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Decision support for emergency response in interdependent infrastructure systems Alutaibi, Khaled 2017

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Decision Support for Emergency Response inInterdependent Infrastructure SystemsbyKhaled AlutaibiB.Sc., King Fahd University of Petroleum and Minerals, 2003M.Sc., King Fahd University of Petroleum and Minerals, 2009a thesis submitted in partial fulfillmentof the requirements for the degree ofDoctor of Philosophyinthe faculty of graduate and postdoctoralstudies(Electrical and Computer Engineering)The University of British Columbia(Vancouver)April 2017c© Khaled Alutaibi, 2017AbstractIn recent years, extreme events, such as hurricanes, earthquakes, floods andfires, occur more frequently and at a higher intensity. The growing com-plexity and interdependence of modern infrastructure systems makes themvulnerable to such events. Emergency response is the process of implement-ing appropriate actions to reduce human and economic losses following theseevents. Efficient response requires an understanding of the existing infras-tructure systems and their interdependencies. In this thesis, we propose adecision support system for helping emergency responders in making efficientdecisions during extreme events. Fires are chosen as an example of the ex-treme events and firefighting operations as the emergency response to theseevents. Everyday, fire managers are faced with making increasingly complexmanpower decisions; trying to minimize costs and risk levels. The effective-ness of firefighting operations is crucial in minimizing both cost of suppres-sion and economic losses. The contributions of this thesis focus on twolevels of fire management plans: operational and strategic. We first developa methodology to optimize the allocation process of firefighting resources inmultiple-fire incidents. The developed methodology employs reinforcementlearning, a machine learning algorithm that optimizes the allocation of fire-fighting units to minimize the total economic losses in the long run. Toconsider the concept of infrastructure interdependencies in evaluating theeconomic impact of the incidents, we model a large petrochemical complexusing the Infrastructure Interdependency Simulator (i2Sim). In addition,a capacity planning methodology is developed to investigate the impact ofmanpower investment on the effectiveness of firefighting operations. Theiideveloped methodology aims at finding the optimal number of firefightersto be recruited to contain fires and effectively extinguish them. It performsan economic analysis to evaluate the efficiency fire management plans. Fi-nally, we propose a methodology to evaluate the effectiveness of emergencyresponse plans in improving infrastructure resilience. This methodology fo-cuses on two dimensions of resilience: resourcefulness and rapidity. Thesedimensions are measured by the optimality of allocating firefighting unitsand by minimizing economic losses. The proposed methodologies are testedusing a case study of a large petrochemical complex and promising resultsare achieved.iiiPrefaceThe contributions pointed in this dissertation have led to a number of al-ready published, or currently under preparation for publications in journalsand conferences. My research work and all my publications have been doneby me under the supervision of Prof. José R. Martí. The co-authors of thepublications have provided us with constructive feedback. The outcomes ofeach chapter in terms of publications are as follows.Major parts of chapter 2 was first presented in the 9th InternationalConference on Critical Infrastructure Protection 2015 and was published asa book chapter in [1] :• K. Alutaibi, A. Alsubaie, J. R. Martí, "Allocation and Scheduling ofFirefighting Units in Large Petrochemical Complexes," InternationalConference on Critical Infrastructure Protection. Springer Interna-tional Publishing, 2015.Work presented in chapter 5 was presented in The International Emer-gency Management Society (TIEMS) 2015 Annual Conference in [2]:• K. Alutaibi, A. Alsubaie, J. R. Martí, "Improving Critical Infrastruc-ture Resilience through Scheduling of Fire-fighting Resources," in TheInternational Emergency Management Society 2015 Annual Confer-ence (TIEMS 2015), 30 Sept.–2 Oct., Rome, Italy.ivTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixGlossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . xivDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . 51.2.1 Emergency Response . . . . . . . . . . . . . . . . . . . 51.2.2 Resources Allocation in Firefighting Operations . . . . 71.2.3 Fire Strategic Planning . . . . . . . . . . . . . . . . . 91.3 Problem Statement and Research Objectives . . . . . . . . . 