DOI: 10.3303/CET24111060 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Paper Received: 19 February 2024; Revised: 24 February 2024; Accepted: 8 July 2024 
Please cite this article as: Eslami Baladeh A., Cheraghi M., Khakzad N., 2024, A Risk-averse Methodology for Firefighting Optimization in  
Process Plants, Chemical Engineering Transactions, 111, 355-360  DOI:10.3303/CET24111060 
  

 CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 111, 2024 

A publication of 

 

The Italian Association 

of Chemical Engineering 

Online at www.cetjournal.it 

Guest Editors: Valerio Cozzani, Bruno Fabiano, Genserik Reniers 

Copyright © 2024, AIDIC Servizi S.r.l. 

ISBN 979-12-81206-11-3; ISSN 2283-9216 

A Risk-Averse Methodology for Firefighting Optimization in 

Process Plants 

Aliakbar Eslami Baladeh, Morteza Cheraghi, Nima khakzad* 

Toronto Metropolitan University, Toronto, Canada 

nima.khakzad@toronotmu.ca  

Despite the incorporation of fire preventive measures in the design and operation of process plants, the threat 

of fire still remains a significant concern in the chemical and process industry. As such, every process plant 

must be equipped with firefighting resources to effectively respond to and manage potential fire incidents.  

Firefighting resources often prove insufficient to adequately protect all endangered facilities during a fire 

incident. Consequently, effective allocation of these limited resources requires a predetermined strategy to 

increase the efficiency of firefighting. 

Such firefighting strategies necessitate consideration of various factors, including the risk of fire spread through 

the plant, the risk of injuries, fatalities, and property losses both inside and outside the plant. Due to the 

complexity of integrating all these relevant aspects, risk-based decision-making approaches can be effective in 

designing firefighting strategies. However, given the nature of safety risks, the adoption of a risk-neutral or risk-

taking approach is inappropriate in decision-making regarding firefighting.  In the field of safety, it is widely 

accepted to be prepared for worst-case scenarios, as emphasized in numerous safety standards. In other words, 

no company seeks to profit by jeopardizing the lives of its employees.  From a safety perspective, addressing 

the consequences of worst-case scenarios may offer more advantages than simply reducing the mean 

consequences in the system.   

This paper introduces a novel risk-averse methodology for determining firefighting strategies aimed at 

minimizing the likelihood and consequences of potential worst-case scenarios in the event of major fires in 

process plants. The presented approach is applied to an illustrative tank terminal, and the subsequent results 

are thoroughly discussed. 

1. Introduction 

Today's systems are becoming increasingly complex, driven by rapid technological advancements, 

interconnected networks, and diverse operational environments. This complexity introduces new challenges 

and uncertainties, necessitating a higher level of safety to mitigate potential risks and ensure operational 

integrity (Coit and Zio, 2019). Furthermore, evolving regulatory standards, heightened public awareness, and 

stakeholder expectations place greater emphasis on organizations to adopt comprehensive safety strategies 

that integrate risk-based decision making(Cheraghi et al., 2024). Risk-based decision making can be 

categorized into three main strategies: risk-averse, risk-neutral, and risk-taking (Baladeh et al., 2017).  

Risk-neutral decision-making focuses on balancing risks and rewards without significant bias towards risk 

avoidance or acceptance. This strategy makes decisions based on expected values, considering both the 

probability and consequences of different outcomes; conventional cost-benefit analysis is an example of such 

decision-makings. It aims to balance between different aspects such as risk, cost-effectiveness of safety 

measures, and performance of the system. However, the effectiveness of a risk-neutral strategy depends 

heavily on the accuracy of its input data, including risk identification and evaluation. There is a significant risk of 

misrepresenting the potential impacts of accidents if risk assessments are based on incomplete data.  On the 

other hand, risk-taking decision-making tries to accept higher levels of risk in pursuit of greater rewards or 

benefits. This strategy prioritizes growth opportunities over potential risks, making it beneficial for prototype 

products or technology companies investing heavily in research and development. In contrast, risk-averse 

355

mailto:nima.khakzad@toronotmu.ca


decision-making prioritizes minimizing risk exposure and aims to avoid or mitigate as much potential hazards 

as possible. This strategy emphasizes safety and reliability over other considerations and tends to choose 

options that have a lower probability of failure, even if they offer lower potential rewards.  However, these 

strategies often come with higher upfront costs in the system. Risk-averse strategies are particularly suitable for 

systems where safety is paramount and the consequences of failures are severe or unacceptable as is the case 

for critical infrastructure systems such as power plants, air traffic control systems, dams, and bridges. 

