MODEL FOR SORTING MUNICIPALITIES BASED ON THE CRITICALITY OF ASSISTANCE FOR COMBATING DROUGHT

ABSTRACT

Vulnerable regions to drought require resource allocation to develop projects to combat low rainfall negative impacts. In this perspective, this study proposes a multicriteria sorting model to categorize municipalities affected by drought in order to allocate resources according to criticality. The proposed model is based on the FlowSort method for sorting municipalities into highly critical, moderately critical, and slightly critical levels to cope with drought. The model was applied in the Apodi-Mossoró river basin in Rio Grande do Norte, Brazil, for sorting 14 municipalities. The findings revealed that the public administration could effectively focus its resources on municipalities experiencing more severe drought conditions. Thus, the public administration can develop strategies, public policies, and actions in coping with extreme difficulty.

Keywords:
drought; multicriteria decision aiding; sorting

1 INTRODUCTION

Drought is a natural disaster caused by the partial or total absence of rainfall for a long time (Neves et al., 2015). Depending on its intensity, duration, and spatial scope, the impacts of drought can affect various activities and aspects of society, such as water supply and energy and food security in the affected region (Marengo et al., 2018; Zeri et al., 2021). Thus, drought is a complex phenomenon that significantly impacts the affected region’s economy and environment (Wilhite & Pulwarty, 2017).

Unlike other natural hazards, drought is characterized by slow onset and evolution, where its effects accumulate over time, and its impacts tend to be amplified in places of multiple vulnerabilities (Zarafshani et al., 2016). Long periods of drought and unfavourable social and environmental aspects contribute to worsening socioeconomic conditions in the affected regions (Sena et al., 2018). Therefore, these places that face droughts need concrete projects to allocate resources to minimize the impacts of this natural disaster.

Several techniques for allocating resources in drought-stricken areas have been proposed in the literature. For example, Rao et al. (2010) proposed an optimization tool based on genetic algorithms to optimize water allocation in London, UK. Tsai et al. (2019) developed an intelligent water allocation system (IWAS) using dynamic systems and a non-dominated genetic ordering algorithm (NSGA-II). Reis et al. (2020) sought to quantify and classify cities at risk of drought using multicriteria decision support techniques. In addition, other approaches have also been developed (Saha et al., 2022; De Araújo et al., 2022; Hoque et al., 2021).

For better drought management, understanding its natural and socioeconomic dimensions is essential. The correct structuring and conduction of decision-making processes related to this context allow for proactive responses to be formalized and better risk management to be developed (Wilhite & Pulwarty, 2017). Furthermore, multicriteria decision support techniques are an interesting ally to this evaluation type, given that they can solve problems or decision situations more rationally and efficiently (Morais et al., 2014).

The multicriteria decision support approach seeks to solve decision-making problems with multiple often conflicting objectives, considering the critical analysis of one or more decision-makers in the decision process (De Almeida, 2013; Roy, 1996). This methodology is used to structure decision problems and, consequently, indicate satisfactory solutions to the problem based on evaluating the alternatives available by the decision maker(s) (Leoneti & Gomes, 2022).

Multicriteria decision techniques can assist decision-makers in obtaining important and efficient decisions that cannot be determined directly through the best possible tradeoffs or compromises between these objectives (Lin, Lee, and Wu, 2010; Abdullah et al., 2021). Over the years, this type of modelling for decision problems has been applied in the most diverse contexts. For example, environmental impact assessment (Do Carmo et al., 2021), sports assessments (Principe et al., 2017; Salles et al., 2022), public safety (Gurgel & Mota, 2013; Gavião et al., 2021), supplier selection (Gonçalves et al., 2021; Gonçalo & Alencar, 2014), flood risk assessment (Silva et al., 2022), critical technologies assessment (Morais et al., 2015) and many other applications. Thus, multicriteria methods can be applied in the most varied decision-making contexts, including problems involving the allocation of water resources.

Furthermore, Cordão et al. (2020) developed a risk map capable of evaluating and classifying urban regions most prone to water scarcity through a methodology that combines elements of Multicriteria Decision Analysis (MCDA) and Geographic Information Systems (GIS). However, an approach capable of classifying the cities with the greatest need for resources to face the drought was not identified, except for a preliminary analysis reported in a conference communication (Castro et al., 2022), which consisted of a pilot application. Overcoming this methodological challenge is one of the goals of this study.