111.4 Thesis Contributions . . . . . . . . . . . . . . . . . . . . . . . 121.5 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . 13v2 System Development . . . . . . . . . . . . . . . . . . . . . . . 152.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.2 Fire Simulation Model . . . . . . . . . . . . . . . . . . . . . . 172.2.1 Fire Severity Measure . . . . . . . . . . . . . . . . . . 172.2.2 Damage Function . . . . . . . . . . . . . . . . . . . . . 182.3 i2Sim Modeling and Simulation Framework . . . . . . . . . . 202.3.1 i2Sim Ontology . . . . . . . . . . . . . . . . . . . . . . 212.3.2 i2Sim Models . . . . . . . . . . . . . . . . . . . . . . . 222.4 Optimization Agent . . . . . . . . . . . . . . . . . . . . . . . 242.4.1 Reinforcement Learning . . . . . . . . . . . . . . . . . 252.4.2 Temporal Difference Learning (TD) . . . . . . . . . . 272.4.3 SARSA Algorithm . . . . . . . . . . . . . . . . . . . . 282.4.4 Reinforcement Learning (RL) Model . . . . . . . . . . 302.5 Economic Efficiency Model . . . . . . . . . . . . . . . . . . . 312.6 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.6.1 Petrochemical Industry . . . . . . . . . . . . . . . . . 352.6.2 Case Study Data . . . . . . . . . . . . . . . . . . . . . 372.6.3 Example of Interdependence in a Petrochemical complex 372.6.4 General Assumptions . . . . . . . . . . . . . . . . . . . 392.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403 Resources Allocation and Scheduling During Multiple-FireIncidents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.2 Resource Allocation and Scheduling Methodology . . . . . . . 453.3 Case Study Modeling . . . . . . . . . . . . . . . . . . . . . . . 483.3.1 Data Description . . . . . . . . . . . . . . . . . . . . . 483.3.2 i2Sim Model . . . . . . . . . . . . . . . . . . . . . . . 493.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . 553.4.1 Damage Functions . . . . . . . . . . . . . . . . . . . . 583.4.2 Human Performance Factor . . . . . . . . . . . . . . . 613.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63vi4 Capacity Planning in the Fire Department . . . . . . . . . 674.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674.2 Proposed Methodology . . . . . . . . . . . . . . . . . . . . . . 684.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . 714.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 765 Improving Resilience of Interdependent Infrastructure Sys-tems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 785.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 785.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . 795.3 Infrastructure Resilience . . . . . . . . . . . . . . . . . . . . . 815.4 Proposed Methodology . . . . . . . . . . . . . . . . . . . . . . 845.5 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . 865.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 926 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 946.1 Resource Allocation and Scheduling During Multiple-Fire In-cidents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 956.2 Capacity Planning of Human Resources . . . . . . . . . . . . 956.3 Improving Resilience of Interdependent Infrastructure Systems 966.4 Future Research Directions . . . . . . . . . . . . . . . . . . . 966.4.1 Improvement to the Fire Damage Assessment . . . . . 966.4.2 Considering Multiple Owners During Multiple-Fire In-cidents . . . . . . . . . . . . . . . . . . . . . . . . . . . 976.4.3 Understanding the Impact of the Human Factor Dur-ing Emergency Response . . . . . . . . . . . . . . . . . 976.4.4 Applications to Other Types of Emergency Response . 98Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100viiList of TablesTable 2.1 Damage assessment table. . . . . . . . . . . . . . . . . . . 19Table 2.2 Look-up table sample. . . . . . . . . . . . . . . . . . . . . 31Table 2.3 List of the petrochemical plants and their products coveredby this case study. . . . . . . . . . . . . . . . . . . . . . . . 42Table 3.1 Sample Data Format . . . . . . . . . . . . . . . . . . . . . 48Table 3.2 Number of used production cells. . . . . . . . . . . . . . . 50Table 3.3 HRT table for Ethylene production cell in Plant 7. . . . . 51Table 3.4 Allocation methods. . . . . . . . . . . . . . . . . . . . . . . 55Table 3.5 Results for the resource allocation methods (U: no. units;T: fire timer). . . . . . . . . . . . . . . . . . . . . . . . . . 57Table 4.1 Strategic planning scenarios costs (in US dollars). . . . . . 72Table 4.2 Comparison of strategic planning scenario costs for lineardamage growth. . . . . . . . . . . . . . . . . . . . . . . . . 74Table 4.3 Comparison of strategic planning scenario costs for slowdamage growth. . . . . . . . . . . . . . . . . . . . . . . . . 