Fires in process plants can lead to catastrophic consequences, including loss of life, property damage, 

environmental pollution, and disruption of operations. The ability to respond effectively to fires not only protects 

personnel, assets, and the environment but also helps in maintaining business continuity, meeting regulatory 

requirements, and preserving the reputation and credibility of the organization within the industry and the 

community. Having firefighting teams ready to suppress fires and cool exposed units is a necessity in every 

process plant. However, assigning a firefighting team to every asset in the plant is often not feasible due to 

limited resources. 

Hence, every plant requires a well-defined firefighting strategy to determine the roles of firefighting team during 

a fire incident. Given that every second counts during a fire, firefighting strategies should be established in 

advance for all possible fire scenarios to save time and respond effectively. By strategically planning and 

optimizing firefighting resources, process plants can minimize response times, contain fires effectively, mitigate 

potential hazards, and reduce the likelihood of catastrophic incidents. This proactive approach not only 

enhances the safety and resilience of process plants but also helps in meeting regulatory requirements, 

maintaining operational continuity, and safeguarding the surrounding community and environment.  

From the firefighting strategy perspective, there are three options for each vessel: (i) suppress the burning 

vessel, (ii) cool the exposed vessel, or (iii) leave the vessel without any intervention. Traditionally, firefighting 

strategies are primarily established based on generic standards and fire protection codes. However, these 

standards often overlook certain influencing factors such as the distance between vessels, their volume, wind 

speed and direction, the flammable chemicals involved, and the effectiveness of the firefighting. As a result, 

some researchers propose more comprehensive models for firefighting strategies by taking into account more 

parameters. 

Due to resource limitations, it is not always feasible to assign a firefighting team to all assets simultaneously. 

This raises the challenge of setting up firefighting strategies and determining how to allocate resources to find 

an optimal approach. Given the complexity of firefighting analysis, a comprehensive approach is necessary to 

automatically determine and evaluate all credible firefighting strategies. In recent years, mathematical modelling 

has proven to be highly effective in optimizing system reliability and safety (Baladeh and Taghipour, 2022, 

Cheraghi and Taghipour, 2024). This approach can also effectively address the complexity of firefighting 

strategies identification by considering various parameters, ensuring robust and reliable firefighting strategies 

in challenging and dynamic environments. Subsequently, optimization models have been developed to select 

firefighting strategies that minimize the total expected cost of fires (Khakzad, 2021a) or their onsite and offsite 

risks (Khakzad, 2023, Khakzad et al., 2023) under limited resources. 

Considering process plants as critical infrastructure systems with potentially significant safety risks, including 

loss of life, environmental damage, and economic impacts, a risk-averse strategy is suitable to minimize the risk 

of catastrophic failures. This paper introduces a novel risk-averse mathematical model for optimizing firefighting 

strategies in process plants. The proposed risk-averse model ensures that the optimization process focuses on 

mitigating high-impact risks and all available resources are allocated to minimizing the worst possible risks. The 

model evaluates firefighting strategies in a comprehensive manner, taking into account factors such as fire 

spread, resource allocation, firefighting effectiveness, and the risk of fatalities.  

The rest of the paper is structured into two main sections. In Section 2, the mathematical model for risk-averse 

optimization of firefighting strategies is developed. Section 3 demonstrates the application of the proposed 

model to an exemplary tank terminal. The main outcomes of the study are summarized in Section 4.  

2. Methodology 

Due to resource limitations, it is not feasible to assign a firefighting truck to cool or suppress every vessel in the 

plant. Therefore, the safety manager faces the challenging task of allocating resources. This task is highly 

complex, as it involves evaluating various factors such as fire spread potential, available resources, and the 

likelihood of death in determining which vessels should be cooled and which ones should be suppressed. To 

deal with this complexity, this paper proposes a mathematical model to determine the optimal firefighting 

strategy. However, the challenge lies in the fact that different residential areas can be affected differently by fire, 

and certain strategies may be more effective in some areas than others. Furthermore, the number of people 

occupying each location can vary in different residential areas, and this variation should be taken into account. 

