Nothing Special   »   [go: up one dir, main page]
Next Article in Journal
Data-Driven Wildfire Spread Modeling of European Wildfires Using a Spatiotemporal Graph Neural Network
Next Article in Special Issue
A Numerical Analysis of Premixed Hydrogen–Methane Flame with Three Different Header Types of Combustor
Previous Article in Journal
Forest Fire Prediction: A Spatial Machine Learning and Neural Network Approach
Previous Article in Special Issue
Investigation of the Coupling Schemes between the Discrete and the Continuous Phase in the Numerical Simulation of a 60 kWth Swirling Pulverised Solid Fuel Flame under Oxyfuel Conditions
You seem to have javascript disabled. Please note that many of the page functionalities won't work as expected without javascript enabled.
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
Fire
Volume 7
Issue 6
10.3390/fire7060206
fire-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite question_answer Discuss in SciProfiles thumb_up
...
Endorse textsms
...
Comment
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

All Lives Matter: A Model for Resource Allocation to Fire Departments in Portugal

by
Milad K. Eslamzadeh
1,*,
António Grilo
1,2 and
Pedro Espadinha-Cruz
1,2
1
UNIDEMI, Department of Mechanical and Industrial Engineering, NOVA School of Science and Technology, Universidade NOVA de Lisboa, 2829-516 Caparica, Portugal
2
Laboratório Associado de Sistemas Inteligentes (LASI), 4800-058 Guimarães, Portugal
*
Author to whom correspondence should be addressed.
Fire 2024, 7(6), 206; https://doi.org/10.3390/fire7060206
Submission received: 10 April 2024 / Revised: 8 June 2024 / Accepted: 12 June 2024 / Published: 18 June 2024
(This article belongs to the Special Issue Combustion and Fire I)
Browse Figures
Figure 1
<p>The PT-RAFD framework-2024, adapted from [<a href="#B9-fire-07-00206" class="html-bibr">9</a>].</p> "> Figure 2
<p>The accessible variables (in green) of the total cost of fire in Portugal.</p> "> Figure 3
<p>(<b>a</b>) The agent-based model implemented in AnyLogic to simulate the travel and response time between PT-FDs and the incidents. (<b>b</b>) Expanded view of an FD (CBV Barcarena) in Lisbon, and utilization of roads by its fire engines.</p> "> Figure 4
<p>The degree of efficiency of PT FDs before and after using PT-RAFD model.</p> "> Figure 5
<p>Number of times efficient FDs appeared as targets for non-efficient FDs in the final dataset, (<b>left</b>): RAFD with using C5; (<b>right</b>): RAFD with relaxing C5.</p> "> Figure 6
<p>Efficiency impact of RAFD with and without C5: (<b>left</b>)—FDs’ efficiency changes post-RAFD implementation; (<b>right</b>)—comparison of RAFD methods on FDs’ efficiency improvement.</p> "> Figure 7
<p>Efficiency changes at the district level with and without using the C5 in PT-RAFD.</p> "> Figure 8
<p>Portuguese districts’ efficiency changes: (<b>left</b>): before RAFD; (<b>middle</b>): after RAFD by using C5; (<b>right</b>): after RAFD by relaxing C5.</p> ">
Review Reports Versions Notes

Abstract

:
Optimizing Resource Allocation in Fire Departments (RAFD) is crucial for enhancing Fire Protection Services (FPS) and ultimately saving lives. Efficient RAFD ensures that fire departments have the necessary resources to respond effectively to emergencies. This paper presents a method for optimizing RAFD based on performance assessment results, examining its impact on Fire Department (FD) efficiency in Portugal. Evaluating data from 353 FDs, two RAFD optimization methods were assessed: one adhering to Portuguese regulations and constraints, such as budget allocation limitations, and another without such constraints. Integrating a slack-based data envelopment analysis model and mixed-integer linear programming, the study found that incorporating FD efficiency scores in RAFD improved overall efficiency at national, district, and FD levels. While adherence to Portuguese regulations led to balanced resource allocation and a 4% performance improvement at the national level, relaxing constraints yielded an 8% improvement, albeit with potential performance deterioration in some FDs. The detailed budget and efficiency metric analysis provided in this paper offers actionable insights for fire protection services enhancement. This underscores the importance of diverse optimization strategies to enhance FD efficiency, with implications for decision-makers at the Portuguese National Authority for Emergency and Civil Protection and similar organizations globally.

1. Introduction

Providing efficient Fire Protection Services (FPS), whose main objectives are to reduce the number of fire incidents and casualties, has always been an important part of public management. It has been in the spotlight due to its indisputable importance to the safety of both people and the environment [1]. Hence, ensuring the perpetual assessment of Fire Department (FD) performance is a compelling imperative for nations and local governing bodies [2,3]. This responsibility assumes a formidable dimension for decision-makers within FPS, owing to the dynamic and evolving nature of societies and the limited financial and technical resources for FPS.
Concurrently, the challenge of providing efficient FPS is rooted in the critical role of Resource Allocation in Fire Departments (RAFD) and the strategic placement of fire stations [4,5]. Therefore, allocating limited resources among FDs to provide efficient FPS in minimum time and cover maximum demands becomes a pivotal goal for FDs, and achieving this goal is contingent upon the judicious selection of RAFD methods and variables [6,7,8].
Due to the essential role of RAFD in improving the performance of FDs in allocating the limited FPS resources (e.g., budget, firefighters, fire engines) among the FDs, the RAFD has been studied at the local or national level [9]. Some of the studies resulted in providing national RAFD models for different countries or cities (e.g., see research about the RAFD methods in Chile [10], Taiwan [11], the UK [12], China [13], India [14], the US [15], South Korea [16], Iran [7], Ukraine [17], and Canada [18]).
To obtain the state of the art in this field, some of the recent RAFD literature in different countries is reviewed in this section. A recent study in Chile [10] used Integer Programming (IP)—one of the most common RAFD models [9]—and Geographic Information System (GIS) analysis to optimize the number of FPS vehicles and their locations based on maximizing the coverage of expected FPS demand in FDs. Balancing the ratio of firefighters and populations of the cities in Thailand to provide more efficient FPS was the objective of a study [11] that applied an omit resource approach for human resource allocation and Data Envelopment Analysis (DEA) for FPS performance assessment
Like other European countries, the FPS authority in Portugal—the National Authority for Emergency and Civil Protection (ANEPC))—faces challenges in delivering efficient fire protection services promptly [4,19,20]. This task of ensuring timely FPS delivery is a common challenge for the ANEPC, reflecting broader concerns shared by nations dealing with the complexities of urban fire management; to address it, multiple studies have been conducted in Portugal, including on optimizing the locations of the Portuguese fire stations [20], a model for the Fire Department Performance Assessment (FDPA) in Portuguese FDs [8], analyzing the urban fire in Portugal [19], assessing and mitigating fire risk in the Portuguese cities [21,22], urban resilience measures in Portuguese districts [23], and characterizations on the urban fire incidents in Portuguese cities [24].
However, to the best of our knowledge, there is no research on Resource Allocation in Fire Departments (RAFD) in Portugal that provides a model for allocating constrained financial and technical resources of the ANEPC among the Portuguese FDs. Therefore, the objective of this research is to develop an RAFD model for Portugal that improves the performance of Portuguese FDs in urban and residential areas.

Portuguese Law for RAFD

According to the publicly published law N.94/2015 in Portugal [25], the referenced budget (RB) of the ANEPC in each year should be allocated to the PT FDi (i ϵ I = [1, …, N]) based on Formula (1):
R B F D i = 10 % R B 1 N + 20 % R B C o v e r e d _ A r e a F D i T o t a l _ C o v e r e d _ A r e a s + 20 % R B P o p u l a t i o n F D i T o t a l _ P o p u l a t i o n + 20 % R B R i s k _ I n d e x F D i T o t a l _ R i s k _ I n d e x + 10 % R B F i r e _ I n c i d e n t s F D i T o t a l _ F i r e _ I n c i d e n t s + 10 % R B F i r e f i g h t e r s F D i T o t a l _ F i r e f i g h t e r s
While the Portuguese RAFD law aligns with the general RAFD framework by providing coefficients for the socioeconomic and spatiotemporal characteristics of PT FDs [9], it does not incorporate the performance of the fire departments into any aspect of the formula. Given the significance of FDPA within the RAFD context [2,4,13,14], the research question endeavors to ascertain whether integrating FDPA results into RAFD in Portugal will enhance the efficiency of the FDs.
While past research in the US has looked at RAFD on a statewide level [15], one of the contributions of this study is that it takes a broader perspective by exploring a nationwide FD-level RAFD and confirming its positive impact on FD performance. This sets the current study apart by offering a detailed understanding of RAFD dynamics at different levels. This study also significantly contributes to the management and distribution of limited resources among Portuguese FDs, particularly their financial resources. The aim is to enhance FD performance in delivering FPS. The RAFD model and findings of this study can assist FPS decision-makers in improving FD performance by facilitating efficient resource allocation. This, in turn, helps FDs more efficiently use financial resources to safeguard lives and properties. Additionally, the findings can inform investigations into optimizing human resources, vehicles, and the size and location of FDs and fire stations to improve overall performance.
Moreover, this study provides valuable insights for policymakers and analysts in the field of fire protection and safety, offering strategies to mitigate economic costs and safeguard civilian and firefighters’ lives. The findings serve as valuable references for governments and governmental organizations, aiding them in making informed budgetary and policy decisions related to fire protection.
A significant contribution of this study is the adaptation of the general RAFD framework to the Portuguese context. This adaptation involves utilizing available and accessible data categories specific to Portugal and employing advanced methodologies such as Agent-Based Modeling (ABM) [26] to simulate an important input variable, response time. Furthermore, this study incorporates the value statistical life (VSL) [27] for accurately calculating the fire cost value, a key output variable essential for comprehensive analysis. Additionally, the RAFD framework employs Mixed-Integer Linear Programming (MILP) [28], enabling a thorough examination of RAFD dynamics within the context of Portugal. These methodological advancements ensure a robust and tailored approach to understanding and optimizing financial resource allocation for Portuguese FD.
Further explanation of these methodologies is provided in detail across the next four sections: Section 2 provides an overview of the RAFD literature; Section 3 outlines the research methodology and expounds upon the ABM and MILP models; Section 4 presents the empirical findings and associated recommendations specific to the Portuguese RAFD landscape. After this, Section 5 undertakes an in-depth examination and discussion of the research findings. Ultimately, this paper culminates with a comprehensive conclusion in Section 5. The abbreviations utilized within this paper are consolidated in Table A1 in the Appendix A.