75Table 4.4 Comparison of strategic planning scenario costs for fastdamage growth. . . . . . . . . . . . . . . . . . . . . . . . . 75Table 5.1 Level of damage and recovery time for applied allocationmethods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86Table 5.2 Recovery time, losses and resilience of the case study fordifferent allocation methods (TLC = 365 days). . . . . . . . 89viiiList of FiguresFigure 1.1 Total number of fires and the cost of suppression theUnited States for the period 1985-2014. . . . . . . . . . . 3Figure 1.2 Emergency Management Phases. . . . . . . . . . . . . . . 6Figure 2.1 Overall architecture of the proposed FMDSS. . . . . . . . 16Figure 2.2 Illustration of the damage function. . . . . . . . . . . . . 19Figure 2.3 Conceptual cell and channel models [3]. . . . . . . . . . . 23Figure 2.4 An example a Human Readable Table (HRT) for an Emer-gency Room (ER) [3]. . . . . . . . . . . . . . . . . . . . . 24Figure 2.5 i2Sim simulation layers [3]. . . . . . . . . . . . . . . . . . 25Figure 2.6 Reinforcement Learning (RL) learning model. . . . . . . . 29Figure 2.7 Illustration of the C+NVC model [4]. . . . . . . . . . . . 33Figure 2.8 An example of interdependencies and relations betweenpetrochemical plants. . . . . . . . . . . . . . . . . . . . . 38Figure 3.1 Resource allocation methodology. . . . . . . . . . . . . . . 46Figure 3.2 Mapping between fire duration and Physical Mode(PM). . 47Figure 3.3 Plant 7 production cells. . . . . . . . . . . . . . . . . . . . 49Figure 3.4 Oil refinery sources. . . . . . . . . . . . . . . . . . . . . . 52Figure 3.5 The i2Sim model for the petrochemical complex. . . . . . 54Figure 3.6 Total losses of different allocation methods. . . . . . . . . 58ixFigure 3.7 Illustration of the difference between different damagefunctions showing level of damage as a function of timeduration of fire for (a) Equation 2.2, linear function re-flecting a constant rate of fire damage growth; (b) Equa-tion 3.1, non-linear damage function reflecting fast dam-age growth; and (c) Equation 3.2, non-linear damage func-tion reflecting slow damage growth. . . . . . . . . . . . . 60Figure 3.8 Total losses of different allocation methods for three dam-age functions. . . . . . . . . . . . . . . . . . . . . . . . . . 61Figure 3.9 Total losses of different allocation methods for three dam-age functions considering the human performance factor. 63Figure 3.10 Comparison of total losses of Method 1 between Case 1,neglecting the human performance factor, and Case 2,considering the human performance factor. . . . . . . . . 64Figure 3.11 Comparison of total losses of Method 2 between Case 1,neglecting the human performance factor, and Case 2,considering the human performance factor. . . . . . . . . 65Figure 3.12 Comparison of total losses of Method 3 between Case 1,neglecting the human performance factor, and Case 2,considering the human performance factor. . . . . . . . . 66Figure 3.13 Comparison of total losses of Method 4 between Case 1,neglecting the human performance factor, and Case 2,considering the human performance factor. . . . . . . . . 66Figure 4.1 Proposed methodology to evaluate long-term planning de-cisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69Figure 4.2 C+NVC curves of three damage growth functions, linear,slow and fast. . . . . . . . . . . . . . . . . . . . . . . . . . 73Figure 5.1 Graphical representation of resilience. . . . . . . . . . . . 83Figure 5.2 Flowchart describing the proposed methodology for as-sessing resilience of infrastructure systems. . . . . . . . . 85xFigure 5.3 Functionality the of the case study after multiple-fire in-cidents using Method 1. . . . . . . . . . . . . . . . . . . . 87Figure 5.4 Functionality the of the case study after multiple-fire in-cidents using Method 2. . . . . . . . . . . . . . . . . . . . 88Figure 5.5 Functionality the of the case study after multiple-fire in-cidents using Method 3. . . . . . . . . . . . . . . . . . . . 88Figure 5.6 Functionality the of the case study after multiple-fire in-cidents using Method 4. . . . . . . . . . . . . . . . . . . . 89Figure 5.7 Resilience curve showing level of functionality of the casestudy over time for Method 1. . . . . . . . . . . . . . . . . 90Figure 5.8 Resilience curve showing level of functionality of the casestudy over time for Method 2. . . . . . . . . . . . . . . . . 91Figure 5.9 Resilience curve showing level of functionality of the casestudy over time for Method 3. . . . . . . . . . . . . . . . . 91Figure 5.10 Resilience curve showing level of functionality of the casestudy over time for Method 4. . . . . . . . . . . . . . . . . 92xiGlossaryC+NVC Cost-Plus-Net-Value Change. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11ER Emergency Room . