Optimizing humanitarian water logistics: facility location and routing in drought-affected Brazilian semiarid northeast

As outlined by the United Nations (1992), disasters are unforeseen catastrophic events that overwhelm a society’s ability to respond, causing substantial losses in human lives, resources, economic stability and the environment, surpassing its capacity to cope. These events can be categorized by their underlying causes as either natural disasters, arising from natural hazards or human-induced disasters, resulting from human actions (Ergun et al., 2010). Disasters can also be classified based on their onset speed, differentiating between rapid-onset events – such as earthquakes and tsunamis – and slow-onset disasters – such as drought (McCann et al., 2011).

Droughts involve a significant reduction in rainfall compared to typical levels in a given region, compromising water availability for both human populations and ecosystems (Ortega-Gaucin et al., 2016). When this prolonged decrease leads to damage and losses that surpass the capacity of the community to cope with its own resources, it is classified as a slow-onset natural disaster (Do Amaral Cunha et al., 2019). Droughts are among the most damaging and costly natural disasters globally, with annual economic losses between US$6 and 8bn (Hoque et al., 2020). Projections indicate that these figures will continue to rise, driven by the anticipated escalation in drought frequency and severity linked to climate change (Wang et al., 2019). The social impacts of droughts are also severe, particularly in rural and low-income regions, where they compromise food security, access to clean water and the overall resilience of vulnerable communities. This context underscores the urgency of improving emergency response strategies and investing in long-term solutions to enhance water resource management in drought-prone areas.

Emergency water trucking (EWT) is frequently employed to support populations affected by the adverse impacts caused by droughts, particularly in dispersed rural communities in developing countries, such as Brazil and southern Africa. EWT serves as a short-term, life-saving measure (Wildman, 2013), providing essential water supplies during crises where existing water systems are compromised due to natural disasters, conflicts or contamination. It is especially critical for displaced individuals in locals with unreliable water access, as inadequate sanitation and hygiene may result in increased illness and mortality (Loo et al., 2012).

Although the EWT is intended as a temporary solution, providing a fragile water supply that is susceptible to logistical challenges, mechanical failures and high costs, it has become a recurring intervention due to unpredictable rainfall patterns. The factors contributing to the ongoing need for EWT in areas prone to drought include inadequate settlement patterns influenced by political interests, commercial motivations and a lack of long-term strategies for allocating resources for water infrastructure development. In addition, frequent borehole breakdowns and community dependency on external aid exacerbate this problem (Wildman, 2013). When scaled to dispersed rural populations, EWT demands a substantial vehicle fleet, increasing transport distances and operating costs. Therefore, it is essential to develop solutions that increase EWT’s financial and technical viability while ensuring efficient and equitable water distribution.

Despite being a common intervention in humanitarian contexts, water trucking has received limited attention in academic research (Sikder et al., 2020). EWT involves transporting water via tanker trucks from various sources to multiple demand points, which can be modeled as a multidepot vehicle routing problem (MDVRP). Vieira et al. (2021) proposed a two-step procedure to optimize this process. The first step involves assigning demand points to water sources as a transportation problem, whereas the second step models treating it as a capacitated vehicle routing problem (CVRP). This procedure was implemented in a real case study, benefiting 17,621 individuals dispersed along 1,069 demand points within a 9,375 km² area in Brazil’s semiarid region. The Federal Government currently manages water distribution in this area through the EWT program, called Operação Carro Pipa (OCP) (Brasil, 2012).

In addition, well drilling is commonly adopted as a strategy to mitigate the impacts of droughts in Brazil’s Northeast (Nunes et al., 2023). The Operação Semiárido program, also sponsored by the Federal Government, included drilling 593 wells, 302 of which successfully yielded water, along with installing 23 reverse osmosis systems for brackish water treatment. This initiative was implemented throughout seven states, serving 80 municipalities and benefiting 69,000 people. The program incurred a total cost of BRL15.7m over three years but resulted in annual budget relief of BRL6m for the OCP (Defesanet, 2022).

However, identifying the most suitable locations for productive artesian wells in water-scarce regions remains a significant challenge (Nunes et al., 2023). In bedrock areas, groundwater is typically restricted to fissured and degraded layers (Nag and Kundu, 2016), leading to aquifers that produce limited water, low flow rates and frequently high ionic concentrations (Limaye, 2002). Consequently, groundwater exploration lacking a comprehensive hydrogeological assessment frequently yields unsuccessful outcomes, because of the intricate and unpredictable nature of groundwater distribution in these environments (Singh et al., 2019).