2. The Literature Review

RAFD has been studied from various perspectives, including the location and allocation of facilities and vehicles, the placement and deployment of firefighters, and budget distribution. These studies employ diverse models, objective functions, and analytical components. Table 1 provides an overview of the reviewed literature in this section. All the papers study the RAFD, and in Table 1, they are categorized by key criteria: type of allocation (vehicle, firefighter, and budget), the FDPA and RAFD models used, the application of GIS and simulation methods, considerations of equity in the RAFD, the inclusion of socioeconomic and spatiotemporal variables, and the presence of case studies. According to the results of the literature review and aligned with the findings of previous studies [4,9], DEA and Linear Programming (LP)—specifically MILP—are the most commonly used methods for FDPA and RAFD, respectively.
Among the reviewed papers, six controlled the effect of RAFD on FD performance by conducting FDPA analysis; however, none of these studies integrated efficiency scores directly into the RAFD optimization process as recommended by the general RAFD framework [9]. Melolidakis (1993) [29] utilized game theory to provide fire stations with bargaining power for acquiring more vehicles using the Shapley–Shubik (S–S) power index. Lan et al. (2007) [2] applied a Multi-Stage Resource Allocation Approach to allocate a limited number of firefighters to stations while improving the stations’ efficiencies, controlled by DEA. In their later study in 2011 [11], Lan et al. applied DEA to evaluate organizational performance and determine the production efficiency of fire services in Taiwan. They used a total efficiency-based scale approach to suggest an ideal human resource allocation model. Fang et al. (2008) [30] employed a two-stage DEA model to allocate firefighters and budget between fire stations in China to improve performance. They used the current number of firefighters and the fire stations’ expenses as inputs, and the proportion of lives saved to lives at risk and the number of emergency calls as outputs, aiming to find the best combination of inputs that produce the best outputs. Recently, Lim et al. (2020) [16] used a revised two-stage DEA model with budget constraints for FDPA in South Korea, using firefighters and fire engines as inputs and damage reduction and rescued lives as outputs.
Table 1. Summary of reviewed RAFD papers, including methods and variables. ReTyp: Resource type, EqM: Equity Method, Sim: Simulation Model, SoEco: Socioeconomic variables, SpTe: Spatiotemporal variable, FF: Firefighters, Veh: Vehicles, Bud: Budget.
Table 1. Summary of reviewed RAFD papers, including methods and variables. ReTyp: Resource type, EqM: Equity Method, Sim: Simulation Model, SoEco: Socioeconomic variables, SpTe: Spatiotemporal variable, FF: Firefighters, Veh: Vehicles, Bud: Budget.
PaperReTypFDPA
Model		RAFD
Model		EqMGISSimSoEcoSpTeCase
Study
Schilling et al., 1979 [31]Veh-LP---YesYesUS
Marianov et al., 1992 [32]Veh-LP---YesYes-
Melolidakis, 1993 [29]Veh-S–S indexYes----Greece
Jayaraman et al., 1995 [33]Veh-LP----Yes-
Revelle et al., 1995 [34]Veh-LP---YesYes-
Athanassopoulos, 1998 [35]FF and VehDEATABRAYes--Yes-UK
Peace, 2001 [12]Veh-Risk-based---YesYesUK
Araz et al., 2007 [36]Veh-LP---YesYes-
Lan et al., 2007 [2]FFDEAMSRAA-----Taiwan
Huang et al., 2007 [28]Veh-LP-YesYes-YesSingapore
Cheu et al., 2008 [37]Veh-LP----YesSingapore
Fang et al., 2008 [30]Bud and FFDEADEA---Yes-China
Lan et al., 2009 [38]FFDEAMSRAA-----Taiwan
Cheu et al., 2010 [39]Veh-LP----YesUS
Lan et al., 2011 [11]FFDEATEBSA---Yes-Taiwan
Chevalier et al., 2012 [40]FF and Veh-LPYesYes-YesYesBelgium
Chalfant et al., 2016 [41]Veh-Distance-based---YesYesUS
Perez et al., 2016 [42]Veh-LP-Yes--YesChile
Wang et al., 2016 [43]Veh-LP----YesChina
Perez et al., 2016 [44]Veh-LP----YesChile
Alavi et al., 2018 [7]Veh-LP-----Iran
Yeboah & Park, 2018 [18]Veh-Risk-based----YesCanada
Kumar et al., 2019 [14]Veh-LP---YesYesIndia
Behrendt et al., 2019 [15]Bud-LPYes--Yes-US
Kovalenko, 2019 [17]Veh-LP---YesYesUkraine
Lim et al., 2020 [16]BudgetDEADEA-----Republic of Korea
Maqbool et al., 2020 [45]Veh-LP-YesYes-YesPakistan
Kumar et al., 2020 [46]Veh-LP---YesYesIndia
Rodriguez et al., 2020 [10]Veh-LP-Yes-YesYesChile
Liu et al., 2021 [47]Veh-Risk-based-Yes--YesChina
Ghasemi et al., 2021 [48]Veh-Simulation--Yes-YesIran
Hajipour et al., 2022 [49]Veh-LP----Yes-
Ming et al., 2022 [13]Veh-LP--Yes-YesChina
Rodriguez et al., 2023 [50]Veh-LP-YesYesYesYesChile
Liu et al., 2023 [51]Veh-Time-based-Yes--YesChina
This PaperBudDEALPYesYesYesYesYesPortugal
The six aforementioned papers are the closest group of reviewed studies to this research since they utilize both FDPA and RAFD analyses in alignment with the general RAFD framework, which serves as the reference framework for this study. A detailed analysis of these papers has been conducted, controlling for other important characteristics based on the reference framework.
Spatiotemporal variables (e.g., traffic, response time, distances) are crucial for FDPA analysis [9], and while many reviewed papers include them, none of these six studies incorporated spatiotemporal variables into their FDPA or RAFD analyses. When important variables like spatiotemporal data are unavailable, some of the reviewed papers used simulation and GIS [28,40,44,50] to generate or collect the necessary information. However, none of the six papers utilized GIS or simulation to include spatiotemporal variables in their analyses. Another critical topic in RAFD studies is the use of equitable resource distribution among FDs to ensure a minimum level of FPS efficiency [15]. Portuguese law also mandates the ANEPC to incorporate equity in the RAFD process [25]. Despite this, only one of the six studies [35] incorporated equity considerations in its RAFD model.
As highlighted in the last row of Table 1, this research comprehensively addresses several key areas, marking significant novelties in the field. It utilizes MILP for RAFD, GIS, simulation for producing response time values, and DEA for FDPA. Moreover, it incorporates equity considerations and includes socioeconomic and spatiotemporal variables in its formulation, setting it apart from previous research by integrating these diverse elements into a cohesive analysis framework. Additionally, this study is grounded in a detailed case study conducted in Portugal.

3. Research Methodology

This study adheres to the RAFD method’s structured four-stage approach proposed by Eslamzadeh et al. (2022, 2023) [8,9]. A pivotal facet of this methodology is the incorporation of the RAFD framework [5], serving as a guiding framework for the selection of input and output variables, as well as the methodology applied in FDPA. Illustrated in Figure 1, the research methodology unfolds through four sequential stages encompassing data gathering, processing, analysis, and reporting. Subsequent sections will delve into each of these stages in greater detail. To address the identified limitations in the RAFD framework’s original implementation and enhance its applicability within the Portuguese context, this study proposes four key recommendations. These are important for improving data collection accuracy and completeness, integrating efficiency metrics into the RAFD process, and expanding resource allocation adjustments. By incorporating these recommendations, decision-makers at the ANEPC and other FPS authorities can optimize their resource allocation strategies, leading to better performance and increased effectiveness of fire departments. These recommendations are grounded in the need to refine data collection practices, ensure comprehensive assessments, and adopt a more flexible approach to resource distribution, ultimately fostering a more robust and efficient firefighting system in Portugal. The graphical structure illustrating the PT-RAFD framework is shown in Figure 1, which has been adapted from the original model presented in [9].