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23FMDSS Fire Management Decision Support System. . . . . . . . . . . . . . . . . . . .2FPA Fire Protection Association . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10FSM Fire Severity Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17HP Human Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61HRT Human Readable Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23i2Sim Infrastructure Interdependencies Simulator . . . . . . . . . . . . . . . . . . . 16LC+L Least Cost Plus Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32NFPA National Fire Prevention Association . . . . . . . . . . . . . . . . . . . . . . . . . . 2NIFC National Interagency Fire Center . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2PM Physical Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21RL Reinforcement Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24RM Resource Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22SARSA State-Action-Reward-State-Action. . . . . . . . . . . . . . . . . . . . . . . . . . . .27xiiTD Temporal Difference Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27USDA U.S. Department of Agriculture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10xiiiAcknowledgmentsI would like to express my heartfelt gratitude to my supervisor, ProfessorJosé R. Martí, for his advice, guidance, wisdom and encouragement through-out the research period. I have been extremely fortunate to have had theopportunity to work under his supervision.Also, I would like to acknowledge and thank Dr. Hermann Dommel,Dr. Martin Ordonez, and Dr. K.D. Srivastava, for serving as committeemembers during my PhD qualifying and departmental examinations and fortheir valuable comments and constructive feedback.I will forever be grateful for the opportunity to be a member of the i2Simgroup. I would like to extend my thanks to my colleagues in the i2Sim groupfor all the discussions, inspirations, and interesting ideas during our weeklymeetings.I would like to acknowledge the financial support provided by the Min-istry of Interior (Civil Defense), Saudi Arabia.A special thanks to my parents for their love and prayers. Also, I thankmy brothers and sisters who gave all the support. Finally, I am forevergrateful to my wife and my children for their unconditional love, patience,understanding and support.xivDedicationTo my children; Joody, Naif and Omar.xvChapter 1Introduction1.1 MotivationIn recent years, extreme events, such as hurricanes, earthquakes, floods andfires, occur more frequently and at a higher intensity. The growing complex-ity and interdependence of modern infrastructure systems, such as water,electrical power and transportation, makes them vulnerable to such events.Emergency response is the process of implementing appropriate actions tohelp reduce human and economic losses following these events. During emer-gency response, crucial decisions are taken among various organizations andat different levels. Efficient response requires an understanding of the ex-isting infrastructure systems and their interdependencies. In this thesis, wepropose a decision support system for helping emergency responders in mak-ing efficient decisions during extreme events. Fires are chosen as an exampleof the extreme events and fire fighting operations as the emergency responseto these events.1Fires are very expensive to fight and may result in devastating human,economic and environmental effects. Everyday, fire managers are faced withmaking increasingly complex manpower decisions; trying to minimize costsand risk levels. Figure 1.1 shows the total number of fires and the costof suppression for the period 1985-2014 as reported by the United StatesNational Interagency Fire Center (NIFC) [5]. Although the number of fireshas not changed so much over the last decade, the cost of fire suppression hasincreased by 33.8 percent. In 2014, the cost of suppression was estimatedat more than $1.5 US billion [5]. Also, the estimated direct economic lossesin 2014, due to fires, was $11.6 US billion. These estimated losses do notinclude indirect losses, such as business interruption [6]. The effectiveness offirefighting operations is crucial in minimizing both cost of suppression andeconomic losses. Therefore, there is a need to develop a Fire ManagementDecision Support System (FMDSS) for fire managers to suppress fires in acost effective way.One of the critical decisions facing fire mangers is how to assign firefight-ing units to respond to multiple simultaneous fire incidents. The typical re-sponse to a single fire incident is not always the best response to multiple fireincidents, and the latter can be improved upon [7]. This type of special as-signment requires deep understanding of the existing infrastructure