To address this challenge and improve water distribution to drought-affected communities, this paper proposes a two-step procedure. The first step involves the design of a facility location-allocation model using mixed-integer mathematical programming to optimize well placement and allocation to demand points. This model seeks to improve the likelihood of locating productive wells while prioritizing the communities most vulnerable to drought. To this end, it incorporates the probability of obtaining a productive well, estimated through the logistic regression model proposed by Vieira et al. (2021), alongside the composite drought risk index calculated by Bravo (2021) for the locations under consideration.

The second step applies a variant of the adaptive large neighborhood search (ALNS) algorithm, originally proposed by Pisinger and Ropke (2007) and later adapted by Erdoğan (2017), to identify the most efficient vehicle routes for water delivery based on the allocations generated in the first step. This integrated approach not only reduces total operational costs but also shortens delivery times and increases service coverage, key elements in emergency response logistics. The proposed methodology therefore offers a robust and flexible framework for enhancing resilience in drought-prone regions.

We apply the proposed procedure to a real-world water distribution case in Brazil’s Northeast. A comparative assessment of the results with those reported by Vieira et al. (2021) and the current practices under Operação Carro Pipa confirms the consistency and the efficiency of the methodology.

The relevance of this study lies in its capacity to support public managers in developing data-driven policies and enhancing the resilience of drought-affected regions. The methodology is designed to be computationally feasible for large-scale applications and adaptable for the use in other vulnerable regions, as well as in different emergency logistics contexts beyond water distribution. Thus, the study contributes to the ongoing efforts to integrate operations research methods into humanitarian and environmental planning, with the goal of achieving more effective and sustainable responses to climate-induced crises.

This paper is further organized as follows. Section 2 presents a review of the relevant literature on facility location and vehicle routing problems. Section 3 describes the proposed two-step methodology, including the location-allocation model for well placement and the solver for the vehicle routing problem (VRP). Section 4 details the application of the proposed model in a case study on water distribution in Brazil’s Northeast Region, highlighting key results and analysis. Finally, Section 5 summarizes the main findings and offers directions for future research.

The Facility Location Problem (FLP) involves determining the most effective placement of a selection of facility sites aimed at covering multiple demand points, while meeting specific constraints and optimizing certain performance measures (Laporte et al., 2019). Early contributions by Hakimi (1964, 1965) introduced two classic variants: the p-center and p-median problems. The p-center formulation focuses on minimizing the greatest distance between any demand point and the nearest facility, aiming to ensure equitable access across the entire network. In contrast, the p-median problem seeks to minimize the total distance from all demand points to their closest facilities, emphasizing overall efficiency in service delivery. Both formulations are particularly relevant in public service planning, such as healthcare, education and emergency response, where either equity or efficiency may be prioritized depending on policy goals.

Later, Toregas et al. (1971) introduced an approach for locating emergency services derived from the Set Covering Problem (SCP). In this model, each candidate facility location is associated with a service radius, typically defined by a maximum travel distance or response time. The model ensures that every demand point falls within the coverage area of at least one facility. The main goal is to identify the smallest number of facilities needed to provide complete coverage of all demand points within the specified limit. This formulation has been widely applied in the design of fire stations, ambulance posts and police stations, where the timeliness of the service is crucial and budgets are often constrained.

Church and ReVelle (1974) examined situations in which the number of available facilities is insufficient to ensure complete service coverage within a defined service radius. To address this limitation, they proposed the Maximal Covering Location Problem (MCLP), which seeks to maximize the demand covered by a fixed number of facilities, subject to a predefined service distance or time constraint. Unlike the SCP, which guarantees full coverage, the MCLP recognizes resource limitations and provides a more realistic basis for planning scenarios of scarcity or emergency deployment.

In a related but distinct line of research, Cornuejols et al. (1977) formulated the Uncapacitated Facility Location Problem (UFLP), originally applied to optimize bank account placements with the goal of minimizing clearing times. This model aims to minimize the total cost, which includes both the fixed costs of operating facilities and the variable costs of serving clients from those locations, without accounting for capacity limitations at the facilities.