356



Therefore, since the death of individuals has the most serious impact as a consequence of fire, resource 

allocation should prioritize minimizing the expected number of deaths in all residential areas. The expected 

number of deaths in each area can be calculated by the multiplying the number of people by the individual risk 

(IR) in that area. In other words, considering the objective function as a total expected number of deaths makes 

the model allocates more resources to areas where more population and protection has is easier. The proposed 

mathematical model, aiming to minimize the total expected number of deaths in all residential areas is 

represented by Equations (1)-(5). 

𝑜𝑏𝑗𝑒𝑐𝑡𝑖𝑣𝑒 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛: min   ∑ 𝑃𝑗 . ∑ 𝐼𝑅𝑗𝑖  

𝐼

𝑖=1

𝐽

𝑗=1

    (1) 

∑ 𝑥𝑖 ≤ 𝐿

𝐼

𝑖=1

 (2) 

∑ 𝐼𝑅𝑗𝑖  

𝐼

𝑖=1

≤ 𝐼𝑅𝑚𝑖𝑛            , ∀ 𝑗 (3) 

∑ 𝑥𝑖𝑤𝑖 ≤ 𝑊𝑚𝑎𝑥

𝐼

𝑖=1

 (4) 

𝑥𝑖  ∈ {0 , 1}     ∀ 𝑖 = 1,2, … , 𝐼 (5) 

Where: 

𝑥𝑖 Decision vector, which indicates the strategy for ith vessel 

L Number of firefighting trucks which can be afforded by the firefighters 

𝑤𝑖 Required water for suppression/ cooling of the ith vessel 

𝑃𝑗 The number of people in the jth residential area 

𝐼𝑅𝑚𝑖𝑛  minimum acceptable Individual Risk for the jth residential area 

𝑤𝑚𝑎𝑥 Total available water for firefighting 

𝐼𝑅𝑗𝑖 Probability of death for the jth residential area from the ith vessel 

The decision variables 𝑥𝑖 can be defined as: 

𝑥𝑖 = {
  1,       𝑖𝑓  𝑖𝑡ℎ 𝑣𝑒𝑠𝑠𝑒𝑙 𝑖𝑠 𝑠𝑒𝑙𝑒𝑐𝑡𝑒𝑑 𝑓𝑜𝑟 𝑐𝑜𝑜𝑙𝑖𝑛𝑔/𝑠𝑢𝑝𝑝𝑟𝑒𝑠𝑠𝑖𝑛𝑔 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑜𝑛
  0,                                             𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒                                                              

 

The model's objective is to minimize the summation of expected number of deaths in all residential areas, as 

expressed by Equation (1). The constraint presented in Equation (2) represents the maximum number of fire 

trucks afforded by the plant. To comply with the land use development regulations, Equation (3) ensures that 

the individual risk (IR) of offsite risks should be less than the values specified in the regulations, which are 

determined based on the type and population of the area. Each vessel requires a specific amount of water for 

cooling or suppression, and since there is a finite amount of water available for firefighting in the plant, the 

constraint in Equation (4) ensures that any feasible solution remains consistent with this limitation. 

3. Application of the methodology to a tank terminal 

Consider an illustrative tank terminal with nine atmospheric tanks Ti (i = 1, …, 9) located near three residential 

areas, a warehouse (𝑗 = 1), a residential community (𝑗 = 2), and a rail station (𝑗 = 3). The layout and location 

of the tanks and heat fluxes from tanks received by the residential areas in the event of tank fire at adjacent 

tanks are illustrated in Figure 1. The safety manager has decided to prepare a firefighting strategy for a future 

scenario in case of tank fire at tank T5 when there are three available firefighting trucks (L=4) and a total of 

19,000 m3 of water available for firefighting (𝑊𝑚𝑎𝑥). There are 5 people in the warehouse (𝑝1 = 5), 100 people 

in the rail station (𝑝2 = 100) and 50 people in the residential community (𝑝3 = 50). The land use development 

regulations in this region (1995) imply that the individual risk for the warehouse should be less than 1E-04, for 

the rail station less than 1E-06, and for the residential area less than 1E-05. The safety manager is seeking the 

best strategy to effectively allocate firefighting resources in order to minimize the total expected number of 

deaths in the three residential areas. Even though the fire is currently confined to tank T5, there is a risk that it 

could spread to other nearby tanks, triggering a domino effect. To calculate the probability of fire spread to the 

other tanks, the law of total probability and the chain rule (Khakzad, 2021a) or the Noisy-OR techniques 

(Khakzad, 2021b) can be utilized. However, compared with the former approach, the Noisy-OR technique 

extensively simplifies probability calculations but at the cost of resulting in less precise probabilities. 

