81

The performance of the C5 criterion for alternative A12 was not obtained because the municipality was created recently. Therefore, the average per capita income of all municipalities was adopted for it. Regarding the weights of the criteria, the DMs were informed about the significance of the criteria, there being a criterion with a weight 2× that is twice as important as a criterion with weight x. From this information, each DM freely assigned the values of the weights for each criterion and could modify them as often as necessary. Regarding the parameters, there was a consensus on using the same preference functions (usual and U-shape). For the criteria to which the usual function was assigned, the DMs agreed that any difference in the performance of the alternatives implies preference. The U-shape function was chosen because the DMs considered it necessary to consider an indifference threshold for criteria with a large range of values.

Next, the PROMETHEE II method was applied in order to rank the alternatives for each DM using Visual PROMETHEE software. The rankings and scores obtained by the individual and group stages are presented in Figure 3.

Fig. 3.

Rankings obtained from the individual and group decisions.

Fig. 3.

Rankings obtained from the individual and group decisions.

Sensitivity analysis was performed on the results obtained based on the variation in the weights assigned to each criterion for each DM. For this analysis, we used the walking weights procedure whereby the weights were increased and decreased by 20%. As illustrated in Pinto et al. (2017), Figure 4 presents the minimum and maximum placements for each alternative, obtained from the sensitivity analysis.

Fig. 4.

Minimum and maximum placements of each alternative during sensitivity analysis.

Fig. 4.

Minimum and maximum placements of each alternative during sensitivity analysis.

As seen in Figure 4, from the sensitivity analysis, the alternatives are placed in different positions in the DMs' rankings. For D1, it is observed that the greatest variation occurs for alternative A2, which varies between fifth and second place. Therefore, the DM should re-evaluate the weights assigned to each criterion, thereby ensuring that the weights used adequately reflect his/her vision. For the decision-maker D2, the variation is smaller, alternatives A11 and A12 being those with the greatest range of positions in the ranking. For decision-maker D3, alternatives A10, A12, and A13 have a maximum variation of two positions. It is concluded from the analysis that the results obtained, for the most part, are relatively stable, with variations that have little impact on the result.

One of the concerns of methods that use pairwise comparisons is rank reversal when this leads to the inclusion or exclusion of alternatives. However, in this specific case, this issue is not relevant since all possible alternatives (municipalities) of the hydrographic basin areas of the Apodi and Mossoró rivers were considered.

With the ranking and the scores of each alternative, the DMs' opinions were aggregated to obtain the position of the group, as shown in Figure 3. In this case, all DMs had the same decision-making power. Sensitivity analysis was performed based on variations in the DMs' weights. This operation did not yield any significant changes in the ranking. Thus, only tiebreakers were performed between the alternatives that had the same position in the initial ranking.

## Discussion of the results

From the analysis of the results obtained, as expressed in Figure 3, some results stand out. First in the ranking was the municipality of Mossoró (A4). This is because it is the largest municipality in the delimited region and it relies on the water supply from mains lines that collect water from the reservoirs. The large numbers of the population affected and the economic factors involved also influenced its positioning, which was shared by all DMs. It should be noted that part of the municipality's water supply is sourced from wells, which is not a long-term solution for compensating for the lack of water. The municipality of Apodi (A8) is in second place in the ranking, specifically due to economic and social factors. Baraunas (A2) and Caraubas (A10) are in third and fourth places, respectively. The municipality of Areia Branca (A1) is in fifth place in the group's final ranking and is tied with the municipality of Campo Grande (A12). Areia Branca is very important for the industrial sector because it accounts for an important part of the national production of salt. The municipality of Janduís (A13) appears to be in an advantageous position in the ranking, mainly because its water supply is primarily sourced from dams and because no wells are used to supply its water.

When comparing the group ranking to the results of each DM, a certain degree of consistency is observed in the first positions of the ranking. For all DMs, A4, A8, and A2 are in the first three positions, with A4 being in the first position for all three DMs. The A10 alternative, in fourth place for the group ranking, is also positioned at the top of the ranking for the three DMs. There is a potential point of conflict with regard to evaluating alternative A13, which is positioned in the seventh position of the group ranking while varying from the fifth to the tenth position in the individual evaluations. In this case, the municipality has a low HDI, a low per capita income, and low water levels in the reservoirs. Therefore, the variation in the weights attributed to these criteria by the DMs leads to this variation in the position of the ranking. To solve the conflict, the analysis can be traced back to previous phases to refine the evaluations and to deal with the discrepancies found, as well as to discuss the factors that led the DMs to reach the final ranking. In general, the global ranking obtained mirrors the DMs' individual evaluations quite closely.