Although both MCLP and UFLP have significantly advanced facility location modeling, most real-world applications involve facilities with finite resources or capacities. As such, incorporating capacity constraints is vital for developing practical and implementable location strategies that more accurately reflect operational realities.

Similarly, basic model formulations can be readily adapted to account for service and setup costs, in addition to capacity constraints. These enhanced formulations, known as the Capacitated Facility Location Problem (CFLP), introduce limitations that restrict each facility from serving more demand than its available capacity. For example, Current and Storbeck (1988) applied this framework to develop capacitated versions of the Set Covering Problem (SCP) and the Maximal Covering Location Problem (MCLP). Subsequently, Sankaran and Raghavan (1997) built upon the traditional CFLP by incorporating variable facility sizes, offering a more comprehensive framework for modeling complex, real-world facility location decisions. These advancements allow for greater alignment between model outputs and actual resource availability, improving the feasibility and sustainability of implementations strategies.

Regarding approaches to solving facility location problems, many practical instances are not inherently “integer-friendly” and often demand the application of heuristics and metaheuristics. Among the most applied techniques are tabu search and genetic algorithms. For example, Alp et al. (2003) introduced a genetic algorithm to address the p-median problem, whereas Mladenović et al. (2003) employed a variable neighborhood search combined with two tabu search heuristics to solve the p-center problem. In addition, various decision support systems (DSSs) are employed to solve different FLPs. SITATION, created by Daskin (2002), is a solver capable of addressing UFLP, MCLP, SCP, p-center and p-median problems involving as many as 150 locations. The Orloca (Operations Research LOCational Analysis) model employs algorithms to address the Fermat-Weber minimum location problem (Muñoz-Márquez, 2008). The Library of Location Algorithms (LoLAs) supports a wider range of problem categories (Kalcsics et al., 2011). More recently, Erdoğan et al. (2019) developed the FLP Spreadsheet Solver, an open-source spreadsheet-based DSS, capable of solving all the primary location problems previously listed. The tabu search algorithm can provide near-optimal solutions for FLPs involving locations up to 200. This limitation typically stems from GIS-related service constraints, although it can be manually adjusted by the user when necessary.

Addressing the challenge of access and equity to drinking water in rural Sub-Saharan Africa, Zhai et al. (2023) developed a study in collaboration with nongovernmental organizations (NGOs) – (charity: Water and Relief Society of Tigray - REST) in the Tigray region of Ethiopia. The study proposed a fully functional programming model to support decisions on the location of new wells and pumping systems to serve over 3 million beneficiaries. The study compares the current decentralized practice of NGOs with alternative models, demonstrating that a “centralized” model, which encourages collaboration and resource sharing among neighboring communities, most improves both access (by reducing travel distances) and equity. Furthermore, our authors propose a stochastic optimization model to mitigate the risks of “supply shocks” (such as civil war), providing a tool for infrastructure planning in highly unstable environments.

VRP is a well-established topic in logistics, focused on determining optimal routes that minimize transportation costs for a fleet of vehicles departing from a depot (Erdoğan, 2017). Since its initial formulation by Dantzig and Ramser (1959), numerous variants of the VRP have been developed. However, a review of the literature reveals that not all problem classes have received equal attention. One such underexplored class is the MDVRP (Vidal et al., 2012). Research on this problem remains relatively scarce (Francis et al., 2008), despite its importance in various applications, including the tourism sector (Gavalas et al., 2014), humanitarian logistics (Özdamar and Demir, 2012), waste collection (Hemmelmayr et al., 2014) and healthcare (Erdoğan, 2017). Understanding and improving MDVRP solutions directly contributes to more resilient and efficient logistics planning.

The MDVRP comprises a group of customers to be attended by vehicles from multiple depots. Each customer should be served (visited) only once by any vehicle in the fleet. Each vehicle visits several customers in a specific order along its route before returning to its origin depot (Stodola, 2018). Because it is an NP-hard problem, its resolution via an exact algorithm is time-consuming and computationally intractable (Ho et al., 2008). The computational reach of exact algorithms for the VRP is limited to 200 customers for most problem variants and decreases significantly as they become more realistic, including features such as a heterogeneous fleet or distance constraints (Erdoğan, 2017). Therefore, heuristic and metaheuristic algorithms are widely used (Stodola, 2018), including tabu search (Soto et al., 2017), ALNS (Pisinger and Ropke, 2007; Erdoğan, 2017), iterative local search (Subramanian et al., 2010), the genetic algorithm (Ombuki-Berman and Hanshar, 2009; Vidal et al., 2012), simulated annealing (Lim and Zhu, 2006) and the ant colony optimization algorithm (Kaabachi et al., 2017; Stodola, 2018; Silva Júnior and Leal, 2021). These approaches have shown promising results in balancing solution quality and computational efficiency, especially when applied to large-scale, real-world scenarios.