Gonçalo & Morais (2018) presented a collective decision multicriteria model capable of ranking municipalities devastated by drought and thus guiding efforts in allocating resources to mitigate the effects of drought in northeastern Brazil. Despite the interesting contributions arising from the research, the authors directed the study toward the ranking problem. However, for management purposes, a better strategy could be to categorize the municipalities into classes of the criticality of assistance, sorting them. Alvarez et al. (2021) recommend using the latter to categorize the alternatives of a decision problem in just one class, especially for complex problems, such as the allocation of resources to face drought.

Although there are methodologies capable of generating feasible information about the drought for public administration, the literature encourages the development of new proposals (Neves et al., 2015). Above all, the inclusion of new approaches in the literature that use multicriteria techniques in drought disasters is necessary (Abdullah et al., 2021) since they may be able to indicate appropriate responses and the most effective actions for public administration to mitigate the effects of drought (Neves et al., 2015).

Therefore, this research aims to propose a multicriteria model capable of classifying municipalities affected by drought to prioritize them in the resource allocation process and minimize the impacts of this natural disaster. This way, strategies, public policies, and actions can be developed to face the drought, making it possible to allocate resources to cities according to their actual needs.

2 PROPOSED MULTICRITERIA SORTING MODEL

To aid the public administration in allocating resources to drought-affected cities, a multicriteria model was proposed to facilitate the decision-making procedure. This approach employs the decision model-building framework given by De Almeida (2013).

The multicriteria model that will support public organizations in coping with the drought has four (4) significant steps: (i) decision-maker identification, (ii) definition of municipalities that will be evaluated, (iii) preference elicitation, and (iv) Sorting of drought-affected cities by FlowSort Method. Figure 1 presents the steps of this model.

Figure 1
General steps to implement the proposed model.

Identifying the decision-maker who will be contacted to establish the sorting strategy is the first step of the model. The decision-maker is an important actor in a decision-making process (De Almeida, 2013), and their correct identification is critical for a decision-making process to be conducted correctly (Huang et al., 2011).

In the second stage of the model, the decision-maker must choose the alternatives the algorithm will evaluate. The alternatives will be cities (municipalities) affected by drought. It is advisable to choose municipalities that have historically and presently experienced drought. The municipalities will be the alternatives to the decision problem and will be evaluated by criteria from studies that address the same topic (Gonçalo & Morais, 2018; Tsai et al., 2019; Kumar et al., 2016; Ribeiro et al., 2021). The criteria are presented in Table 1.

Table 1
Criteria Evaluation.

Code	Criteria	Description	Type	Literature
Cr1	Reservoir Index	Indicates the current level, as a percentage, of water reservoirs belonging to the municipality.	Minimization	Gonçalo & Morais (2018)
Cr2	Sanitary Sewage Coverage Index	Determines the percentage of sanitary sewage coverage in the municipality.	Minimization	Ribeiro et al. (2021)
Cr3	Water Coverage Index	Determines the percentage of water coverage in the municipality	Minimization	Kumar et al. (2016)
Cr4	Population	Determines the number of inhabitants residing in the municipality.	Maximization	Tsai et al. (2019)
Cr5	Human Development Index (HDI)	Determines the economic development level and the Municipality’s quality of life in normalized values.	Minimization	Gonçalo & Morais (2018)

Preference elicitation is the third step of the model. The decision-maker will express his preferences for two (2) specific activities: (i) define the importance degree of the criteria through the ROC procedure and (ii) define the limiting profiles between categories. The Rank-Order Centroid (ROC) method established by Edwards & Barron (1992) will be utilized for the first activity. This approach sets a numerical number to each criterion’s weight by ordering the importance of the factors from most to least important based on the decision-maker preference. This technique is a surrogate weight procedure used as a substitute or approximation of the real weight the decisionmaker assigns each criterion. Morais et al. (2015) argue that this procedure can be helpful in multicriteria research that aims to reduce the effort that the decision-maker needs to make to define the importance degree of the criteria. Equation (1) below shows how to calculate the value of the criteria weights.