357



 

Figure 1. The layout and location of tanks in the tank terminal and offsite targets 

Ignoring the fire spread paths which consist of more than two tanks, due to their low probabilities, the conditional 

fire spread probabilities given the tank fires at T5 can be calculated as: 

𝑃1 = 1 − {𝑃(𝑇1̅|𝑇5) × (1 − 𝑃(𝑇2|𝑇5)𝑃(𝑇1|𝑇2, 𝑇5)) × (1 − 𝑃(𝑇4|𝑇5)𝑃(𝑇1|𝑇4, 𝑇5))} 

𝑃2 = 1 − {𝑃(𝑇2
̅̅̅|𝑇5) × (1 − 𝑃(𝑇3|𝑇5)𝑃(𝑇2|𝑇3, 𝑇5)) × (1 − 𝑃(𝑇1|𝑇5)𝑃(𝑇2|𝑇1, 𝑇5)) × (1 − 𝑃(𝑇6|𝑇5)𝑃(𝑇2|𝑇6, 𝑇5))

× (1 − 𝑃(𝑇4|𝑇5)𝑃(𝑇2|𝑇4, 𝑇5))} 

𝑃3 = 1 − {𝑃(𝑇3
̅̅̅|𝑇5) × (1 − 𝑃(𝑇2|𝑇5)𝑃(𝑇3|𝑇2, 𝑇5)) × (1 − 𝑃(𝑇6|𝑇5)𝑃(𝑇3|𝑇6, 𝑇5))} 

𝑃4 = 1 − {𝑃(𝑇4̅|𝑇5) × (1 − 𝑃(𝑇1|𝑇5)𝑃(𝑇4|𝑇1, 𝑇5)) × (1 − 𝑃(𝑇7|𝑇5)𝑃(𝑇4|𝑇7, 𝑇5)) × (1 − 𝑃(𝑇2|𝑇5)𝑃(𝑇4|𝑇2, 𝑇5))

× (1 − 𝑃(𝑇8|𝑇5)𝑃(𝑇4|𝑇8, 𝑇5))} 

𝑃6 = 1 − {𝑃(𝑇6
̅̅̅|𝑇5) × (1 − 𝑃(𝑇3|𝑇5)𝑃(𝑇6|𝑇3, 𝑇5)) × (1 − 𝑃(𝑇9|𝑇5)𝑃(𝑇6|𝑇9, 𝑇5)) × (1 − 𝑃(𝑇2|𝑇5)𝑃(𝑇6|𝑇2, 𝑇5))

× (1 − 𝑃(𝑇8|𝑇5)𝑃(𝑇6|𝑇8, 𝑇5))} 

𝑃7 = 1 − {𝑃(𝑇7
̅̅̅|𝑇5) × (1 − 𝑃(𝑇8|𝑇5)𝑃(𝑇7|𝑇8, 𝑇5)) × (1 − 𝑃(𝑇4|𝑇5)𝑃(𝑇7|𝑇4, 𝑇5))} 

𝑃8 = 1 − {𝑃(𝑇8
̅̅̅|𝑇5) × (1 − 𝑃(𝑇9|𝑇5)𝑃(𝑇8|𝑇9, 𝑇5)) × (1 − 𝑃(𝑇7|𝑇5)𝑃(𝑇8|𝑇7, 𝑇5)) × (1 − 𝑃(𝑇6|𝑇5)𝑃(𝑇8|𝑇6, 𝑇5))

× (1 − 𝑃(𝑇4|𝑇5)𝑃(𝑇8|𝑇4, 𝑇5))} 

𝑃9 = 1 − {𝑃(𝑇9̅|𝑇5) × (1 − 𝑃(𝑇8|𝑇5)𝑃(𝑇9|𝑇8, 𝑇5)) × (1 − 𝑃(𝑇6|𝑇5)𝑃(𝑇9|𝑇6, 𝑇5))} 

Where, 𝑃(𝑇�̅�|𝑇𝑗) = 1 − 𝑃(𝑇𝑖|𝑇𝑗)  is the probability of fire not spreading from 𝑇𝑗 to 𝑇𝑖. It is worth noting that since 

T5 are burning: P5 = 1. 