Erdoğan (2017) also provided an open-source Excel-based tool, called VRP Spreadsheet Solver, capable of solving more than 64 variants of the VRP. It was implemented via a variant of the ALNS based LNS algorithms of Pisinger and Ropke (2007). The solver can address both capacitated VRP and distance-constrained VRP instances with up to 200 customers within reasonable computational time, making it a practical option for applied problem-solving in humanitarian logistics contexts.

Vieira et al. (2021) propose a two-step methodology to address large-scale emergency water distribution in drought scenarios, modeled as a MDVRP. In the first step, the problem is formulated as a classical transportation model, where demand points are assigned to water sources. The model minimizes total transportation costs, subject to supply and demand balance constraints, vehicle capacity restrictions, and operational time limits that ensure each truck can complete its delivery and return to the depot within a working day. This stage reduces the MDVRP complexity by partitioning the network into smaller subproblems. In the second step, each subproblem is treated as a CVRP, solved through different heuristic and metaheuristic approaches. Among them, the authors apply the Clarke and Wright heuristic and the metaheuristics ALNS (Erdoğan, 2017) and the Multiple Ant Colony System with Random Variable Neighborhood Descent (Silva Júnior and Leal, 2021).

This section outlines the proposed procedure for planning humanitarian logistics related to water supply for populations affected by drought. The problem involves two key classical operational research challenges: the Facility Location Problem (FLP) in the first step and VRP in the second step.

The methodology consists of supporting location decisions of new artesian wells to reduce the need for trucks to distribute drinking water. An artesian well is always located near a cistern (demand point), which serves a community. People in this community travel on foot from their homes to collect water from these cisterns using buckets. Locations that receive a well can serve as a source of water for the nearest cistern as well as for trucks to load and distribute water to cisterns without wells. In addition to wells, trucks can load water from another sources such as dams, water suppliers and water treatment plants. Furthermore, for cisterns that do not have well installed, water delivery continues to be carried out by trucks and the water source and cistern allocations obtained in the first phase are used to calculate routes in the second phase. It is worth noting that water delivery by trucks is continuous throughout the year and in the same quantity, to all cisterns that do not have wells, regardless of the uncertainty of drought, as this is the emergency delivery of drinking water for human consumption, in places without the availability of drinking water sources near these communities.

This paper seeks to evolve the methodology proposed by Vieira et al. (2021), which only support the decisions of allocate water sources to cisterns and routes trucks, by including the decision to locate new artesian wells, because the Brazilian Army carries out these two activities in the Brazilian semiarid region. The proposal is that the location of the wells is implemented whenever resources are made available for this purpose and that the second phase is conducted monthly, to plan deliveries by trucks.

In the first step, we address the problem of selecting optimal locations for artesian wells to provide water to a specified set of cisterns. Candidate locations for well installations are categorized into three sets: existing wells (⁠$V1$⁠,), feasible sites for new wells (⁠$V2$⁠) and locations that cannot be considered as wells (⁠$V3$⁠). Notably, vertices in V3 remain unassigned to any cistern and are excluded from consideration as potential well locations. This classification reflects realistic geographic constraints and regulatory limitations that influence decision-making in drought-prone regions. In addition, incorporating fixed infrastructure and environmental feasibility ensures that the model remains grounded in operational applicability.

In the second step, after establishing the locations and assigning each cistern to its corresponding water source, we proceed to identify the most efficient delivery routes by solving the VRP to optimize water distribution to cisterns. The main contributions of the paper are in the solving of the Facility Location Problem (FLP) with probabilistic modeling of well success and integration of drought risk index, integrated with the VRP using the ALNS metaheuristic.