$w_i\left(ROC\right)=\frac{1}{n}\sum _{j=1}^n\frac{1}{j}j=1,2,\dots ,n.$ (1)

The second activity is the definition of limiting profiles between categories. The limiting profiles delimit the class scope in that each category has a lower limiting profile and an upper limiting profile, which is also the lower limiting profile of the class immediately subsequent (Alvarez et al., 2021). For this, it is necessary to define categories/classes that will be considered in the approach. These categories are based on literature, and much research has frequently considered three groups for sorting alternatives (Emamat et al., 2022). The class will be denoted by C ₁ ,C ₂ , . . . ,C _n and ordered by preference (C ₁ > C ₂ > · · · > C _n ), that is, the alternative classified in category C ₁ will be more preferred than the alternative classified in category C ₂, and so on, successively (Nemery & Lamboray, 2008). Therefore, three (3) categories were established for the decision problem: C ₁ Highly critical, C ₂ Moderately critical, and C ₃ Slightly Critical. The categories description can be seen in Table 2.

Table 2
Description of the categories/classes.

Category/Class	Description
C1 - Highly critical	These municipalities present highly critical drought conditions and urgently need resources to combat drought.
C2 - Moderately critical	These municipalities present moderately critical drought conditions and have intermediate resource needs to combat drought.
C3 - Slightly Critical	These municipalities present slightly critical drought conditions and have resource needs to combat drought.

As defined in Table 2, the first group presents the most critical alternatives, while the last group contains the best alternatives. That is, the alternatives classified in the first category have the worst performances in the established criteria, indicating that they are the cities most affected by drought and, consequently, are the municipalities highly critical to allocate resources. On the other hand, the alternatives in the last category have the best performances in the established criteria, indicating that they are the cities least affected by drought and, therefore, are considered slightly critical to allocate resources. Finally, the intermediate group comprises municipalities with moderate criticality to face drought, but their situation may worsen if not assisted in the medium term.

In the final step, the multicriteria sorting method developed by Nemery & Lamboray (2008), FlowSort, will be applied to sorting drought-affected cities. We chose the FlowSort method based on the decision-makers preference structure, the potential for performance compensation between criteria, and the expected outcome of the model, following the recommendation of Roy & Słowiński (2013).

Firstly, the preference structure of the decision-maker considers incomparability. There are cases where the decision-maker is unable to compare municipalities, and in cases where comparison is possible, there is a slight preference for a specific alternative. Conversely, the decision-maker considers the consequences of each city in each criterion separately, without compensating between different attributes. Additionally, the decision problem requires a technique capable of ordering the categories according to drought criticality levels while classifying the alternatives separately. In other words, we need to evaluate each alternative individually, considering only the defined limiting profile for each category. Therefore, we will use the FlowSort method to evaluate the cities/municipalities (alternatives), considering the decision-maker’s preferences. This approach will enable the public administration to allocate resources for drought mitigation more effectively by utilizing the results obtained from the evaluation.

According to Nemery & Lamboray (2008), FlowSort is a multicriteria sorting methodology based on the PROMETHEE (Preference Ranking Organization Method for Enrichment Evaluation) methodology, which seeks to classify alternatives into completely ordered categories/classes through independent assignments. For this, each category is numerically delimited by two (2) limiting profiles between categories defined by the decision-maker: (i) lower limiting profile and (ii) upper limiting profile. These limiting profiles will be denoted r _n and r _(n+1) , where n is the number of categories defined for the problem. Thus, a category C _n is delimited by a lower limiting profile (r _n ) and an upper limiting profile r _(n+1) . In this way, the method manages to classify the alternatives independently, considering the outranking relationship of each alternative with the limiting profiles separately (Nemery & Lamboray, 2008).

Subsequently, the preference index π _(a,r ) must be identified between alternative a and each limiting profile r _i in each criterion g _j weighted by weight w _j , as observed in Equation 2. After this definition, three large (3) indices can be calculated for each alternative and the limiting profiles: positive flow (φ ⁺ ), negative flow (φ ^- ) and net flow (φ), as observed in equations 3, 4 and 5, respectively.