The probability of fire spread to an exposed tank can be estimated using dose-effect relationships such as probit 

functions as (Landucci et al., 2009):  

𝑡𝑡𝑓𝑖𝑧 = 0.0167 𝑒(9.88−2.67×10−5𝑉𝑖−1.13 ln 𝑄𝑖𝑧 ) (6) 

𝑌𝑖𝑧
𝑑 = 9.26 − 1.85 ln 𝑡𝑡𝑓𝑖𝑧 (7) 

P(𝑇𝑖|𝑇𝑧) = 𝜙(𝑌𝑖𝑧
𝑑 − 5) (8) 

where 𝑄𝑖𝑧 (kW/m2) is the heat radiation tank 𝑇𝑖 receives from tank 𝑇𝑧, 𝑉𝑖 (m
3) is the volume of the tank 𝑇𝑖, 𝑡𝑡𝑓𝑖𝑧 

is the time to failure (min) of the tank 𝑇𝑖, Y
d is the damage probit value, and P(𝑇𝑖|𝑇𝑧) is the probability of fire 

spread to the tank 𝑇𝑖 from tank 𝑇𝑧. 𝜙(. ) is the cumulative density function of standard normal distribution.  

The probability of death for an individual, Individual Risk (𝐼𝑅𝑗𝑖) in residential area of j due to the tank fire at tank 

𝑇𝑖 can be calculated through the following probit function (Assael and Kakosimos, 2010) :  

𝑌𝑗𝑖
𝑓

= −36.38 + 2.56 ln(𝑡𝑒 . 𝑄𝑗𝑖) (9) 

358



𝐼𝑅𝑗𝑖 = 𝜙(𝑌𝑖𝑗
𝑓

− 5) (10) 

where 𝑄𝑗𝑖 (kW/m2) is the received heat radiation to residential j from tank 𝑇𝑖, and 𝑌𝑗𝑖
𝑓
 is the fatality probit value, 

and 𝑡𝑒(𝑠) is the exposure time of the individual (set as 60 s).  

When suppressing a burning tank, the emitting heat flux from the tank would be a factor of the original heat and 

the suppression inefficiency as 𝑄𝑚𝑜𝑑𝑖𝑓𝑖𝑒𝑑 = (1 − 𝛼) 𝑄𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙. Likewise, when cooling an exposed tank, the 

amount of heat radiation received by the tank would be a factor of the original heat and cooling inefficiency as 

𝑄𝑚𝑜𝑑𝑖𝑓𝑖𝑒𝑑 = (1 − 𝛽) 𝑄𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 (Landucci et al., 2015) . Therefore, to use Equation (5) for calculation of fire spread 

probabilities between two adjacent tanks, 𝑇𝑙 & 𝑇𝑘, the received heat radiation to tank 𝑇𝑖 should be modified as: 

𝑄𝑖 = (1 − 𝛽𝑥𝑖){(1 − 𝛼𝑥𝑙) 𝑞𝑙𝑖 + ((1 − 𝛼𝑥𝑘) 𝑞𝑘𝑖)} 
(11) 

In this example, the suppression and cooling efficiencies are assumed to be α = 0.4 and β = 0.6.  The volume 

of tanks T1, T4, T5, T7, and T8 is 50,000 m3, while the volume of T2, T3, T6 and T9 is 80,000 m3. The required 

water for cooling tanks T1, T4, T7 and T8 is 3,000 m3, for tanks T2, T3, T6, and T9 it 5,000 m3, and the required 

water for suppression tank T5 is 6,000 m3. The heat fluxes received by the tanks 𝑇𝑧 or residential areas in the 

event of tank fire at tank 𝑇𝑖 are listed in Table 1.  