For the first step, we implement a modified version of a location-allocation model designed to determine optimal sites for water wells and assign them to demand points. This approach is built upon the integer programming formulation of the facility location problem introduced by Erdoğan et al. (2019), but includes several important modifications to tailor it to the specific requirements of our study. First, we chose to split the objective function related to total cost into two distinct components: transport cost and setup cost, resulting in four objective functions instead of three. In addition, we adjusted the objective function to prioritize maximizing demand coverage. While Erdoğan et al. (2019) focused on the probability of a facility meeting demand at specific locations, our model incorporates the probability of groundwater occurrence. Moreover, a drought vulnerability parameter, formulated from the composite drought risk index, was integrated to guide the prioritization of high-risk locations.

Consider a directed graph $G=(V,A)$⁠, where the vertex set $V$ is divided into three disjoint subsets $V1$⁠, $V2$ and $V3$⁠. The first subset $V1$ includes vertices representing existing wells. The second subset $V2$ consists of potential well sites, specifically those with a groundwater occurrence probability of 50% or higher. The third subset $V3$ contains vertices that cannot be designated as wells, defined as those with a groundwater occurrence probability of less than 50%. The groundwater occurrence probability $pi$ is estimated using equation (1), based on the logistic regression model developed by Vieira et al. (2021), considering the following predictor variables: lithotype (lit_i), lineament density (lin_i), surface drainage (dren_i) and distance to the nearest structural lineament (dist_i). The arc set A contains all arcs connecting the vertices in V, including self-arcs $i, i ∀i∈V$⁠:

Each vertex $i∈V$ has a demand $qi$ in liters of drinking water, a groundwater occurrence probability $pi$⁠, estimated using equation (1), and a drought composite index $IRi$⁠, linked to the region it belongs to. The composite index used here is based on the one proposed by Bravo (2021), reflecting the combined influence of climatic conditions (hazard) and societal factors (vulnerability) related to drought. The indices consist of several normalized indicators, with their weights established using the Analytic Hierarchy Process (AHP) method. The hazard index incorporates variables such as rainfall, evapotranspiration, temperature (maximum, mean and minimum), humidity, solar radiation and wind speed. The vulnerability index assesses exposure, sensitivity and adaptive capacity. In addition, each vertex $i∈V1∪V2$ incurs a setup cost $si$ if i is selected to host a well, along with an estimated capacity $Qi$⁠. The total number of wells that can be installed is limited by a predefined upper bound m. The binary parameter $α$ is given a value of 1 if all m facilities should be located and 0 otherwise. The parameter $δ$ indicates the maximum service distance. For every arc $i, j∈A$⁠, there is an associated distance $dij$⁠, and the average cost of truck transportation per unit of distance per liter of drinking water is denoted by c.

Let $xij$ be binary variable equal to 1 if vertex i is served by a facility in j and 0 otherwise. Similarly, let $yj$ be equal to 1 if a well is installed at vertex j and 0 otherwise. In addition, let w denote the maximum distance between any demand point and the facility assigned to serve it. Table 1 summarizes all sets, parameters and decision variables required for the problem formulation.

The complete mathematical model is then defined by expressions (2) through (14):

s.t:

The objective function (2) seeks to maximize coverage by enhancing the probability of obtaining a productive well (⁠$pi$⁠) and prioritizing locations with higher drought risk (⁠$IRi)$⁠. In addition, following a lexicographic order, the function minimizes transport costs, setup costs and the maximum distance between each demand point and its assigned water source. This search order was defined based on an interview conducted with one of those responsible for drilling wells carried out by the Brazilian Army in 2019.

Constraints (3) assure that every cistern is assigned to a water source. Constraints (4) specify that a water source must be established at node j so that a cistern i can be served by it. Constraints (5) ensure that, for each source, the total demand of the points it serves does not exceed its capacity. Constraint (6) limits the number of facilities located to the maximum allowed (m). If $α=1$⁠, indicating that all m facilities must be located, constraint (7), along with constraint (6), enforces this condition. Constraints (8) ensure that w is at least as large as the distance between each cistern and the water source assigned to serve it. Constraints (9) prevent the allocation of any cistern to a water source that is farther than the designated coverage distance (⁠$δ$⁠). Constraints (10) restrict the decision variables $xij$ to binary values. Constraints (11), (12) and (13) specify that nodes in $V1$ must be facilities, nodes in $V2$ may be facilities, and nodes in $V3$ cannot be facilities. Finally, constraint (14) ensures that variable w remains nonnegative.