$\pi \left(a,r_i\right)=\sum _{j=1}^n{P}_j\left(a,r_n\right)w_j$ (2)

${\varphi }_{R_i^{*}}^{+}\left(a\right)=\frac{1}{\left|R_i^{*}\right|-1}\sum _{n\in R_i^{*}}\pi \left(a,r\right)$ (3)

${\varphi }_{R_i^{*}}^{-}\left(a\right)=\frac{1}{\left|R_i^{*}\right|-1}\sum _{r\in R_i^{*}}\pi \left(r,a\right)$ (4)

${\varphi }_{R_i^{*}}\left(a\right)={\varphi }_{R_i^{*}}^{+}\left(a\right)-{\varphi }_{R_i^{*}}^{-}\left(a\right)$ (5)

After defining the positive, negative, and net flows for each alternative, as well as for the limiting profiles, the action will be assigned to its respective category through the decision rules set forth by equations 6, 7, and 8, as follows:

$C_{{\varphi }^{+}}\left(a\right)=C_{n}if{\varphi }_{R_i}^{+}\left(r_n\right)\ge {\varphi }_{R_i}^{+}\left(a\right)>{\varphi }_{R_i}^{+}\left(r_{n+1}\right)$ (6)

$C_{{\varphi }^{-}}\left(a\right)=C_{n}if{\varphi }_{R_i}^{-}\left(r_n\right)\ge {\varphi }_{R_i}^{-}\left(a\right)>{\varphi }_{R_i}^{-}\left(r_{n+1}\right)$ (7)

$C_{\varphi }\left(a\right)=C_{n}if{\varphi }_{R_i}\left(r_n\right)\ge {\varphi }_{R_i}\left(a\right)>{\varphi }_{R_i}\left(r_{n+1}\right)$ (8)

The model evaluates whether alternative a performs below or above the limiting profiles for positive and negative flows. For this, the rule expressed by the net flow is used to strictly assign the alternative to a category and maintain consistency in its assignment. Thus, the sorting for each city/municipality (alternative) can be obtained, guiding the decision-maker in this decisionmaking process.

Finally, this stage will be finished with a sensitivity analysis that will be performed to verify the robustness of the model results. For this, the stability of the alternatives sorted in the categories will be analyzed by varying the weight assigned to each criterion by 20%, identifying inconsistencies and ensuring the reliability of the results.

3 CASE STUDY IN THE BRAZILIAN SEMI-ARID REGION

This section exhibits the proposed model capacity to classify municipalities within a droughtaffected region, so supporting government decision-making in establishing policies for resource reallocation and minimizing drought’s consequences. The implementation of this study adheres to the stages shown in Figure 1.

3.1 First Step: Decision-maker identification

Initially, the decision-maker who will be consulted for the development of this study was defined. In this case, it will be the Operational Management Coordinator of the Water Management Institute of the State of Rio Grande do Norte (IGARN) in Brazil. The coordinator has experience in Civil Engineering, with an emphasis on Hydraulic Engineering, working mainly in the water availability assessment, water demand, hydrological risks, and management of water resources since 1972. His broad and proven knowledge makes him able to act as a decision-maker in this process.

Among his responsibilities, the coordinator highlights the development and articulation of water management processes and regulation of their uses, aiming to ensure water supply in quality and quantity appropriate to the use of current and future generations. In addition, the decision-maker strives to protect against droughts, floods, and other catastrophic events that threaten public health, public safety, and economic and social losses.

Although considered an individual decision, other actors can influence the decision-making process, such as the presidents of watershed committees, water bodies monitoring, planning, and finance coordinators, who are experts in the context of the decision-making process, as they have factual information about the problem under analysis. We consider it an individual decision because all drought-fighting operations are authorized and coordinated by the chosen decision-maker.

Once the decision-maker for this decision-making process has been identified, the following phase specifies the cities/municipalities affected by drought (alternatives).

3.2 Second Step: Definition of municipalities that will be evaluated

The decision-maker considered the municipalities currently experiencing water and social crises due to drought for this problem. In this case, some alternatives (municipalities) may be considered for the problem. However, municipalities in the Brazilian semiarid region stand out because it is considered the most populous and socially fragile drought-affected region in the world, with approximately 28 million inhabitants (Marengo et al., 2008; INSA, 2023), in addition to presenting irregular rainfall distribution in its flat and rocky lands (Alvalá et al., 2019). Therefore, the drought in this region affects the quantity and quality of available water for consumption, generating social, food, and health insecurity among the population (Menezes et al., 2021).

The Brazilian semiarid region encompasses various Brazilian regions, notably part of the Northeast region of Brazil. Due to its high spatiotemporal variability, land degradation, and high soil aridity, it is considered the most susceptible area to desertification in Brazil (Brito et al., 2017). The semiarid region of Northeast Brazil has a continental area of about 309,000 km2 and na annual precipitation of less than 800 mm, making it one of the most vulnerable regions in the world to the impacts of climate change (Marengo et al., 2018; Brito et al., 2017).