3.1. First Stage: Data Gathering

The initial phase of this study, data gathering, was dedicated to acquiring essential information from various public and private sources. Since urban (residential) fires require FPS approaches that are completely different from wildfires [15], the focus of this research is on urban fires and allocating resources to the FDs that are providing FPS to the residential areas of Portugal. According to the FDPA framework [9], four categories of data are required for RAFD analysis: incident, spatiotemporal, travel time, and socioeconomic.
  • Category 1, response and operation time data: The duration values in the ANEPC dataset were the vehicle’s idle time, not the incident response time. In other words, the provided duration was the time between a vehicle’s departure from the station and its return, not until its arrival at the incident location. Therefore, an ABM has been used to simulate the interaction between PT-FDs, vehicles, and fire incidents to find the response time based on geographical data. Further details about the ABM are provided within the analysis stage section;
  • Category 2, PT census and economic data: the public database of the National Institute of Statistics of Portugal [52] was utilized for accessing Portuguese data, including the Gross Reported Income (GRI), and population at district level in 2020, and the public database of the World Bank [53] for the Gross National Income (GNI) per capita of US and PT;
  • Categories 3 and 4, PT FDs, incidents, and spatiotemporal data: The ANEPC played a crucial role in providing these two categories of information regarding PT-FDs and 72,176 urban incidents over the years 2012–2020. Considering the RAFD framework [9], the majority of the required data for RAFD analysis were included in the ANEPC’s datasets, which are the FD’s number of firefighters, vehicles, locations, annual governmental budget, covered area, and incidents’ times, locations, durations, and number and severity of injuries. However, the fire cost, which is one of the important metrics for the RAFD [9,15], was not available in the ANEPC’s databases at the time of this research.
The cost of fire is defined by the US National Fire Protection Association (NFPA) [54] as the “total cost of fire as the collective of all net expenditure on fire protection and all net losses due to fire incidents”. As depicted in Figure 2, and according to the NFPA, the cost of fire is a mixed metric that consists of active and passive fire protection expenditures such as fire insurance, direct human loss and property damages, and indirect losses due to nonphysical damages and interruptions in production and service provision.
Recommendation 1: The fire cost is one of the undesirable outcomes of the FPS and fire incidents that plays a key role in FDPA and RAFD analysis [9]. It is a mixed metric that uses the components in Figure 2. This study suggests that PT FDs record and update the components of the total fire cost.
Although the ANEPC’s datasets provided some of the required metrics for the cost of fire (e.g., FD expenditure: operation, human resources, vehicles, and infrastructure, direct human loss: number of deaths and severity of injuries), the financial costs of human casualties are still the missing components of the fire cost in Portugal. A common approach for calculating the cost of human casualties is using the VSL [15]. As mortality risk decreases across the population, the incidence of fatalities diminishes, resulting in an overall reduction in deaths. The quantification of these risk reductions is commonly assessed through the metric known as VSL, which represents the monetary value attributed to each expected life saved [55]. Formula (2) can be used for calculating the VSL in different countries, here Portugal, based on the US-VSL [27]:
VSLPT = VSLUS × (Average.IncomePT/Average.IncomeUS)Income.Elacticity
The 2020 VSLUS value, according to the US Department of Transportation was USD 11.6 million. For the Average.Income of the US and PT, the GNI per capita has been used [27], and according to the World Bank data for 2020, the GNI per capita for the US was USD 64,650, and for PT, it was USD 21,850. Since the Income.Elasticity in Portugal was not publicly available, it was considered 1.00 as suggested for international countries [27]. Therefore, the 2020 VSL in Portugal was USD 3,920,495, and this value will be the basis for the further calculation of the cost of fire and potential loss in Portugal in this research.

3.2. Second Stage: Data Preprocessing

The datasets acquired from the ANEPC exhibited minor discrepancies, characterized by instances of incomplete, incorrect, missing, and outlier values. Following an in-depth analysis of FDs and incident data spanning from 2012 to 2020 and subsequent consultation with the ANEPC’s experts, it was determined that the most comprehensive dataset was from the year 2020.
Although there are municipal, private, and voluntary FDs providing FPS in Portugal, the main incident dataset consisted of 7038 fire incidents that occurred in 410 voluntary FDs in Portugal because the financial data of the municipal and private FDs were not accessible. The incident and FD data were fragmented across multiple datasets, containing intricate details deemed unnecessary for the scope of this study. Therefore, a meticulous data preprocessing protocol was implemented, encompassing cleansing, integration, reduction, and transformation steps. These measures were undertaken to ensure the integrity and suitability of the data for subsequent evaluation and analysis processes [56,57]. After the data processing stage, the recorded data of 5698 incidents in 353 FDs with all the necessary details was aggregated into one dataset for the analysis stage. Further explanations of the preprocessing steps are provided in Table 2. This dataset served as the foundational basis for the RAFD analysis conducted in this research endeavor.
Recommendation 2: The reliability and validity of analyses like RAFD or FDPA are dependent on the accuracy and completeness of the referenced datasets. This underscores the importance for FD commanders and firefighters to diligently record incident and managerial information with the utmost precision and thoroughness. This is an important practice to prevent any potential loss of required data for future FDPA and RAFD analyses.

3.3. Third Stage: Analysis

The PT-RAFD model is based on the general RAFD framework [9], and uses the following three models:
  • The ABM for simulating the interactions between FDs and incidents and gathering the response time and suppression operation durations;
  • The Data Envelopment Analysis (DEA) for conducting the PT-FDPA analysis and calculating the efficiencies of PT-FDs;
  • The MILP for finding the optimized version of the RA that minimizes the cost of fire and improves the performance of PT-FDs;
  • The ANEPC’s experts and decision-makers had the responsibility of validating and confirming the reliability of the analytical process and findings of this study. This expert group consisted of the former director of the ANEPC and the current dean of Portugal’s National School of Firefighters, the ANEPC’s national senior chief technician, and two chief commanders of FDs.

3.3.1. Agent-Based Modeling (ABM)

ABM is a computational technique that models the behavior and outcomes of a complex system by simulating the autonomous agents, such as individuals or organizations, that act and interact within it. ABM can represent the diversity, adaptation, and emergence of the system through the agents’ rules and behaviors. To find the travel time between PT-FDs and the incidents, a model with four agents has been created, which includes the FD, vehicle, incident, and demand.
Illustrated in Figure 3a,b, the travel time between the station and incident locations was obtained by simulating the interactions between PT-FDs and the incident location. The ABM consisted of four agents, i.e., the FD, vehicle, incident, and demand, and was implemented on actual road maps of Portugal within AnyLogic software (Version 8.8.1) [58].
The average speed of fire engines is set at 45 km/h [37]. Although the current computation does not incorporate specific traffic regulations or congestion scenarios due to computational constraints, the tool could be readily updated to accommodate such factors. The ABM ran with all the 2020 incidents, and the obtained response times were added to the incident record for further FDPA and RAFD analysis.

3.3.2. Data Envelopment Analysis (DEA)

This stage began with analyzing the performance of the PT-FDs in accordance with the PT-FDPA model [8] using a slack-based DEA with the variable return to scale format that was output-oriented. The DEA model creates a frontier line from the best-performing FDs (decision-making units) and considers all the provided desired or undesired input and output variables. Then, it compares the FDs with the frontier group and provides the efficiency of each FD in comparison to the target FDs on the frontier line, and the slacks are the input excesses and output shortfalls of the FDs.
Tone (2001) [59] proposed the Slacks-Based Measure (SBM) version of the DEA to solve this deficiency. The SBM model differs from traditional radial efficiency models by considering all slack variables in the assessment of efficiency [59,60]. The SBM model allowed us to simultaneously conduct FDPA and calculate the slacks, representing excesses of the input and shortfalls of the output [8].
Let FD = {FD1, …, FDn} present a set of n FDs, each with i inputs and j outputs. X and Y denote the input and output variables of the reference set FD, respectively, with P defining the production possibility set for FD. For an FD with m inputs and s outputs—denoted by a pair of nonnegative vectors (x, y) where x ∈ R + m are the inputs vector and y ∈ R + s are the outputs vector—the SBM efficiency score can be defined as follows [8]:
f * x , y = MIN λ , s − , s + ⁡ f x , y , s − , s + 1 − 1 m ∑ i = 1 m s i − x i / 1 − 1 s ∑ j = 1 s s j + y j
s . t . x = X λ + s −
y = Y λ + s +
λ ∈ R + n , s − ∈ R + m , s + ∈ R + s ,
where vectors s + and s − represent inefficiency slack vectors [61]; f * x , y is the SBM efficiency score assigned to a new FD with input–output pair (x, y). According to Tone (2001) [59], an FD is deemed efficient if f * x , y equals one and the optimal slacks s + * and s − * are zero for every optimal solution [8]. The SBM DEA method has been used for PT-FDPA with multiple nonnegative desired inputs and multiple nonnegative undesired outputs; however, the FDPA evaluators have more alternatives according to their objectives [4]. The weighting of inputs and outputs was treated equally, as recommended by an expert group, and set to one to maintain their values. The nonnegative desirable inputs in the model encompassed the financial budget of the fire departments, along with the counts of vehicles and firefighters. Conversely, the nonnegative undesirable outputs included the total number of incidents attended by the fire departments, the total cost of fires, and the overall duration of fire incidents. Employing an output-oriented and slack-based Data Envelopment Analysis (DEA) model, this study utilized the DeaR-Shiny online solver [62], and the primary objective function of this model was to minimize the cost of fire. To ensure consistency and reliability, all inputs and outputs were assigned a uniform weight of one, maintaining the potency of their current values, as validated by the expert group. For further details about the slack-based DEA model and PT-FDPA, please refer to Eslamzadeh et al. (2023) [8]. The DEA results are provided in Section 3.