In the second step of the proposed procedure, we apply a variant of the ALNS algorithm, originally developed by Pisinger and Ropke (2007) as LNS and further adapted by Erdoğan (2017). This step aims to compute the most efficient routes for multiple CVRPs, using the allocation results from the location-allocation model as input. The ALNS employs a set of removal (destroy) and insertion (repair) heuristics, which are adaptively selected at every iteration using a roulette wheel mechanism weighted by their historical performance. To navigate the solution space, the algorithm balances diversification, achieved by randomly removing customers from the solution, with intensification, which involves the reinsertion of customers and the application of four distinct local search operators: Exchange, 1-opt, 2-opt and Vehicle-Exchange. The algorithm’s objective function is structured to maximize the total profit gathered, offset by the travel costs, the fixed costs of vehicle use and penalties for any time window violations. However, when applied to the OCP, these time window constraints are disregarded, as water deliveries are permissible across the entire 6:00 a.m. to 6:00 p.m. window. Consequently, the constraints are streamlined to cover vehicle visit rules and the specifications of customers and vehicles. This includes ensuring all customers are visited exactly once by a single vehicle that must return to its water source, alongside respecting constraints for water flow conservation, sub-tour elimination and specific vehicle limitations.

The decision to keep the location–allocation and routing stages separate stems from the structural and computational differences between the two problems. The location–allocation stage was formulated and solved as an exact mixed-integer programming model to determine the optimal configuration of fixed facilities (water sources and wells), considering capacity and spatial coverage constraints. The routing stage, in contrast, was treated independently through a metaheuristic approach, which is more suitable for addressing the high combinatorial complexity and the operationally dynamic nature of water distribution by trucks. This separation ensures global optimality for strategic location decisions while maintaining flexibility and computational efficiency in generating feasible and high-quality routes, according to specific demand and water availability conditions in each scenario.

To assess the applicability of the proposed two-phase logistics strategy for delivering water to drought-impacted regions, we conducted a case study centered on the state of Rio Grande do Norte, located in Brazil’s Northeast. This region is part of the Brazilian semiarid zone, which is historically marked by chronic water shortages, high climate variability and limited infrastructure, making it an ideal context for testing emergency water distribution models. The analysis was based on data derived from the actual distribution practices under the Operação Carro Pipa (OCP). Our approach was evaluated by comparing its outcomes against both the historical data.

The data utilized encompassed 1,069 demand points distributed across 16 municipalities in Northeast Brazil, specifically within the state of Rio Grande do Norte, under the OCP operation. The area is served by five water sources – Neto Galvão, Kero Água, Mangabeira, Poré and Conceição. Figure 1 displays the locations of these springs alongside the demand points. These sources were selected based on their operational history and accessibility under OCP guidelines.

We used the OCP database to obtain the precise locations of the cisterns and the number of individuals served. Using a standard of 20 liters of water per person per day, annual demands were estimated, as droughts typically occur on a yearly basis. Distances between sources and demand points were obtained through Google Maps Distance Matrix API, with a coverage limit set at 250 km, in line with OCP’s operational constraints. This threshold was essential to realistically constrain routing decisions and to replicate the program’s field limitations.

Hydrogeological variables such as lithology, drainage density and fracture features were sourced from shape files from the Brazilian Geological Survey and processed using QGIS. These variables were vital for calculating groundwater occurrence probabilities using the logistics regression model adapted from Vieira et al. (2021).

Furthermore, average well flow rates were estimated at 10 m³/h, assuming an 8-hour daily operation, as per data from the 1st Construction Engineering Battalion. Based on this, the annual water supply capacity of each well was computed. The cost to establish an artesian well—under freshwater-only conditions – was estimated at US$3,596.70, based on available information. This cost estimation was considered in the model to enable cost-benefit comparisons between centralized distribution from existing springs and the deployment of new wells.

The OCP employs a calculation methodology based on the Transport Unit of Measure – TUM, as defined by equation (15). This equation incorporates the water truck capacity (Ca), the distance from each water source and its respective consumption site (Di), the number of trips required (Nt), and a road condition multiplier index (Mi) from Table 2. We assumed that all roads are paved (⁠$Mi=0.49$⁠) and the water truck capacity is equal to 12 m³. This methodology reflects a practical approach used by the Brazilian Army to estimate operational effort and transport costs:

We relied on data from the DRAI platform (available at Link to to cited articleLink to the cited article.) to obtain the drought composite index values by municipality. For our analysis, we selected 2019 as the base year, as it represents the most recent and complete data set available. Examining the drought index on a monthly basis revealed that November consistently showed the highest values across municipalities, signaling a dry period. Figure 2 illustrates the index values for the selected year, while Table 3 categorizes these indices for a clearer understanding. The index serves as a proxy for water stress levels, supporting decisions related to emergency supply deployment and prioritization of infrastructure investments.