According to data from the National Water Agency and Basic Sanitation (ANA, 2022) for the year 2022, several states in the semiarid region of Northeast Brazil presented some drought situations, some being more severe than others. However, the state of Rio Grande do Norte presented the most critical drought situation among the states in the Northeast. January 2022 stood out, in which 100% of its territory was in a general state of drought, with 62% of its territorial range characterized as severe drought, 25% as moderate drought, and 13% as weak drought, due to negative precipitation anomalies. Thus, the municipalities in this region have many drought indices and can be classified for prioritizing public policies to combat drought.

To simplify, fourteen (14) municipalities from the semiarid region of Rio Grande do Norte with reservoirs greater than 5.000000m³ (five million cubic meters) were selected and analyzed based on five (5) significant criteria outlined before. The selection of these cities for the application of this methodology was influenced by the severity of drought in this region and the fragile socioeconomic and water conditions of the communities (Da Silva et al., 2020). Figure 2 shows the municipalities location.

Figure 2
Municipalities evaluated.

With the help of the database of federal and state public agencies, secretariats, systems, and institutes in Brazil (ANA, 2022; IBGE, 2021; SNIS, 2021; IGARN, 2022), the evaluation matrix of the municipalities regarding the evaluation criteria was formulated and presented in Table 3.

Table 3
Evaluation matrix.

Code	Municipality	Reservoir Index (Cr1)	Sanitary Sewage Coverage Index (Cr2)	Water Coverage Index (Cr3)	Population (Cr4)	HDI (Cr5)
A1	Tenente Ananias	13.27%	28.8%	62.29%	10923	0.529
A2	Pilões	25.29%	23.7%	94.08%	3869	0.646
A3	Pau dos Ferros	30%	22.73%	100%	30600	0.614
A4	Campo Grande	30.92%	16.6%	67.36%	9670	0.678
A5	Umarizal	65.33%	4.7%	97.89%	10485	0.621
A6	Caraúbas	70.92%	12.7%	83.22%	20541	0.618
A7	Lucrécia	35.93%	62.76%	65.61%	4025	0.638
A8	Severiano Melo	14.79%	10.1%	100%	1743	0.604
A9	Encanto	72.24%	16.3%	92.17%	5697	0.629
A10	José da Penha	79.67%	7.05%	78%	5941	0.608
A11	Marcelino Vieira	74.67%	30.2%	80.4%	8325	0.609
A12	Rafael Fernandes	75.55%	19.5%	26.64%	5128	0.608
A13	Riacho da Cruz	70.82%	57.9%	55.7%	3614	0.584
A14	Rodolfo Fernandes	68.74%	22.3%	100%	4467	0.604

After defining the alternatives and structuring the evaluation matrix, the next step is preference elicitation to the decision problem, which includes defining the importance degree of criteria and limiting profiles between categories.

3.3 Third Step: Preference elicitation

Following the steps of the proposed model, the preference elicitation step is divided into two (2) specific activities: (i) define the importance of the criteria through the ROC procedure and (ii) define the limiting profiles between categories. For the first activity, the Rank-Order Centroid (ROC) procedure will be used to define the criteria weights, which denote the element importance, and incorporates the order information of the criteria in defining cardinal values to the constructs of the decision problem. Zardari et al. (2015) report that the main advantage of the ROC procedure is the ease of obtaining information from the decision-maker. This procedure presents itself to a decision-maker as a straightforward and trustworthy method for recommending weight values for a number of elements sorted according to their significance. Thus, the results regarding the criteria ranking and their respective weights assigned by the ROC procedure can be observed in Table 4 below.

Table 4
Order of importance and criteria weight.

Order of importance of the Criteria	Weight by the ROC procedure
Water Coverage Index (Cr3)	0.4567
Reservoir Index (Cr1)	0.2567
Population (Cr4)	0.1567
Sanitary Sewage Coverage Index (Cr2)	0.09
HDI (Cr5)	0.04

According to the decision-maker preference, the most important element was the ”Water Coverage Index (Cr3)” criterion, receiving the highest weight value of 0.4567 in the ROC procedure. Consequently, the ”Reservoir Index (Cr1)” criterion was considered the second most important construct in the evaluation, with a weight of 0.2567. Following this, the ”Population (Cr4)” criterion received the third highest importance, with a value of 0.1567. In addition, the ”Sanitary Sewage Coverage Index (Cr2)” attribute also gained the fourth highest numerical importance, with a value of 0.0900. Lastly, the ”HDI (Cr5)” element received the lowest importance among the evaluation elements, with a value of 0.0400.