Table 1. Heat radiation 𝑄𝑖𝑧to tank 𝑇𝑖 (kW/m2) if tank fire at tank 𝑇𝑧 

i 

z 

  T1 T2 T3 T4 T5 T6 T7 T8 T9 Residential 

community 

warehouse Rail station 

T1 - 70 - 70 65 0 - - - 3 - - 

T2 60 - 80 55 80 75 - - - - 15 - 

T3 0 60 - - 55 80 - - - - 15 - 

T4 50 45 - - 70 - 70 65 - 3 - - 

T5 35 50 45 50 - 70 45 70 65 - - - 

T6 - 45 60 - 60 - - 55 80 - - 20 

T7 - - - 50 45 - - 70 - 3 - - 

T8 - - - 35 50 45 50 - 70 - - - 

T9 - - - - 45 60 - 60 - - - 20 

 

Based on the proposed model, the optimal firefighting strategy when tank T5 is on fire would be to cool tanks 

T4, T6, and T9 while suppressing T5. This approach aims to prevent the spread of fire to tanks located closer 

to the public areas, thereby minimizing the probability of fatalities in those areas. The individual risks under the 

optimal strategy for each residential area are provided in Table 2. In the optimal solution, suppressing tank T5 

is crucial since it is a burning tank, leaving us with only 3 trucks and 13,000 m3 of water for cooling the other 

tanks. Given that the occupancy of the warehouse is just 5 people, cooling of tanks T2 and T3 would be of a 

lower priority. Additionally, by comparing the required water for tanks T1, T4, and T7 (3,000 m3) with that for 

tanks T6 and T9 (5,000 m3), it is noted that protecting the residential community requires less water than the 

rail station. As a result, tanks T1, T4, and T7 are selected for cooling in the optimal solution to protect the 

residential community from possible fire spread to the other tanks. The total of 19,000 m3 of water used in this 

strategy meets the model's requirements. 

Table 2. Optimal firefighting strategies for different models 

Residential area Individual risk (𝐼𝑅𝑗) 

Warehouse (j = 1) 4.60E-05 

Residential community (j = 2) 6.66E-16 

Rail station (j = 3) 2.86E-07 

4. Conclusions    

This paper presents a risk-averse mathematical model to optimize firefighting strategies at process plants.  The 

model prioritizes risk of death over other consequences of fire, reflecting the belief that in the process industry, 

companies should prioritize public safety over other safety objectives in the event of major accidents such as 

tank fire. Moreover, the model's capacity to handle large-scale problems makes it applicable across a wide 

range of chemical and process plants. It offers a robust tool for decision-making to enhance system safety and 

359



minimize the fatalities. By determining the optimal strategies for every possible fire scenario, firefighting teams 

can respond promptly and effectively during a fire incident. As further research, considering the cost of damage 

could be valuable extensions to this work, enhancing the model's applicability and impact in real-world 

firefighting operations. 

Nomenclature

𝐼𝑅𝑗𝑖 – probability of death for the jth residential area 

from the ith vessel 

𝐼𝑅𝑚𝑖𝑛 – minimum acceptable Individual Risk for the 

jth residential area 

L – number of available  firefighting trucks 

P(𝑇𝑖|𝑇𝑧) – probability of fire spread to the tank 𝑇𝑖 

from tank 𝑇𝑧 

𝑃𝑗 – number of people in the jth residential area 

𝑄𝑗𝑖 – received heat radiation to residential j from 

tank𝑇𝑖, kW/m2 

𝑄𝑖𝑧 – heat radiation tank 𝑇𝑖 receives from tank 

𝑇𝑧,kW/m2  

𝜙(. ) – cumulative density function of standard 

normal distribution 

𝑡𝑒(𝑠) – exposure time of the individual 

𝑡𝑡𝑓𝑖𝑧 – time to failure (min) of the tank 𝑇𝑖 

𝑉𝑖 – volume of the tank𝑇𝑖, m3 

𝑤𝑖 – required water for suppression/ cooling of the 

ith vessel 

𝑤𝑚𝑎𝑥 – total available water for firefighting 

𝑥𝑖 – decision vector, which indicates the strategy for 

ith vessel 

𝑌𝑗𝑖
𝑓
 – fatality probit value of the heat radiation to 

residential j from tank 𝑇𝑖 

𝑌𝑑 – damage probit value 

Acknowledgments 

Financial support provided by the Natural Sciences and Engineering Research Council of Canada (NSERC) via 

Discovery (RGPIN/ 03051-2021) and Launch Supplement (DGECR/00220-2021) grants is appreciated.  

References 

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	A Risk-Averse Methodology for Firefighting Optimization in Process Plants