Finally, we established a maximum of 385 potential wells, corresponding to locations with a probability of 50% or more of encountering groundwater. In a real-world scenario, this maximum would be limited by budget constraints. However, our model does not mandate the installation of all 385 wells; rather, it focuses on cost-effectiveness. Consequently, if the model identifies a solution requiring fewer wells, such an option would be deemed more financially beneficial. This allows the strategy to adapt flexibly to real conditions and resource availability, promoting economically viable and operationally scalable interventions in drought-prone regions.

This section presents the computational outcomes used to verify the reliability and consistency of the proposed approach. The location-allocation model was executed using AIMMS software on a system equipped with an Intel Core i7 processor and 8 GB of RAM, running a 64-bit Windows operating system. The optimization utilized the CPLEX 22.1 solver to address the mixed-integer programming (MIP) model. The lexicographically ordered minimization objective function was configured using AIMMS’s Generated Mathematical Programming, specifying a 10% relative tolerance between objectives. This means that each objective is optimized between the optimal solutions to the previous optimization problems. That is, for each objective, the relative tolerance specifies the maximum allowable deviation from the optimal value of that objective. The formulation involved a total of 547,600 variables, of which 546,860 were integers. The solver achieved optimal solutions in approximately 5,033.83 s. This computational effort highlights the model’s scalability and confirms its feasibility for large-scale real-world applications.

During the first phase, the model identified the optimal number and placement of wells, assigning each demand point to either a newly drilled well or an existing spring. The solution recommended the installation of 83 wells to supply 396 demand points, collectively benefiting 1,390 individuals. Figure 3 indicates the exact locations of these wells and which demand points they serve. The remaining demand was addressed by two of the existing springs: Neto Galvão, which serves 50 locations, and Poré, which serves the remaining 623. This allocation reflects a hybrid supply strategy that prioritizes cost-effective well deployment while maintaining the use of existing infrastructure, thus improving service coverage in remote areas.

The second phase employed the ALNS metaheuristic, proposed by Erdoğan (2017), to address the vehicle routing problem. For each identified water source, delivery routes were established to serve the associated demand points. This method was chosen due to its proven efficiency in solving large and complex routing problems under tight operational constraints. For instance, Figure 4 shows the delivery routes set up to serve the demand points in the municipality of Jucurutu.

Table 4 presents the total distance for the routes generated by the metaheuristic, considering the 83 wells, and compares it to the optimization conducted by Vieira et al. (2021) and the current operational metrics of the OCP. The first column of Table 4 lists the municipality names, and for each approach, we present the number of cisterns supplied (NC), the fleet size (V) and the total distance traveled per year. The final row of Table 4 summarizes the number of customers served, the fleet size, and the annual distance traveled for all the cases considered: the existing OCP operation, Vieira’s procedure and our proposed procedure.

According to Table 4, the proposed strategy reduced the total fleet size from 96 to 59 vehicles across the 16 municipalities. This reduction proved to be very similar to that obtained by Vieira et al. (2021). The improvement in the total distance traveled per year was significant, even compared with the results of Vieira et al. (2021). There was a 49.89% decrease in the total distance traveled annually in comparison with the current OCP operation and a 34.33% reduction compared with Vieira’s procedure. These results demonstrate not only improved logistical efficiency but also a substantial reduction in operational pressure on the fleet, potentially increasing vehicle lifespan and decreasing maintenance frequency. Moreover, such reductions contribute to lower carbon emissions, reinforcing the environmental benefits of the proposed strategy.

Table 5 compares the annual costs per municipality for the proposed procedure with those reported by Vieira et al. (2021) and the existing OCP operation. Cost estimates are based on transportation values used in Vieira et al. (2021), and well installation expenses are derived from data in Nunes et al. (2023). By incorporating both fixed and variable costs, the analysis captures the financial trade-offs between infrastructure expansion and operational efficiency, which are central to public policy and budget planning in water-scarce regions.