The set criteria are important for the evaluation, according to the decision maker’s preferences. The first criterion, Reservoir Index, is essential to assess the climate and manage water resources, indicating the occurrence or absence of climatic phenomena in the municipalities, such as precipitation and evapotranspiration rate. The second criterion, the Sanitary Sewage Coverage Index, indicates whether the municipality has basic sanitation, which is essential to avoid wasting water and preserve it efficiently. The third criterion, the Water Coverage Index, reveals the effective distribution of water to the drought-affected resident. The fourth criterion, Population, identifies the extent of drought impacts on the municipality’s habitants. Finally, the fifth criterion, HDI, shows important information about the city’s social vulnerability to the drought impacts, indicating its resilience in coping the natural disasters.

The second activity is defining limiting profiles. In this case, the decision-maker opted for a direct (exact) evaluation of the values related to the limiting profiles between categories. Although this activity is more costly for the decision-maker (Cailloux et al., 2012), the decision-maker chose this type of evaluation to faithfully represent their preferences, indicating the possible practical interpretation these thresholds represent in each criterion. Some proposals in the multicriteria classification literature also use this type of evaluation (Araz & Ozkarahan, 2007; Yu, 1992; Kang et al., 2020). As a result, Table 5 shows the values associated with the limiting profiles between categories for each criterion.

Table 5
Limiting profiles between case study categories/classes.

Limiting Profiles	Reservoir Index (Cr1)	Sanitary Sewage Coverage Index (Cr2)	Water Coverage Index (Cr3)	Population (Cr4)	HDI (Cr5)
Limiting Profiles 1 (r 1)	40%	30%	30%	10000	0,3
Limiting Profiles 2 (r 2)	60%	60%	70%	3000	0,6

Lastly, the decision-maker chose the Usual evaluation type (Type I) for each criterion. This information is required as one of the FlowSort method’s input parameters. It reflects that any difference in performance between pairs of alternatives will represent a strict preference of the decision-maker, with the preference and indifference thresholds of each criterion being zero (Brans & Vincke, 1985; Nemery & Lamboray, 2008). With the information and parameters previously defined, it is feasible to classify all the municipalities engaged in the decision problem.

3.4 Fourth Step: Sorting of drought-affected cities by FlowSort Method

Assessment and alternatives sorting will be carried out using the multicriteria method FlowSort (Nemery & Lamboray, 2008) based on the decision maker’s preference information and the specified information for each approach parameter. The aim is to effectively tackle the drought impacts by identifying the criticality of each municipality. Table 6 shows the results.

Table 6
Net flows of the alternatives and limiting profiles.

Municipality	ϕ (r 1 )	ϕ (r 2 )	ϕ (a i )
Tenente Ananias (A1)	0.4158	-0.9208	0.505
Pilões (A2)	0.5743	-0.505	-0.0693
Pau dos Ferros (A3)	0.4158	-0.505	0.0891
Campo Grande (A4)	0.5743	-0.9604	0.3861
Umarizal (A5)	0.6733	-0.2475	-0.4257
Caraúbas (A6)	0.6733	-0.2475	-0.4257
Lucrécia (A7)	0.6634	-0.8713	0.2079
Severiano Melo (A8)	0.5743	-0.3465	-0.2277
Encanto (A9)	0.8317	-0.2475	-0.5842
José da Penha (A10)	0.8317	-0.2475	-0.5842
Marcelino Vieira (A11)	0.9208	-0.2475	-0.6733
Rafael Fernandes (A12)	0.3762	-0.703	0.3267
Riacho da Cruz (A13)	0.9208	-0.6634	-0.2574
Rodolfo Fernandes (A14)	0.8317	-0.2475	-0.5842

Following the application steps of the FlowSort method, the performance of each alternative was compared pairwise with the performances of the limiting profiles between categories established for the decision problem. The model identified the preference index between an alternative and each limiting profile based on pairwise comparisons. Subsequently, the model obtained the indices of net flows (φ) of each alternative and the limiting profiles using Equation (5).