3.3.3. Mixed-Integer Linear Programming (MILP)

The MILP, as the most frequent RAFD method [9], has been implemented for RA optimization in PT FDs. Let us assume the following:
  • n is the number of FDs that are evaluated with respect to one another;
  • t is the reference year;
  • V is the value statistical life;
  • li is the (≥0) value of the actual loss in FDi (i = 1, …, n);
  • ci is the (≥0) value of the total cost of fire in FDi;
  • fi is the efficiency of FDi where (1 ≥ fi > 0);
  • bi is the (≥0) value of the financial budget of FDi.
The objective function of the model is to minimize the total cost of fire Q, and the Gurobi solver (http://www.gurobi.com, accessed on 15 September 2023) has been used to solve it. As discussed in the previous stage, Q consisted of the expenditures of active and passive protection and direct and indirect losses, and the VSL is a measure for converting the fire casualties to a financial metric.
Similarly, the value of statistical injuries [54] is a similar metric that provides coefficients for calculating the cost of injuries to fire based on the severity of the injuries (minor = 0.003 V, moderate = 0.047 V, serious = 0.105 V, severe = 0.266 V, critical = 0.593 V, and unsurvivable = 1 V). In the ANEPC’s datasets, four categories of casualties were provided: number of deaths, critical, serious, and minor injuries. Therefore, as shown in Table 3, the direct or actual loss of fire in Portugal was calculated from the number of fire casualties in a particular FDi i ϵ I during the year 2020 by using Formula (4):
li = (deaths × V) + (critical_injuryi × 0.593 V) + (serious_injuryi × 0.105 V) + (minor_injuryi × 0.003 V)
The total cost of fire in FDi is the sum of the actual loss and the total expenditure of the FDi provided by the ANEPC. However, considering the performance of the FDs, the degree of their efficiency has a direct effect on the RAFD efficiency [4,8]. Therefore, with the confirmation of the expert group, the inefficiency of the FDs (1 − fi) calculated by the slack-based DEA model of FDPA [8] was added to the total cost of the FDi. In this case, the budget of the efficient FDs will remain the same but the inefficient FDs will receive more budget to help them take corrective action in the next financial year. Therefore, the total cost of fire is ci = li + (1 − fi).bi. After calculating the total cost of fire of the FDs, the MILP functions and constraints will be as follows:
MIN ⁡ C = ∑ i = 1 n c i = ∑ i = 1 n l i + 1 − f i . b i
s . t . ∑ i = 1 n c i = 80,000,000 ∀ i = 1 , … , n ;
The decision factor of MILP is the FD’s financial budget (bi), and its objective function model is to minimize the total cost of fire C = {c1, …, cn} by optimizing the financial resources F = {f1, …, fn}. The following constraints limit the total allocatable resources to EUR 80 million, according to the ANEPC total budget for 2020. Therefore, the MILP will try to allocate the budget and will keep the total sum of the allocated budget equal to EUR 80 million.
0.95 b i t ≤ b i t + 1 ≥ 1.1 b i t ( C 5 )
Constraint 5, denoted as C5 for clarity throughout the paper, complies with the RAFD law in Portugal [25], where the total allocated budget to FDi in the new year should be within 95% to 110% of its budget in the last year. Although the expert group confirmed the use of constraints and inefficiency values in the PT-RAFD model, the model will be run both with and without C5, incorporating both efficiency (fi) and inefficiency (1 − fi) to verify changes in FDs’ efficiencies without limiting the optimization system to Portuguese legal allocation boundaries.
In summary, the PT-RAFD model consisted of three important steps: Firstly, leveraging ABM to determine travel times between FDs and incidents (i.e., response times) as one of the inputs of the FDPA analysis. Secondly, employing DEA for FDPA analysis to assess FD efficiencies, integrating response times alongside financial and technical inputs as well as undesirable outputs. Lastly, employing MILP to optimize the allocation of the ANEPC’s resources among FDs and incorporating FD efficiencies into the actual cost of fire to minimize overall expenses. To validate the results, the previous financial budget of FDs was replaced with the recommended budget by the PT-RAFD model, and their performance with the new budget was re-evaluated using the FDPA model. All the results were controlled and verified by experts from the ANEPC, ensuring the reliability and applicability of the findings.

3.4. Fourth Stage: Reporting

In the final stage of the PT-RAFD framework, the findings of the research are synthesized and presented to ANEPC decision-makers. This pivotal stage serves as a conduit for communicating the results of the PT-RAFD model, allowing decision-makers to gain valuable insights into the performance of PT FDs and FPS. Section 4 of the research outlines the empirical findings derived from the PT-RAFD model, and Section 5 delves into detailed discussions surrounding these findings, providing nuanced insights and actionable recommendations for improving FD and FPS performance. The overarching goal of the reporting stage is to empower ANEPC decision-makers to undertake corrective actions within their strategic framework for RAFD. By leveraging the insights gleaned from the PT-RAFD model, decision-makers can enact informed strategies to enhance FDs and FPS performance, ultimately contributing to the safety and well-being of communities across Portugal.

4. Findings

This section provides and discusses the results of the analysis stage to provide an answer to the research question and shows that integrating FDPA results into RAFD in Portugal will enhance the efficiency of the FDs. The analysis stage commenced with the performance evaluation of 353 FDs in Portugal using the FDPA model [8]. Subsequently, three rounds of RAFD optimization were performed using MILP.
The first round integrated the inefficiencies of the FDs (1 − fi) and C5, which stipulates the budget change threshold mandated by Portuguese law. The second round relaxed this constraint, allowing MILP to allocate resources without any limitations. In the third round, both C5 and the efficiency (fi) were directly incorporated into the optimization process. In the RAFD methods, with and without C5, the inefficiencies from the previous year (ci = li + (1 − fi).bi) were utilized in the RAFD objective function.
Following each round, the FDPA analysis was conducted to assess changes in the FDs’ efficiency scores using different RAFD methods. Notably, the third RAFD method led to the deterioration of performance in 115 FDs and was thus excluded from further analysis and discussion. Table A2 in the Appendix A presents the performance scores for all Portuguese FDs based on three FDPA analyses: their current performance score, their performance score after budget reallocation using C5 in the RAFD optimization, and their performance score after budget reallocation without C5 in the RAFD optimization.
As illustrated in Figure 4, after conducting two runs of the PT-FDPA model—one with and one without C5—and subsequently verifying efficiency using the FDPA model, the results indicated that while optimizing budget allocation within the confines of Portuguese law improved the overall efficiency of FDs from 0.5037 to 0.5137, it did not change the number of efficient FDs. However, the second run of the model, which involved relaxing C5 and allowing the MILP to optimize budget allocation to minimize the total fire cost of FDs, yielded even more promising outcomes. Not only did the average efficiency of FDs improve to 0.5335 but there was also a substantial increase in the number of efficient FDs from 16 to 22.
The results of the PT-FDPA model offer a clear response to the research question, demonstrating that incorporating FDPA results and efficiencies of PT-FDs in RAFD leads to enhanced performance of FDs in Portugal. These results indicate that utilizing FDs’ efficiency for optimizing the RAFD notably enhances their performance. However, considering C5, which mandates keeping changes between 95% and 110% of their last-year budget, it is evident that the RAFD primarily enhances the performance of low-efficient FDs while maintaining the performance of FDs with higher degrees of efficiency unchanged. This suggests that the RAFD model effectively targets areas where improvements are most needed, ensuring efficient allocation of resources while preserving the performance of already efficient FDs.
On the contrary, relaxing C5 allowed the PT-RAFD model to optimize the budget primarily based on last year’s efficiencies, allocating a larger share of the budget to low-performing FDs and less to more efficient ones, aiming to maximize overall efficiency; consequently, improvements were observed across almost all FDs. However, it is worth noting that while the differences between FDs’ last-year and optimized budgets were generally within ±30% of the last year’s budget, there were instances with higher percentage changes.
The results of the analysis stage highlight efficient FDs as target points for other FDs to improve their performance. The slack-based Data Envelopment Analysis (DEA) within the FDPA model identifies the variables and degree of improvement necessary for each non-efficient FD to reach the target point. Figure 5 illustrates the frequency with which a specific efficient FD is selected as a target for a non-efficient FD in both runs of the RAFD and FDPA models.
In the next section, the findings will be thoroughly investigated and discussed, providing detailed insights into the results obtained. Additionally, recommendations will be provided for FPS decision-makers based on the analysis conducted.

5. Discussion

This section will explain the implications of the findings and offer actionable suggestions for improving the performance of PT FDs. As depicted in Figure 6 and detailed in Table 4, analysis reveals that incorporating C5 in the PT-RAFD model—limiting RAFD changes between 95% and 110% of FDs’ last-year resources—does not degrade the efficiency of any FDs while enhancing the performance of 47% of FDs (165 out of 353). Conversely, relaxation of C5 improves the efficiency of over 60% of FDs (213 out of 353), though it is accompanied by deterioration in 125 FDs. Moreover, direct comparison shows that the relaxation method yields higher improvement in the efficiency of 181 FDs but lower results for 157 FDs compared to including C5. These findings suggest that while optimized RA can enhance performance for many FDs, it may also incur cost deterioration for some. Given that Portuguese RAFD law emphasizes socioeconomic and spatiotemporal characteristics of FDs, relaxing C5 may optimize RAFD without due consideration of these factors, leading to improved performance for most FDs at the expense of efficiency for some.
Recommendation 3: Incorporate efficiency as a variable in the national RAFD Formula (1) within Portuguese Law. Conducting RAFD optimization based on FDPA results will enable FPS decision-makers to comprehensively assess different RAFD strategies and select the most suitable option based on its impact on FD efficiency.
On the district level, as shown in Figure 7, the results of the PT-RAFD model under C5 demonstrate improvements across all PT districts; however, upon relaxing C5, while many districts experience significantly higher efficiency increases, there is an overall decrease in efficiency in five districts: Aveiro, Beja, Braga, Porto, and Santarém. This indicates that although removing C5 leads to considerable positive changes in PT-FDs’ efficiency levels, certain districts see a negative impact on their FPS performance due to the new budget allocation. This underscores the need for attention from the ANEPC and FPS decision-makers in Portugal to establish an optimal constraint that allows for greater improvements in PT FDs’ performance while also mitigating the negative effects of RAFD.
The PT-RAFD model in both runs, as shown in Figure 8, led to an increase in the number of districts with over 50% efficiency. Before optimization, there were eight districts exceeding this threshold. After utilizing the PT-RAFD with C5 to optimize their budget, the number of districts with over 50% efficiency increased to 11. Furthermore, relaxing C5 resulted in 14 districts surpassing the 50% efficiency mark. However, after relaxing C5, two of the five districts with deteriorated efficiency experienced significant declines: Braga with a decrease of −2.72% and Porto with a decrease of −3.14%. The other three districts saw changes of less than −1%.
Further investigation revealed that the primary cause of deterioration in the PT-RAFD version with relaxation of C5 is that the optimization changes in 307 FDs, out of 353, exceeded the threshold set by C5. Additionally, this method reduced the budget of 203 FDs, predominantly those with higher budgets, while increasing the budget of 150 low-performing FDs. Conversely, in the PT-RAFD version using the change threshold of C5, the numbers were reversed: more FDs experienced an increased budget (189 FDs) and there were 164 instances of budget reduction. As one of the key inputs of the FDPA model for analyzing FD performance is their budget, and one of the outputs is their total cost, the relaxed method ultimately resulted in more efficient FDs, while the method using C5 led to a more balanced distribution of efficiency without deterioration in FD performance.
In comparison to the recent FDPA study in Portugal by Eslamzadeh et al. (2023) [8], the results of this study demonstrate a significant improvement in the percentage of FDs with less than 50% efficiency across all districts of Portugal. The comparison provided in Table 4 reveals that after optimizing budget allocation, the number of low-performing FDs decreases in all districts. Moreover, employing the RAFD optimization method with relaxed C5 yields the most favorable outcomes. It is important to note that this study marks the first implementation of RAFD in Portugal, making direct comparisons with previous studies limited; however, the improvements observed in FD efficiency underscore the potential of RAFD to enhance the performance of FPS.
The findings in this paper offer valuable insights for ANEPC decision-makers. Given the complexity of FD performance, influenced by factors such as socioeconomic conditions, spatiotemporal dynamics, and FD resources, this research provides a nuanced understanding of how different RAFD optimization strategies impact FD efficiency and how efficiency scores can guide the RAFD. The detailed analysis of allocated budgets and efficiency metrics equips decision-makers with actionable information for optimizing RA and enhancing FPS effectiveness at both national and district levels.
Recommendation 4: Embrace a broader scope for changes beyond the 95 to 110% threshold of FDs’ last year’s resources, as evidenced by the findings of this study. This expansion demonstrates the potential to elevate FD performance without adverse effects on other FDs. By adopting this adjustment, RAFD optimization can effectively elevate the overall FPS performance at both national and district levels, fostering a more robust and efficient firefighting system in Portugal.
The detailed allocated budget in both PT-RAFD methods, along with the slack results for inefficient FDs and their efficiency distance from the target FDs in the PT-FDPA, are additional outcomes of this research that offer valuable insights for corrective actions. This information is readily available upon readers’ request, providing an opportunity to delve deeper into the specific budget allocations and performance metrics of individual FDs. By reviewing and analyzing these details, FPS stakeholders can gain a comprehensive understanding of the allocation process and identify areas for improvement, thereby facilitating informed decision-making and strategic planning within the firefighting sector.
The findings presented in this paper hold significant managerial implications for ANEPC’s decision-makers and other stakeholders involved in FPS management. By clarifying the complex link between RA techniques and FD efficiency, this research provides actionable insights for optimizing RAFD and enhancing FPS effectiveness. Specifically, the nuanced analysis of allocated budgets and efficiency metrics equips decision-makers with the information needed to make informed decisions at both national and district levels.
The recommendation to record and update components of the total fire cost, as well as the emphasis on the importance of accurate and comprehensive data collection practices, addresses key deficiencies in current methodologies. Moreover, the integration of efficiency metrics into the RAFD process, as suggested, enables decision-makers to comprehensively assess different RAFD strategies and select the most suitable option based on its impact on FD efficiency. Additionally, the suggestion to embrace a broader scope for changes in resource allocation thresholds offers a pathway to elevate FD performance without compromising the efficiencies of other FDs. Finally, the detailed examination of allocated budgets and efficiency metrics, along with the results for inefficient FDs, provides valuable information for corrective actions and strategic planning within the FPS sector. By leveraging these insights, ANEPC decision-makers and FPS managers can refine their resource allocation strategies and enhance the overall efficiency and performance of FPS in Portugal.