The first column of Table 5 lists the municipalities, whereas the subsequent columns detail the annual costs for water delivery for all the cases considered: the existing OCP operation, Vieira’s procedure and our proposed procedure. For the proposed procedure, Table 5 also includes the number of wells located (NW) in each municipality, along with their respective installation costs and transportation costs for the vehicle routes established to serve each area. The final row of Table 5 summarizes the total annual costs for all the cases, including the costs of well installation and water transportation, reflecting the contribution of the newly established wells. This detailed cost breakdown allows for better strategic planning and supports evidence-based decision-making regarding future investments in drought mitigation infrastructure and logistics.

Table 6 presents a detailed year-by-year cost comparison over a projected 10-year period, reflecting the expected useful life of the wells, including both installation and operational expenses, as well as cumulative saving to current OCP practices and Vieira et al. (2021)’s optimization approach.

In the initial year, the proposed procedure experiences deficits, primarily due to the installation costs of the wells. However, this expense is a one-time investment. From the second year onward, the financial outlook improves significantly as the annual transportation costs are reduced by half. This reduction enables the initial investment in drilling to be paid off by the end of the second year, compared with the current OCP operating costs, and by the end of the third year, compared with the costs that result from the procedure proposed by Vieira et al. (2021), leading to ongoing cost savings in the following years. Such economic dynamics demonstrate the long-term viability of the model, especially when applied in regions where water scarcity is a persistent issue and repeated annual interventions are required. Therefore, while the upfront costs present a challenge, the long-term benefits of the proposed procedure become evident over time. This transition from short-term deficit to sustained savings reinforces the strategic value of infrastructure investments in humanitarian logistics.

Furthermore, Table 6 highlights substantial cost savings achieved through our proposed procedure – approximately 39% compared to the current OCP operation and around 20% relative to the method proposed by Vieira et al. (2021). These results indicate that the proposed hybrid strategy not only improves operational efficiency but also contributes to budgetary optimization, making it a compelling alternative for public policies aimed at drought mitigation.

This study introduces a two-step methodology designed to enhance the distribution of water to drought-affected populations. In the first phase, a mathematical model was formulated to address the facility location and allocation of wells, identifying the optimal number and placement of these water sources while efficiently assigning demand points. In the second phase, the ALNS algorithm, adapted from the approach proposed by Erdoğan et al. (2019), was applied to solve the vehicle routing problem, enabling the estimation of fleet size and total travel distance for water delivery.

The method was tested through a case study involving water distribution in Brazil’s drought-prone semiarid region. Its performance was evaluated against both the current operational strategy adopted by the OCP and those reported by Vieira et al. (2021). Results indicate operational efficiency, including reductions in travel distance, fleet size and annual distribution costs. Such outcomes confirm both the reliability and the practical value of the proposed approach. In addition, the model succeeded in maintaining service levels while significantly reducing logistical burdens, which is crucial for long-term operational sustainability.

From the perspective of disaster response logistics, the approach offers valuable contributions. The observed cost savings have the potential to extend service coverage, enabling aid to reach a larger segment of the affected population. Moreover, the strategic installation of new wells reduces reliance on water transportation, thereby enhancing regional resilience to drought conditions. Although the methodology was tested in a specific geographic and operational context, its modular and adaptable structure makes it suitable for application in other regions facing similar challenges.

Given the projected increase in the frequency and intensity of disaster events due to climate change, the development and application of decision support tools—such as the one proposed in this study—are of critical importance. These tools enhance the ability of disaster-response managers to operate under uncertainty, allocate scarce resources efficiently, and maximize the coverage and effectiveness of humanitarian assistance. Moreover, incorporating geospatial and hydrogeological data into the optimization framework strengthens its predictive capacity, providing a robust basis for proactive planning.

In this context, we suggest a relevant avenue for future research. A promising extension of the current work would involve integrating the proposed facility location model with an ant colony optimization (ACO) algorithm for vehicle routing. This combined approach could be evaluated in terms of solution quality, computational efficiency and operational feasibility. The resulting performance metrics should be compared with those reported by Vieira, as well as with the baseline results established in this study. Such comparative analysis would help validate the robustness of different heuristics and guide their application in real-world emergency logistics planning. Another direction for future research, the integration of the two phases within a two-stage stochastic programming framework could be explored, allowing well location decisions to account for multiple drought scenarios, with vehicle routing decisions adapting to the realized conditions.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.