In order to achieve strict alternatives sorting into a single category, Equation 8 was considered, which will compare the net flow performances of each alternative with the respective net flows of the limiting profiles generated by their independent evaluation. Thus, the criticality sorting of the municipalities can be seen in Figure 3.

Figure 3
Sorting of municipalities criticality affected by drought.

The application of the multicriteria method allowed each of the fourteen (14) evaluated municipalities to be classified into only one category. In this way, the results showed that the municipality with a highly critical need for resources to face the drought is Tenente Ananias (A1). After its performance, municipalities with moderate criticality could be more focused, such as Pilões (A2), Pau dos Ferros (A3), Campo Grande (A4), Lucrécia (A7), Severiano Melo (A8), Rafael Fernandes (A12) and Riacho da Cruz (A13). Finally, public policies to combat drought could be directed to municipalities with slightly critical, such as Umarizal (A5), Caraúbas (A6), Encanto (A9), José da Penha (A10), Marcelino Vieira (A11), and Rodolfo Fernandes (A14), as they do not have urgent needs for government support, despite still being impacted by the drought.

Despite the already-mentioned advantages of applying the ROC procedure in multicriteria models, the literature argues that the procedure presents an excessive dispersion of values attributed to the criteria (Zardari et al., 2015). Thus, the sensitivity analysis of the sorting was realized to examine the impact of this procedure on the proposed approach.

The sensitivity analysis aims to perform variations of the input parameters of a method to identify the impacts on its results. This step is relevant when decision methodologies work with quantitative data. In classification models, in particular, the sensitivity analysis will verify possible changes in the classifications indicated by the model. It is up to this procedure to assess their occurrence degree (De Almeida, 2013).

For this stage, an isolated evaluation of parameters was performed. The importance (weight) attributed to each criterion was reduced and increased by 20%, generating ten (10) new classifications for each alternative. The statistical indices of the classifications of the municipalities resulting from the sensitivity analysis can be seen in Table 7.

Table 7
Sensitive Analysis of the classifications.

Municipality	Highly Critical	Moderate Critical	Slightly Critical
Tenente Ananias (A1)	90%	10%	0%
Pilões (A2)	0%	100%	0%
Pau dos Ferros (A3)	0%	100%	0%
Campo Grande (A4)	0%	100%	0%
Umarizal (A5)	0%	0%	100%
Caraúbas (A6)	0%	0%	100%
Lucrécia (A7)	0%	100%	0%
Severiano Melo (A8)	0%	90%	10%
Encanto (A9)	0%	0%	100%
José da Penha (A10)	0%	0%	100%
Marcelino Vieira (A11)	0%	0%	100%
Rafael Fernandes (A12)	20%	80%	0%
Riacho da Cruz (A13)	0%	100%	0%
Rodolfo Fernandes (A14)	0%	0%	100%

Considering the results obtained from the sensitivity analysis, it can be observed that only three (3) municipalities showed significant variations in their classifications when compared to the previous stage. These municipalities were Tenente Ananias (A1), Severiano Melo (A8), and Rafael Fernandes (A12).

The first municipality, Tenente Ananias (A1), was sorted as highly critical in 90% of the simulated cases, the same sorting as obtained initially. However, the municipality obtained 10% of the simulated cases with a lower category than the original, presenting moderate criticality. To the second municipality, Severiano Melo (A8), the simulated data showed that in 90% of the sorting, the municipality had moderate criticality, similar to the initial classification. However, the statistical indices report that 10% of the simulated data consider that the municipality should have a lower category than the original, indicating slightly critical resource needs.

Moreover, for the third municipality, Rafael Fernandes (A12), it was found that 80% of the new classifications consider a moderate criticality, but 20% of the simulated cases already consider it as having a highly critical, needing more resources to mitigate the effects of this disaster. Finally, the other municipalities obtained identical classifications to the categorization suggested by the proposed model in 100% of the simulated cases, making the data relevant.

3.5 Discussions

Population growth, socioeconomic instabilities, and remote access locations make it difficult for public Population growth, socioeconomic instabilities, and remote access locations make it difficult for public representatives to make decisions regarding crises in the semi-arid region of Brazil, particularly concerning a long-standing issue: the drought in northeastern Brazil. For this reason, the public administration needs concrete projects to allocate resources to support decision-making in coping with the drought. In this perspective, the proposed multicriteria model sought to act under this approach.