In this context of droughts, the State of Rio Grande do Norte has been carrying out emergency actions, which have included drilling deep wells and installing desalinators, to convert impure water from these wells to drinking water. Another action that is being taken involves installing emergency water mains, which carry water from reservoirs that still have stored water. There is also an alternative water supply program. In this program, water tank trucks are used to carry water from storage points to certain locations, especially small towns. Measures are also taken to prepare for the rainy season, such as the desorption and cleaning of rivers and canals to guarantee the flow of water when the rainy season returns.

In addition, some interventions and policies can be undertaken in order to improve the results of water resources management. Initially, it is suggested investment be made to inspect the use of water in the region. Conflicts over water use are quite common, including occurrences of water theft. It is also necessary to better plan and manage the current dam structure in the region. When rains occur, the main reservoirs of the State receive water only when the various smaller dams overflow. This delays replenishment of the most important reservoirs for supply, while smaller reservoirs supplying small communities, often without adequate control, are supplied quickly. Thus, investments in the distribution network should be made to ensure the distribution of piped water to the most remote communities, since this will discourage using illegal and low-quality water sources. The State can also invest in alternative water sources, such as by increasing investment in harvesting rainwater and in desalination plants, thus taking advantage of access to the sea. Such measures can minimize the negative effect of drought periods by enabling an emergency supply in the short and medium term. Another important source of water involves the drilling of wells to use water from the State's underground aquifers. Finally, there is a need for constant investment in the process of raising awareness of the local population as to the conscious use of water.

Regarding the application in the hydrographic basin of the Apodi and Mossoró rivers, the importance of the city of Mossoró for the region is highlighted. It is also worth mentioning that it is quite common for residents of neighboring municipalities to go to Mossoró to seek medical attention and attend educational institutions, mainly universities. However, the municipality has its supply complemented by water from deep wells, which provides a certain guarantee of supply to the city. It should be noted, however, that drilling wells is not feasible for most municipalities since not all areas have adequate access to aquifers. Thus, for other cities, such as Janduís and Campo Grande, the situation is more complicated since the water from wells is not available to the water company, which therefore uses a rotational water supply system when the city is supplied for only part of the month. Hence, it is important that managers also pay attention to smaller municipalities and areas farthest from the cities. The use of water tank trucks, in this context, should prioritize the supply of those areas in which the population density is lowest, thereby guaranteeing subsistence conditions for these populations.

## Conclusions

Considering the projections of climate change for the region, there is a tendency for the duration of drought periods to increase because of a reduction in rainfall. Thus, a more efficient allocation of resources is necessary in order to maximize socioeconomic gains. The use of the proposed model can support decision-making regarding how best to use resources to combat the effects of drought, as well as how to facilitate discussion and to seek consensus among the various stakeholders. In this context, a group multicriteria model was proposed to rank the municipalities of the region so as to direct the efforts of the public administration in the fight against drought and to mitigate its effects. The model considers the points of view of the various stakeholders involved and was applied to the Apodi-Mossoró river basin to verify its functionality. In this instance, the PROMETHEE GDSS method was selected and the preferences of three decision-makers were evaluated.

In future research, the proposed model can be used by members of the State Council of Water Resources directly involved in the problem. Based on analyzing the data, it will be possible to empirically support the decision-making process of the managers in the sector. It is also suggested that experts in the directly affected areas, including specialists in water resources, public health, and society, evaluate the proposed model. Therefore, it is intended to create a forum for discussions to define the entire structure of criteria to be considered for resource allocation, and for the region's water managers to take an active part in this. The use of the PROMETHEE GDSS fuzzy method will also be recommended to make it easier for the decision-makers to define the parameters. There is also a possibility of using voting procedures in case there is a larger number of decision-makers involved.

## Acknowledgments

This work is part of a research project supported by the National Research Council (CNPq, grant: 309143/2014-4). The authors would like to express their sincere appreciation to the anonymous referees who provided constructive comments which enhanced the quality of this paper.

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