6. Conclusions

In conclusion, this paper has significantly contributed to our understanding of the critical role played by RAFD in shaping the performance of Portuguese FDs within the FPS framework. Through the development of a comprehensive RAFD model tailored to the Portuguese context and an in-depth analysis of various optimization strategies, valuable insights have been provided regarding their impact on FD efficiency. The examination was conducted at both district and FD levels, revealing substantial performance improvements when FD efficiency scores were integrated into RAFD. Furthermore, this study underscores the importance of incorporating legal constraints, such as budget allocation limits, into the PT-RAFD model. While adherence to these constraints led to modest efficiency gains of nearly 4%, relaxing specific RAFD thresholds resulted in more significant improvements of nearly 8%. However, it is noteworthy that this approach led to performance deterioration in a minority of FDs. The detailed analysis of budget allocations and efficiency metrics provides decision-makers at ANEPC and similar organizations with actionable insights for optimizing RA and enhancing FPS effectiveness across both national and district levels.
This approach aligns with existing research highlighting the importance of performance-based resource allocation in improving FPS performance. By grounding RAFD decisions in FD performance metrics, our study offers a novel framework for optimizing RA strategies in FPS. Additionally, our findings highlight the need for a nuanced approach to RAFD optimization, considering both legal constraints and performance metrics to balance efficiency gains with potential trade-offs.
For decision-makers at the ANEPC and counterparts worldwide, the results and recommendations of this study offer practical guidance for optimizing RAFD and improving FPS effectiveness. By leveraging the insights gained from the analysis, decision-makers can make informed decisions to enhance FD performance and ensure community safety.
Despite these valuable insights, it is essential to acknowledge this study’s limitations. The focus on urban areas in Portugal may limit the generalizability of findings to other regions or countries with different contexts. Urban areas typically have different risk profiles, resource availability, and operational challenges compared to rural areas. Therefore, the applicability of the findings to rural settings remains uncertain. Future research should address this by expanding studies to include rural areas and regions with varying risk profiles.
The reliance on available data and models introduced another limitation. While this study utilized the best available data, certain key data points, such as risk indices, operational costs, and property losses, were not included. These omissions can affect the comprehensiveness of the analysis. Future research should aim to collect and incorporate these missing data points to enhance the robustness of the findings.
Additionally, the study’s model does not fully capture the dynamic nature of fire risks and resource allocation needs. Fire risks and resource demands can fluctuate due to various factors, including seasonal changes, changes in the characteristics of the residential areas, and local events. Future research should explore dynamic models that can adapt to these fluctuations, providing more responsive and effective resource allocation strategies.
Finally, the absence of certain socioeconomic and spatiotemporal indicators (e.g., income level, historical neighborhoods, critical buildings and infrastructure, and regional fire risk index) in the current model limits the ability to fully understand their influence on FD performance. These indicators can provide deeper insights into how different variables affect fire department operations and resource needs. Future research should investigate these indicators to offer a more comprehensive understanding of the factors influencing FD performance.
Looking ahead, future research should consider emerging factors like climate change and technological advancements in preventive and suppression activities. Examining how these factors affect FD performance and resource allocation could uncover new FPS strategies for enhancing efficiency and effectiveness. Collaborating with international counterparts to compare RAFD frameworks across different countries may also yield valuable lessons and best practices. By addressing these limitations and exploring new avenues, future research can continue to refine and improve resource allocation strategies for fire departments, ultimately contributing to safer and more resilient communities.

Author Contributions

Literature Review and investigation, M.K.E.; conceptualization and methodology, M.K.E., A.G. and P.E.-C.; software M.K.E.; validation, M.K.E., A.G. and P.E.-C.; formal analysis, M.K.E.; investigation, M.K.E.; resources, M.K.E.; data curation, M.K.E.; writing—original draft preparation, M.K.E.; writing—review and editing, M.K.E., A.G. and P.E.-C.; visualization, M.K.E.; supervision, A.G. and P.E.-C.; project administration, A.G.; funding acquisition, A.G. and P.E.-C. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by Fundação para a Ciência e a Tecnologia, IP under the grant number [DSAIPA/DS/0088/2019] and the APC was funded by the same grant.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The original data presented in the study are openly available in FigShare at https://doi.org/10.6084/m9.figshare.c.6436232.v1 (accessed on 17 March 2024).

Acknowledgments

The authors would like to thank: the Fundação para a Ciência e a Tecnologia, IP, for funding this research project (DSAIPA/DS/0088/2019); António Grilo and Pedro Espadinha-Cruz acknowledge Fundação para a Ciência e a Tecnologia (FCT-MCTES) for its financial support via the project UIDP/00667/2020 and UIDB/00667/2020 (UNIDEMI); the ANEPC for providing data on Portuguese fire incidents and relevant assistance; the ANEPC experts for reviewing the research progress and verifying the results including Jose Pedro Lopes (ANEPC), Comandante Alexandre Penha (ANEPC), Augusto Leite (ANEPC), and two chief commanders of FDs (who preferred to stay anonymous); and the anonymous reviewers for providing their constructive and valuable suggestions that improved the paper’s quality.

Conflicts of Interest

The authors declare no conflict of interest.