systemsand their interdependencies. Current technologies can help build a decisionsupport system capable of planning better responses during multiple fireincidents that affect critical facilities.According to the National Fire Prevention Association (NFPA), thenumber of assigned firefighting units to respond to a fire incident should2Figure 1.1: Total number of fires and the cost of suppression theUnited States for the period determined by either risk analysis, pre-fire planning or both [8]. Typi-cally, experts make resource allocation decisions based on their experienceand available information about the incident. The size of the fire is usuallythe major factor in assigning the number of units. Other important factorssuch as economic impact or criticality of the site are not taken into accountby traditional decision-making procedures. Better responses are required inthe form of allocating an optimum number of firefighting units to minimizethe economic losses.Identifying potential economic consequences of fires is crucial in thedecision-making process. Decision support systems based on economic mod-els can help not only determine the most efficient allocation of limited re-sources, but also with strategic fire management planning and budget re-quest justification. The evaluation of economic consequences requires a deep3understanding of the infrastructure systems’ behavior during fires. As in-frastructure systems do not exist in isolation from one another, an incidentin one system may result in disruption to the functionality of other criticalinfrastructure systems. As a result, the indirect losses far exceed the directproperty losses [9]. The evaluation of economic impact due to fires requiresmethodologies that address the performance of infrastructure systems (e.g.,the transportation system) and also the interdependencies between them(e.g., the effect of electricity on communication). The proposed work uti-lizes the concept of the infrastructure interdependencies in evaluating theeconomic impact of the incidents.This research project supports two levels of fire management plans: op-erational and strategic. The operational level involves daily decisions aboutallocating and scheduling firefighting resources to fire locations (e.g., thenumber of firefighters assigned to a fire). The strategic level of planning in-cludes medium to long term time horizons such as the evaluation of potentialbenefits and consequences of alternative management plans (e.g., increasingthe number of firefighters). The proposed work in this thesis can be usedbefore an accident for training and planning, during an accident for decisionsupport, or after an accident for evaluating suppression strategies. The workis also applicable for wildfires.Recent incidents have highlighted the limitations of existing responsesystems such as a lack of situational awareness and effective coordination be-tween emergency response departments (e.g., fire, police) [10]. Increasinglythe emphasis has shifted from protection and prevention towards prepared-ness and response [11]. This shift is realized by the concept of resilience. The4effectiveness of the emergency preparedness and response plan has a highimpact on infrastructure resilience. In this thesis, we study the resilience ofinfrastructure systems as affected by fire incidents. We propose a method-ology to evaluate the impact of resources allocation decisions during fireincidents in improving infrastructure resilience. This methodology can beused for any type of hazards. It can also be used for other resource allocationproblems in any interdependent environment such as telecommunications,transportation, electric power grids and water supply systems.In the following, a literature review is provided on different topics coveredin this thesis.1.2 Literature Review1.2.1 Emergency ResponseThe concept of emergency management has received considerable atten-tion in recent years. In the literature, it is common to define four phasesof emergency management: mitigation, preparedness, response and recov-ery [12], [13], [14]. Figure 1.2 shows the four phases of emergency manage-ment.The mitigation phase involves the policies and measures that are takento reduce the probability of emergency situations or reduce the negativeimpact of unavoidable situations. The preparedness phase includes all plan-ning and training activities designed to minimize losses when an emergencyoccurs. The response phase includes efforts that are taken immediately af-ter a disaster strikes, such as saving lives and fighting fires. The recovery5phase involves all the operations to return life to normal and to restore basicservices [14].Figure 1.2: Emergency Management Phases.Even though all phases are overlapping, the focus of this