The results of the proposed model demonstrated that the public administration could direct efforts and public policies in the municipalities that present a more critical state of drought than other evaluated municipalities. In this case, initially, resources could be allocated in the municipality classified in the first category, given the high criticality of the region affected by the drought, demonstrating its urgent need for action to minimize the damage associated with this natural disaster. Subsequently, municipalities with moderate criticality could be served due to their growing needs as the drought persists in the region. Finally, the critical municipalities could be helped, given that they have stable conditions, even though they are impacted by drought.

In addition, including the ROC procedure in defining the weight of the criteria made the decisionmaking process less tiring, given that partial information is more accessible for the decisionmaker to defer when compared to exact information. The ease of application of the procedure allows the decision maker to obtain cardinal values practically, but no less reliable, for the evaluation criteria weights. Thus, this procedure allows an easy understanding of the parameters that describe the multicriteria decision problem and a quick representation of its preference structure.

Finally, the study conducted a sensitivity analysis to identify the influence of the ROC weights in the model, resulting in a few sorting divergences. The municipalities that obtained variations in the classifications presented inferior performances in criteria 1 and 3, considered the essential criteria for the decision-maker: the situation of the reservoir and the index of total water supply, respectively. Therefore, even if insignificant, the sorting variation can be justified by the criticality of the municipalities evaluated in these criteria. In most variations, a lower rating than the original was considered, reflecting a possible lower need for resources in the long term.

4 MANAGERIAL IMPLICATIONS

Several managerial implications emerge from an analysis of the results depicted in Figure 3. First, the proposed model could guide mitigation measures for this natural disaster. Drought events necessitate the implementation of both shortand long-term coping measures. Thus, the proposed model could encourage the development of public policies to allocate short-term resources, considering the real needs of a location impacted by drought.

In addition, the use of the proposed model, when compared with the traditional allocation of resources, could be more beneficial for public management because of the consideration of the multiple criteria involving water resource management. Consequently, the use of the model proposed by the public managers permits an efficient allocation of resources, directing the efforts of the public administration in the fight against the drought and mitigating its effects.

The public administration is accountable for designing and implementing concrete drought mitigation projects. The projects satisfy the immediate and long-term needs of the population, such as providing drinking water using water trucks, building water wells, implementing water conservation programs, prioritizing municipalities for food distribution, assistance financial support for low-income families, and access to health services.

Therefore, a concrete resource allocation project that considers the water and socioeconomic aspects of municipalities affected by drought can become a valuable tool in the strategic planning of a public administration. Supporting the decision-making process is particularly important for public sector organizations due to their limited resources. Thus, the proposed model could better achieve the government’s strategic objectives.

5 CONCLUSIONS

Throughout history, several regions of the world have experienced drought. Efforts, techniques and public policies were developed to propose adequate responses and the most effective actions to mitigate the effects of drought. The proposed multicriteria model aims to aid decision-making in coping with drought by identifying municipalities’ criticality levels and facilitating resource allocation in drought-affected regions.

Using a multicriteria approach, the methodology proposed in this article aimed to classify the criticality of municipalities for the subsequent resource allocation process in response to the drought. With this, it was possible to determine the level of urgency of the locations affected by the drought and, as a result, develop appropriate public policies for these areas.

Using the multicriteria approach in public administration can support the shortand long-term decision-making process in drought-stricken regions, particularly the Brazilian semiarid. With this, public managers can identify the municipalities most affected by the drought and direct strategic actions to these locations. This methodology is practical and possible to replicate in similar situations.

Finally, the study’s limitations were associated with data collection from the decision-maker, especially information on the limiting profiles between categories, because of the excessive effort that the decision-maker took to define the values that delimited the classifications. For future studies, the model could be adapted for group decision-making considering partial information in limiting profiles between categories.

Acknowledgements

The present work was carried out with the support of the Coordination of Improvement of Higher Education Personnel - Brazil (CAPES) with financing code 001, Foundation for the Support of Science and Technology of the State of Pernambuco (FACEPE), and also by the National Council for Scientific and Technological Development Brazil (CNPq).

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Publication Dates

• Publication in this collection
  24 June 2024
• Date of issue
  2024

History

• Received
  27 Apr 2023
• Accepted
  02 July 2023