Appendix A

Table A1. List of abbreviations used in the paper.
Table A1. List of abbreviations used in the paper.
AbbreviationFull PhraseAbbreviationFull Phrase
ABMAgent-Based ModelingIPInteger Programming
ANEPCAutoridade Nacional de Emergência e Proteção Civil (National Authority for Emergency and Civil Protection)MILPMixed-Integer Linear Programming
DEAData Envelopment AnalysisPTPortuguese/Portugal
FDFire DepartmentRAResource Allocation
FDPAFire Departments’ Performance AssessmentsRAFDResource Allocation in Fire Departments
FPSFire Protection ServicesSBMSlack-Based Model
GISGeographic Information SystemVSLValue statistical life
Table A2. FDs’ efficiency scores before optimization and after optimizing RAFD with/without using the constraint 5 (C5).
Table A2. FDs’ efficiency scores before optimization and after optimizing RAFD with/without using the constraint 5 (C5).
FD CodeFD NameCurr Eff %Relax C5%Use C5%FD CodeFD NameCurr Eff%Relax C5%Use C5%FD CodeFD NameCurr Eff%Relax C5%Use C5%
101Aveiro373935903Gouveia4848571329Leixões100100100
102Ílhavo384035904Pinhel4448461330Paços Ferreira474740
104Ovar434540905Cast Rodrigo7070661331Avintes636355
105OliVAzeméis353729906Meda4346581332Leça Balio10010068
106Aveiro333434907Trancoso3639421333Paço Sousa464949
107Feira505048908Almeida5050601334Baião414345
108Estarreja414339909VN Foz Côa5959591335Lordelo545448
109Alberg Velha323332910Seia3841451336Trofa394135
110Pampilhosa545456912Celorico Beira3739481337Vila Aves535352
111Arrifana616157914Fornos Algodres4547621338Rebordosa444743
112Mealhada535353915Aguiar Beira5757621339S Pedro Cova494946
114S João Madeira505052916Manteigas6161671340Vila Meã384144
115Vagos464840917São Romão4646561341Melres100100100
116Esmoriz424546919Soito6161771344Pedrouços100100100
117Anadia505046922VFranca Naves6060702203Portuenses727260
118Águeda2729251001Alcobaça3840351404Benavente464861
119Sever Vouga4648511003Caldas Rainha2931251405Rio Maior474751
120Vale Cambra3537371004Marinha Grande4447371406Ourém272929
121Lourosa3941341005Martinh Porto5151601408Constância404256
122OliVBairro4547441006Pombal2123171409VN Barquinha535362
123Castelo Paiva2931301007Bombarral5555611411Torres Novas333532
124Arouca3840371008Óbidos3739441412Salvat Magos545455
125Murtosa4649471009Nazaré5353511414Mação505059
126Fajões4949511010Peniche3637361416Golegã757587
201Beja2830271011Figueiró Vinhos3740491417Ferreira Zêzere535360
202Odemira4547401012Alvaiázere4747531418Entroncamento626262
203Moura3941381013Vieira Leiria5050611420Almeirim565657
204Aljustrel7070671014Cast Pêra5656731421Chamusca626262
206Cuba1001001001015Porto Mós4244431425Caxarias585862
207F Alentejo5454591016Ansião4447471426Samora Correia474753
209Almodôvar7272731018Batalha3942381428Fátima424546
210Ourique6666691019Pataias7575731429Abrantes353735
211Serpa5252451020Maceira3234311502Setúbal505041
213Castro Verde7171671021Mira Aire76761001503Cacilhas333430
214Vidigueira6565691022Leiria2729241504Sul e Sueste394141
215VN Milfontes8787931023Juncal6565691505Sesimbra384034
303Guimarães3942291024Benedita4747511506Montijo404337
304Vizela3841361025Ortigosa5454461507Alcacér Sal777770
305Barcelos3637271101Barcarena4949561508Almada515157
307Fafe3335291102VFranca Xira5252501509Santiago Cacém626253
308VN Famalicão2829231103Cascais5757481510Barreiro454844
309Esposende7272631104Loures3638351511Trafaria515155
310Póvoa Lanhoso3739381105Arruda Vinhos5454541512Moita555548
311Amares4547461106Colares5353651513Palmela434542
312 Barcelinhos3335271107Sintra3435431514Sines626258
313Vila Verde3941371109Bucelas6868741515Alcochete505051
314Fão6969541110Oeiras4446401516Grândola414341
315Celorico Basto3638351111Paço Arcos7777661517Pinhal Novo464946
316Famalicenses2628211113Odivelas4244361519Cercal Alentejo616177
317Vieira Minho4848511114Sacavém3638351520Seixal282927
318Cab Basto4345491115Alhandra6565621521Águas Moura515162
319Riba Ave4949481116Algés1001001001522Canha464957
321Viatodos5050511117Torres Vedras2527211524Santo André898992
322Terras Bouro4748551118Amadora4547431525Alvalade100100100
401Mirandela3234311119SPedro Sintra4647511526Amora575746
402Bragança2527251120Carcavelos-S D R5050491603Ponte Lima252625
403M Cavaleiros3536391121Dafundo5353581604Arcos Valdevez464849
404F Espada Cinta4244581122Carnaxide6262571605Caminha565661
405Carraz Ansiães5353651123S Monte Agraço5353561606Monção484852
406Mogadouro4244421124Cadaval5353571607VPraia Âncora737379
407Vimioso5757611125Queluz5656551608Valença585858
408Torre Moncorvo3638461127Camarate6666701609PCoura494958
409Alfândega Fé5050651128Belas3941381610Ponte Barca565664
410Vinhais3740421129Parede4848511611VN Cerveira545458
411Vila Flor4244541130Alverca5353481612Melgaço525257
412Miranda Douro5959641131Alcabideche3941391701Peso Régua434551
413Torre Chama6161861132Moscavide1001001001702Flaviense394048
414Sendim54541001133Mafra3840411703Verde-VReal283031
501Covilhã2425241134Lourinhã3941391704Sanfins Douro8787100
502Sertã2021291135Fanhões7272791705Sabrosa666683
503Fundão2022211137Ericeira5757531706Branca-VReal232529
504Castelo Branco2121211138Agualva-Cacém5656601707Favaios100100100
505Penamacor5656611139Azambuja5858561708VPouca Aguiar394147
506Oleiros3435531140Alcoentre5555641709Mondim Basto454563
507Proença Nova3334451141Alenquer 3336311711Murça646476
508Idanha Nova1001001001142 Póvoa Sta Iria6767601714Montenegro747496
509Velha Ródão73731001143Malveira4042431715Alijó656574
510Belmonte5757641144Alg Mem-Martins3738381716Valpaços464850
511Vila Rei5757761145Cast Ribatejo8484781717Chaves646462
512Cern Bonjardim3537491146Vialonga6868571718Mesão Frio565667
604Coimbra1001001001147Caneças6060671719Montalegre474750
605Cantanhede2931251148Pontinha8787901720Fontes606080
607Soure3032321149Merceana5959651721Vidago383966
608OliVHospital3234351150Montelavar5757661722Boticas474760
609Condeixa Nova3538331201Portalegre3437351724Ribeira Pena606074
610Penacova3133321203Ponte Sôr3032331725de Cerva100100100
611Montemor Velho3840381204Elvas3436331726Sta M Penaguião100100100
612Arganil5858541205Nisa6262591727Salto6363100
613VN Oliveirinha4747631209Campo Maior7373791802Lamego384036
614Tábua4043481210Avis1001001001803Castro D’Aire384043
616Lagares Beira6161661213Monforte1001001001804Pedro Sul535361
617Miranda Corvo3436371302Matosinhos-Leça5656471805Vouzela373945
618VN Poiares5252541303Póvoa Varzim4244341807SJ Pesqueira575774
620Coja4346571304Santo Tirso5050491808Santa Comba Dão404347
621Pampilhosa Serra43451001305Penafiel3941381809Nelas444662
622Penela3537441306Paredes4547461810Tondela373937
623Mira5050521307Lixa4143411811Mortágua424545
701Évora3436301308Valongo4345431813Moimenta Beira343640
702Vendas Novas5656581309Felgueiras3840351814Mangualde384140
703Montemor Novo3942341310Coimbrões4949411815Farejinhas676773
704Estremoz4747481311Carvalhos4547421816Oliveira Frades606070
705Arraiolos6262591312Vila Conde3436261817Canas Senhorim515163
706Regueng Monsar5353581313Gondomar5353451818Armamar595967
707Vila Viçosa 5353641314Valadares5656511819Cabanas Viriato535371
710Redondo7272731315Mamed Infesta5454521820Tabuaço434656
712Portel7676791316Amarante2930301821Carregal Sal474754
802Lagos4649451317Ermesinde4547461822Penalva Castelo494954
804VR Sto António3739381318Areosa-Rio Tinto6666561823Resende454753
806Silves3941391319Entre-os-Rios4949521824Ervedosa Douro737386
807Portimão2930291320Marco Canaveses2931251825Sernancelhe626269
809S. Brás Alportel5757611321Aguda5555461826Cinfães333543
811Monchique1001001001322Cête4747531827Penedono7979100
812Aljezur4144551323Moreira Maia3335271828Nespereira474754
813S Bart Messines4346471324Valbom5555521829Tarouca525252
814Albufeira2930361325Baltar4548421830VNova Paiva474758
815Lagoa3335371326Tirsenses3840411831Sátão434647
816Vila Bispo7373721327Lousada3537331832Vale Besteiros646455
902Sabugal4244551328Freamunde353740