thesis is onthe response phase. Whenever an emergency situation occurs, effective andefficient emergency response can be deeply influenced by efficient alloca-tion of the available resources. In this respect, many researchers have fo-cused on developing approaches dealing with allocation and deployment ofemergency resources [15], [16]. Fiedrich et. al. [15] proposed a dynamicoptimization model for allocating emergency resources to operational areasafter an earthquake. The objective of the model is to minimize the totalnumber of fatalities during the Search-and-Rescue period. Similarly, math-ematical programming models are proposed for allocating and schedulingrescue units by Wex et. al. [17] and Schryen et. al. [18]. Barbarosogluet. al. [19] developed a hierarchical multi-criteria methodology for assigninghelicopters’ tasks during a disaster relief operation. The focus of this workwas to minimize the operational cost. Emergency response during multiplehazard events have been also addressed in several recent publications Dillonet. al. [20], Li et. al. [21] and Abkowitz et. al. [22]. Most of the decision6making process in these studies is based on risk prioritization.The context of this thesis is emergency response during fire incidentsin which FMDSS are used. Fire management systems can be defined asthe set of processes and practices used to minimize the negative impactsof fires. Several review articles have explored the most recent studies inthe development and use of FMDSS (e.g., Martell (2015) [23], Duff et. al.(2015) [24], Pacheco (2015) [25] and Mavsar et. al.(2013) [26]). Most ofthe reviewed systems do not take economic efficiency of fire activities intoconsideration. Effective fire management systems should be able to evaluatethe cost and the damage for fire operations.1.2.2 Resources Allocation in Firefighting OperationsThe key challenge in firefighting operations during large incidents is howto efficiently utilize the available resources to reduce the impact of the fire.In the past decades, researchers have addressed this challenge by designingFMDSS to model fire behavior, dispatch decisions, impact assessment andprocesses optimization, e.g., LANIK [27], DEDICS [28] and WFDSS [29].However, most of the existing work focuses on wildfires and lacks the ca-pability of producing artificial intelligent (AI) decisions for allocating avail-able resources [30]–[31]. A number of models have been developed for firebehavior prediction, such as BEHAVE [32], FARSITE [33], HFire [34] andPrometheus [35]. These models only focus on fire behavior simulation, usingheat and smoke sources [36]. Generally, optimization of firefighting resourcesand simulation of firefighting operations are developed separately withoutintegration into a unifying framework [37]. Such integration is proposed in7this thesis.There is also some research available considering models for fire simu-lations and firfighting resources allocation [38], [39], [40] and [41]. Whilethese models provide considerable insight into the interaction between firedynamics and resources allocation, they are limited to specific types of fires(wildfires) and cannot be extended to fires in interdependent infrastruc-ture systems. Also, they do not capture the effect of emergency respondersdecisions on economic losses during the response efforts. The concept ofinfrastructure systems resilience can assist emergency responders in allocat-ing the optimal number of firefighting units during single or multiple fireincidents in order to minimize both direct and indirect losses and the timerequired to return to normal operation.Most of the existing fire decision models focus on initial assignment ofthe resources without dynamically changing the assigned amounts [42]. Inour work, assignment decisions are made dynamically and associated withthe final expected losses. This representation considers the long-term con-sequences of fire incidents.In recent literature, simulation and optimization models have been in-tegrated for dispatching decisions in firefighting operations. A simulation-based model using stochastic processes and queuing theory was developedin Petrovic, Alderson and Carlson [41] to represent wildfire dynamics andallocate limited resources during suppression. These models have been usedto evaluate the allocation of firefighter resources and evaluate the dispatch-ing rules [43]. Integrated fire behavior simulation and optimization to al-locate firefighting resources has also been addressed in [39], [38] and [40].8Agent-based discrete event simulation models were developed by Hu andNtaimo [37] to simulate fire suppression based on dispatch plans using astochastic optimization model. Lee et. al. [44] developed a model that com-bines an optimization model with