References

  1. Donahue, A.K. The influence of management on the cost of fire protection. J. Policy Anal. Manag. 2004, 23, 71–92. [Google Scholar] [CrossRef]
  2. Lan, C.H.; Chuang, L.L.; Chang, C.C. An Efficiency-Based Approach on Human Resource Management: A Case Study of Tainan County Fire Branches in Taiwan. Public Pers. Manag. 2007, 36, 143–164. [Google Scholar] [CrossRef]
  3. Choi, S.O. Relative efficiency of fire and emergency services in Florida: An application and test of data envelopment analysis. Int. J. Emerg. Manag. 2005, 2, 218. [Google Scholar] [CrossRef]
  4. Eslamzadeh, M.K.; Grilo, A.; Espadinha-Cruz, P.; Rodrigues, J.P.C.; Lopes, J.P. A Framework for Fire Departments’ Performance Assessment: A Systematic Literature Review. Int. J. Public Sect. Manag. 2022, 35, 349–369. [Google Scholar] [CrossRef]
  5. Aleisa, E. The fire station location problem: A literature survey. Int. J. Emerg. Manag. 2018, 14, 291. [Google Scholar] [CrossRef]
  6. Ashe, B.; McAneney, J.; Pitman, A. Is the allocation of resources towards mitigation and response to fire in Australia optimal? J. Risk Res. 2011, 14, 381–393. [Google Scholar] [CrossRef]
  7. Alavi, E.S.; Ghanbari, R. A limited resource assignment problem with shortage in the fire department. Numer. Anal. Optim. 2018, 8, 129–141. [Google Scholar] [CrossRef]
  8. Eslamzadeh, M.K.; Grilo, A.; Espadinha-Cruz, P. A Model for Fire Departments’ Performance Assessment in Portugal. Fire 2023, 6, 31. [Google Scholar] [CrossRef]
  9. Eslamzadeh, M.K.; Grilo, A.; Espadinha-Cruz, P. A Framework for Resource Allocation in Fire Departments: A Structured Literature Review. Fire 2022, 5, 109. [Google Scholar] [CrossRef]
  10. Rodriguez, S.A.; De la Fuente, R.A.; Aguayo, M.M. A facility location and equipment emplacement technique model with expected coverage for the location of fire stations in the Concepción province, Chile. Comput. Ind. Eng. 2020, 147, 106522. [Google Scholar] [CrossRef]
  11. Lan, C.H.; Chuang, L.L.; Chen, Y.F. Optimal human resource allocation model: A case study of Taiwan fire service. J. Stat. Manag. Syst. 2011, 14, 187–216. [Google Scholar] [CrossRef]
  12. Peace, D.M.S. Planning New Standards of Fire Service Emergency Cover for the United Kingdom. Fire Technol. 2001, 37, 279–290. [Google Scholar] [CrossRef]
  13. Ming, J.; Richard, J.-P.P.; Zhu, J. A Facility Location and Allocation Model for Cooperative Fire Services. IEEE Access 2021, 9, 90908–90918. [Google Scholar] [CrossRef]
  14. Kumar, V.; Ramamritham, K.; Jana, A. Resource allocation for handling emergencies considering dynamic variations and urban spaces: Firefighting in Mumbai. In Proceedings of the Tenth International Conference on Information and Communication Technologies and Development—ICTDX ’19, Ahmedabad, India, 4–7 January 2019; ACM Press: New York, NY, USA, 2019; pp. 1–11. [Google Scholar]
  15. Behrendt, A.; Payyappalli, V.M.; Zhuang, J. Modeling the Cost Effectiveness of Fire Protection Resource Allocation in the United States: Models and a 1980–2014 Case Study. RISK Anal. 2019, 39, 1358–1381. [Google Scholar] [CrossRef]
  16. Lim, D.; Kim, M.; Lee, K. A revised dynamic data envelopment analysis model with budget constraints. Int. Trans. Oper. Res. 2020, 29, 1012–1024. [Google Scholar] [CrossRef]
  17. Kovalenko, R.; Kalynovskyi, A.; Nazarenko, S.; Kryvoshei, B.; Grinchenko, E.; Demydov, Z.; Mordvyntsev, M.; Kaidalov, R. Development of a method of completing emergency rescue units with emergency vehicles. East.-Eur. J. Enterp. Technol. 2019, 4, 54–62. [Google Scholar] [CrossRef]
  18. Yeboah, G.; Park, P.Y. Using survival analysis to improve pre-emptive fire engine allocation for emergency response. Fire Saf. J. 2018, 97, 76–84. [Google Scholar] [CrossRef]
  19. Bispo, R.; Vieira, F.G.; Bachir, N.; Espadinha-Cruz, P.; Lopes, J.P.; Penha, A.; Marques, F.J.; Grilo, A. Spatial modelling and mapping of urban fire occurrence in Portugal. Fire Saf. J. 2023, 138, 103802. [Google Scholar] [CrossRef]
  20. Gomes, M.I.; Jóia, A.C.; Pinela, J.; Chibeles-Martins, N. Are the Portuguese Fire Departments Well Located for Fighting Urban Fires? In Operational Research; Almeida, J.P., Alvelos, F.P.E., Cerdeira, J.O., Moniz, S., Requejo, C., Eds.; Springer Proceedings in Mathematics & Statistics; Springer Nature: Cham, Switzerland, 2023; Volume 437, pp. 99–111. ISBN 978-3-031-46438-6. [Google Scholar]
  21. Santos, C.; Ferreira, T.M.; Vicente, R.; Mendes da Silva, J.A.R. Building typologies identification to support risk mitigation at the urban scale—Case study of the old city centre of Seixal, Portugal. J. Cult. Herit. 2013, 14, 449–463. [Google Scholar] [CrossRef]
  22. Tozo Neto, J.; Ferreira, T.M. Assessing and mitigating vulnerability and fire risk in historic centres: A cost-benefit analysis. J. Cult. Herit. 2020, 45, 279–290. [Google Scholar] [CrossRef]
  23. Rezvani, S.; De Almeida, N.; Falcão, M. Climate Adaptation Measures for Enhancing Urban Resilience. Buildings 2023, 13, 2163. [Google Scholar] [CrossRef]
  24. Nunes, P.M.P. Incêndios em Edifícios na Cidade de Lisboa: Análise e Caracterização das Ocorrências no Período de 2010 a 2014. Master’s Thesis, Instituto Superior de Educação e Ciências-ISEC Lisboa, Lisbon, Portugal, 2015. [Google Scholar]
  25. Assembleia da República Portugal. Lei n.o 94/2015, de 13 de Agosto; Diário da República, 1.ª Série; Assembleia da República Portugal: Lisbon, Portugal, 2015; pp. 5815–5817. [Google Scholar]
  26. Breslin, D.; Dobson, S.; Smith, N. Improving the effectiveness of fire prevention using the “premonition” agent-based model of domestic fire risk behaviours. Int. J. Emerg. Serv. 2019, 8, 280–291. [Google Scholar] [CrossRef]
  27. Viscusi, W.K.; Masterman, C.J. Income Elasticities and Global Values of a Statistical Life. J. Benefit-Cost Anal. 2017, 8, 226–250. [Google Scholar] [CrossRef]
  28. Huang, Y.; Fan, Y.; Cheu, R.L. Optimal Allocation of Multiple Emergency Service Resources for Protection of Critical Transportation Infrastructure. Transp. Res. Rec. J. Transp. Res. Board 2007, 2022, 1–8. [Google Scholar] [CrossRef]
  29. Melolidakis, C. Designing the allocation of emergency units by using the Shapley-Shubik power index: A case study. Math. Comput. Model. 1993, 18, 97–109. [Google Scholar] [CrossRef]
  30. Fang, L.; Zhang, C.-Q. Resource allocation based on the DEA model. J. Oper. Res. Soc. 2008, 59, 1136–1141. [Google Scholar] [CrossRef]
  31. Schilling, D.; Elzinga, D.J.; Cohon, J.; Church, R.; ReVelle, C. The Team/Fleet Models for Simultaneous Facility and Equipment Siting. Transp. Sci. 1979, 13, 163–175. [Google Scholar] [CrossRef]
  32. Marianov, V.; ReVelle, C. The capacitated standard response fire protection siting problem: Deterministic and probabilistic models. Ann. Oper. Res. 1992, 40, 303–322. [Google Scholar] [CrossRef]
  33. Jayaraman, V.; Srivastava, R. A service logistics model for simultaneous siting of facilities and multiple levels of equipment. Comput. Oper. Res. 1995, 22, 191–204. [Google Scholar] [CrossRef]
  34. Revelle, C.; Snyder, S. Integrated fire and ambulance siting: A deterministic model. Socioecon. Plann. Sci. 1995, 29, 261–271. [Google Scholar] [CrossRef]
  35. Athanassopoulos, A.D. Decision Support for Target-Based Resource Allocation of Public Services in Multiunit and Multilevel Systems. Manag. Sci. 1998, 44, 173–187. [Google Scholar] [CrossRef]
  36. Araz, C.; Selim, H.; Ozkarahan, I. A fuzzy multi-objective covering-based vehicle location model for emergency services. Comput. Oper. Res. 2007, 34, 705–726. [Google Scholar] [CrossRef]
  37. Cheu, R.L.; Huang, Y.; Huang, B. Allocating Emergency Service Vehicles to Serve Critical Transportation Infrastructures. J. Intell. Transp. Syst. 2008, 12, 38–49. [Google Scholar] [CrossRef]
  38. Lan, C.H.; Chuang, L.L.; Chen, Y.F. Performance efficiency and resource allocation strategy for fire department with the stochastic consideration. Int. J. Technol. Policy Manag. 2009, 9, 296–315. [Google Scholar] [CrossRef]
  39. Cheu, R.L.; Lei, H.; Aldouri, R. Optimal Assignment of Emergency Response Service Units With Time-Dependent Service Demand and Travel Time. J. Intell. Transp. Syst. 2010, 14, 220–231. [Google Scholar] [CrossRef]
  40. Chevalier, P.; Thomas, I.; Geraets, D.; Goetghebeur, E.; Janssens, O.; Peeters, D.; Plastria, F. Locating fire stations: An integrated approach for Belgium. Socioecon. Plann. Sci. 2012, 46, 173–182. [Google Scholar] [CrossRef]
  41. Chalfant, B.A.; Comfort, L.K. Dynamic decision support for managing regional resources: Mapping risk in Allegheny County, Pennsylvania. Saf. Sci. 2016, 90, 97–106. [Google Scholar] [CrossRef]
  42. Pérez, J.; Maldonado, S.; Marianov, V. A reconfiguration of fire station and fleet locations for the Santiago Fire Department. Int. J. Prod. Res. 2016, 54, 3170–3186. [Google Scholar] [CrossRef]
  43. Wang, J.; Liu, H.; An, S.; Cui, N. A new partial coverage locating model for cooperative fire services. Inf. Sci. 2016, 373, 527–538. [Google Scholar] [CrossRef]
  44. Perez, J.; Maldonado, S.; Lopez-Ospina, H. A fleet management model for the Santiago Fire Department. Fire Saf. J. 2016, 82, 1–11. [Google Scholar] [CrossRef]
  45. Maqbool, A.; Usmani, Z.u.A.; Afzal, F.; Razia, A. Disaster Mitigation in Urban Pakistan Using Agent Based Modeling with GIS. ISPRS Int. J. Geo-Inf. 2020, 9, 203. [Google Scholar] [CrossRef]
  46. Kumar, V.; Ramamritham, K.; Jana, A. Effective Handling of Emergencies in Resource Constrained Urban Areas by Considering Dynamics: A Performance Analysis. Transp. Res. Procedia 2020, 48, 345–362. [Google Scholar] [CrossRef]
  47. Liu, D.; Xu, Z.; Wang, Z.; Fan, C. Regional evaluation of fire apparatus requirements for petrol stations based on travel times. Process Saf. Environ. Prot. 2020, 135, 350–363. [Google Scholar] [CrossRef]
  48. Ghasemi, P.; Babaeinesami, A. Simulation of fire stations resources considering the downtime of machines: A case study. J. Ind. Eng. Manag. Stud. 2020, 7, 161–176. [Google Scholar] [CrossRef]
  49. Hajipour, V.; Fattahi, P.; Bagheri, H.; Babaei Morad, S. Dynamic maximal covering location problem for fire stations under uncertainty: Soft-computing approaches. Syst. Assur. Eng. Manag. 2021, 13, 90–112. [Google Scholar] [CrossRef]
  50. Rodriguez, S.A.; De la Fuente, R.A.; Aguayo, M.M. A simulation-optimization approach for the facility location and vehicle assignment problem for firefighters using a loosely coupled spatio-temporal arrival process. Comput. Ind. Eng. 2021, 157, 107242. [Google Scholar] [CrossRef]
  51. Liu, D.; Xu, Z.; Yan, L.; Wang, F. Applying Real-Time Travel Times to Estimate Fire Service Coverage Rate for High-Rise Buildings. Appl. Sci. 2020, 10, 6632. [Google Scholar] [CrossRef]
  52. Instituto Nacional De Statistica. Gross Reported Income (GRI) per Capita in 2020; Instituto Nacional De Statistica: Lisbon, Portugal, 2020; p. 1. [Google Scholar]
  53. The World Bank. GNI per Capita, Atlas Method (Current US$)—Portugal; The World Bank: Washingtn, DC, USA, 2020. [Google Scholar]
  54. Zhuang, J.; Payyappalli, V.M.; Behrendt, A.; Lukasiewicz, K. Total Cost of Fire in the United States; Fire Protection Research Foundation of NFPA and Department of Industrial and Systems Engineering, University at Buffalo: Getzville, NY, USA, 2017; p. 55. [Google Scholar]
  55. Robinson, L.A.; Hammitt, J.K.; O’Keeffe, L. Valuing Mortality Risk Reductions in Global Benefit-Cost Analysis. J. Benefit-Cost Anal. 2019, 10, 15–50. [Google Scholar] [CrossRef] [PubMed]
  56. Sun, D.Z. Innovation and Entrepreneurship in the 4th Industrial Revolution. In Proceedings of the Joint Workshop on Entrepreneurship, Lae, Papua New Guinea, 18 July 2018; pp. 1–34. [Google Scholar]
  57. Eslamzadeh, M.K.; Jassbi, J.J.; Cruz-Machado, V. In Light of Industry 4.0: The Trends of the 4th Industrial Revolution’s Key Technologies in Human Well-being Studies. In Proceedings of the ICDSST 2020, Zaragosa, Spain, 27–29 May 2020; Linden, I., Turón, A., Dargam, F.C.C., Jayawickrama, U., Eds.; University of Zaragoza: Zaragoza, Spain, 2020; pp. 159–166. [Google Scholar]
  58. AnyLogic Company. AnyLogic. Available online: https://www.anylogic.com (accessed on 21 September 2023).
  59. Tone, K. A slacks-based measure of efficiency in data envelopment analysis. Eur. J. Oper. Res. 2001, 130, 498–509. [Google Scholar] [CrossRef]
  60. Bolós, V.J.; Benítez, R.; Coll-Serrano, V. Continuous models combining slacks-based measures of efficiency and super-efficiency. Cent. Eur. J. Oper. Res. 2022, 31, 363–391. [Google Scholar] [CrossRef]
  61. Guo, I.-L.; Lee, H.-S.; Lee, D. An integrated model for slack-based measure of super-efficiency in additive DEA. Omega 2017, 67, 160–167. [Google Scholar] [CrossRef]
  62. Benítez, R.; Coll-Serrano, V.; Bolós, V.J. deaR-Shiny: An Interactive Web App for Data Envelopment Analysis. Sustainability 2021, 13, 6774. [Google Scholar] [CrossRef]
Fire 07 00206 g001
Figure 1. The PT-RAFD framework-2024, adapted from [9].
Figure 1. The PT-RAFD framework-2024, adapted from [9].
Fire 07 00206 g001
Fire 07 00206 g002
Figure 2. The accessible variables (in green) of the total cost of fire in Portugal.
Figure 2. The accessible variables (in green) of the total cost of fire in Portugal.
Fire 07 00206 g002
Fire 07 00206 g003
Figure 3. (a) The agent-based model implemented in AnyLogic to simulate the travel and response time between PT-FDs and the incidents. (b) Expanded view of an FD (CBV Barcarena) in Lisbon, and utilization of roads by its fire engines.
Figure 3. (a) The agent-based model implemented in AnyLogic to simulate the travel and response time between PT-FDs and the incidents. (b) Expanded view of an FD (CBV Barcarena) in Lisbon, and utilization of roads by its fire engines.
Fire 07 00206 g003
Fire 07 00206 g004
Figure 4. The degree of efficiency of PT FDs before and after using PT-RAFD model.
Figure 4. The degree of efficiency of PT FDs before and after using PT-RAFD model.
Fire 07 00206 g004
Fire 07 00206 g005
Figure 5. Number of times efficient FDs appeared as targets for non-efficient FDs in the final dataset, (left): RAFD with using C5; (right): RAFD with relaxing C5.
Figure 5. Number of times efficient FDs appeared as targets for non-efficient FDs in the final dataset, (left): RAFD with using C5; (right): RAFD with relaxing C5.
Fire 07 00206 g005
Fire 07 00206 g006
Figure 6. Efficiency impact of RAFD with and without C5: (left)—FDs’ efficiency changes post-RAFD implementation; (right)—comparison of RAFD methods on FDs’ efficiency improvement.
Figure 6. Efficiency impact of RAFD with and without C5: (left)—FDs’ efficiency changes post-RAFD implementation; (right)—comparison of RAFD methods on FDs’ efficiency improvement.
Fire 07 00206 g006
Fire 07 00206 g007
Figure 7. Efficiency changes at the district level with and without using the C5 in PT-RAFD.
Figure 7. Efficiency changes at the district level with and without using the C5 in PT-RAFD.
Fire 07 00206 g007
Fire 07 00206 g008
Figure 8. Portuguese districts’ efficiency changes: (left): before RAFD; (middle): after RAFD by using C5; (right): after RAFD by relaxing C5.
Figure 8. Portuguese districts’ efficiency changes: (left): before RAFD; (middle): after RAFD by using C5; (right): after RAFD by relaxing C5.
Fire 07 00206 g008
Table 2. The four steps of the data preprocessing stage.
Table 2. The four steps of the data preprocessing stage.
StepsProcess Details
CleansingRecovering the correct values for the noisy (incomplete, incorrect, or missing) records from other ANEPC datasets or removing the irrecoverable noisy and outlier records (i.e., 20 incidents recorded as less than 10 or more than 1440 min in duration).
IntegrationCollecting the required data about incidents and FDs from all provided datasets by the ANEPC and integrating them into one dataset.
ReductionRemoving:
-
Unnecessary, or irrelevant granular data for PT-RAFD (e.g., details of the suppression or FD maintenance cost, incident codes);
-
57 FDs with one or more zero values in financial resources, number of incidents, and covered population fields.
TransformationThe processed dataset, which underwent cleaning, integration, and reduction, was converted into comma-separated formats to facilitate the subsequent analysis stages.
Table 3. The values of VSL and VSI in Portugal between the years 2015 and 2021.
Table 3. The values of VSL and VSI in Portugal between the years 2015 and 2021.
YearGNI
Per Capita		VSLVSI Ratios and Values
Minor
0.003		Moderate
0.047		Serious
0.105		Severe
0.266		Critical
0.593		Unsurvivable
1.0
201520,4603,469,02210,407163,044364,247922,7602,057,1303,469,022
201619,9403,454,77810,364162,375362,752918,9712,048,6833,454,778
201720,0603,455,11710,365162,390362,787919,0612,048,8843,455,117
201822,0603,650,01610,950171,551383,252970,9042,164,4593,650,016
201923,2003,823,98311,472179,727401,5181,017,1792,267,6223,823,983
202021,8503,920,49511,761184,263411,6521,042,8522,324,8543,920,495
202123,8903,974,36911,923186,795417,3091,057,1822,356,8013,974,369
Table 4. Comparison of the number and percentages of FDs with less than 50% efficiency before and after using the RAFD optimized budget with and without C5, relative to Eslamzadeh et al., 2023 [8].
Table 4. Comparison of the number and percentages of FDs with less than 50% efficiency before and after using the RAFD optimized budget with and without C5, relative to Eslamzadeh et al., 2023 [8].
Districts and No. of FDsRecent Study’s ResultsUsing RAFD with C5Using RAFD Relaxing C5
Aveiro (24)2395.83%1979.17%1875.00%
Beja (12)541.67%325.00%433.33%
Braga (18)1688.89%1688.89%1372.22%
Bragança (14)1071.43%964.29%642.86%
Castelo Branco (12)758.33%758.33%650.00%
Coimbra (17)1482.35%1376.47%952.94%
Évora (9)444.44%333.33%333.33%
Faro (11)1090.91%872.73%763.64%
Guarda (16)1168.75%956.25%425.00%
Leiria (23)2191.30%1460.87%1356.52%
Lisboa (46)2043.48%1839.13%1736.96%
Portalegre (7)342.86%342.86%342.86%
Porto (42)3071.43%2661.90%2969.05%
Santarém (17)1270.59%847.06%423.53%
Setúbal (23)1669.57%1043.48%1252.17%
Viana Castelo (10)550.00%440.00%220.00%
Vila Real (23)1043.48%1043.48%521.74%
Viseu (29)1241.38%1758.62%1034.48%
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Share and Cite

MDPI and ACS Style

K. Eslamzadeh, M.; Grilo, A.; Espadinha-Cruz, P. All Lives Matter: A Model for Resource Allocation to Fire Departments in Portugal. Fire 2024, 7, 206. https://doi.org/10.3390/fire7060206

AMA Style

K. Eslamzadeh M, Grilo A, Espadinha-Cruz P. All Lives Matter: A Model for Resource Allocation to Fire Departments in Portugal. Fire. 2024; 7(6):206. https://doi.org/10.3390/fire7060206

Chicago/Turabian Style

K. Eslamzadeh, Milad, António Grilo, and Pedro Espadinha-Cruz. 2024. "All Lives Matter: A Model for Resource Allocation to Fire Departments in Portugal" Fire 7, no. 6: 206. https://doi.org/10.3390/fire7060206

APA Style

K. Eslamzadeh, M., Grilo, A., & Espadinha-Cruz, P. (2024). All Lives Matter: A Model for Resource Allocation to Fire Departments in Portugal. Fire, 7(6), 206. https://doi.org/10.3390/fire7060206

Article Metrics

Back to TopTop