a stochastic simulation model to assignthe number of resources by type that must arrive at the fire within a spec-ified time limit and budget. An intelligent resource allocation system tominimize the damage due to wildfire was introduced by Homchaudhuri [45],who used a genetic algorithm optimization to determines the location of thefirefighting crews. However, this system and the other wildfire FMDSSs arelimited to this particular fire type and cannot be extended to interdependentinfrastructure systems.1.2.3 Fire Strategic PlanningFire managers are faced with two types of decisions: strategic and opera-tional (tactical). The strategic decisions involves making long term plan-ning on budget allocation and the deployment or relocation of firefightingresources before fires occur. A number of strategic fire management systemshave been developed in different countries and throughout the years. Ex-amples of these systems are LEOPARDS [46], KITRAL [47], SINAMI [48]and FPA [49].The Level of Protection Analysis System (LEOPARDS) [46] is a Cana-dian model developed in 1995. The model focuses on strategic fire man-agement planning at a regional level. It uses historical data, such as fireweather, fire incidence data, operational rules and infrastructure informa-tion, to evaluate the fire pre-suppression and suppression activities under9budget constraints.In 1996, the University of Chile and the Chilean Forest Service intro-duced a fire management tool called KITRAL ("fire" in indigenous Chileanlanguage) [47]. The objective of KITRAL is to improve the efficiency offorest fire management at the national level. It evaluates different fire man-agement plans at both strategic and operation levels. Based on fire behaviorsimulation, it provides an optimal deployment of firefighting resources. Also,it evaluates different strategic deployment plans by simulating future firesand choosing the most effective plan. The LEOPARDS and KITRAL modelshave the same limitation in that they do not consider the potential damageto goods and services caused by fires [26].SINAMI is another strategic fire management planning tool developedin Spain. This model uses the historical data of the last 10-years to an-alyze the relation among different budget levels and potential losses. Aneconomic analysis is used to determine the most efficient fire managementprograms and budget [48]. This analysis considers the management costs(pre-suppression and suppression costs) and the net value change of an arrayof limited number of goods and services.In 2006, the U.S. Department of Agriculture (USDA) Forest Service andthe US Department of Interior developed the Fire Protection Association(FPA) system to evaluate the effectiveness of alternative fire managementprograms [49]. It uses cost-effective analysis to find the optimal allocationof pre-suppression resources, including numbers, types and locations of firestations. A goal programming model is used to decide the effectiveness ofalternative fire programs. The FPA model does not involve any theoretical10economic foundation in their analysis [26].Among the above FMDSSs, SINAMI model performs an economic analy-sis based on the Cost-Plus-Net-Value Change (C+NVC) concept to evaluatethe efficiency fire management programs [26]. The C+NVC concept eval-uates the fire operation costs and the related damage caused by fires. Inthis thesis, the C+NVC concept is incorporated within the decision supportsystem.Although earlier efforts have focused on strategic planning, economicefficiency analysis is also important for operational decisions and activi-ties [50]. Operational decisions (tactical decisions) are crucial for any firemanagement system and its goal is to provide optimal decisions in order tominimize the resulted damage by fighting fires in efficient ways. Operationalplanning, such as evaluating alternative fire suppression strategies, has beenthe focus of several recent research projects and papers. However, few re-cent studies attempted to include economic tools in the design of efficientfire management strategies such as Ntaimo et. al. [51, 52] and Arrubla [53]. Mendes [54] stated that there is a clear need to incorporate eco-nomic analysis in this area. In this thesis, we use economic analysis to helpfire managers to determine appropriate responses during daily operations.1.3 Problem Statement and Research ObjectivesEmergence response during fire incidents is a challenging problem. Wheneconomic efficiency is considered, infrastructure interdependence makes thisproblem more complex. An ineffective response can greatly impact theresilience of the disrupted infrastructure. There is a need to incorporate11economic efficiency into the decision making process, primarily during firesuppression planning, capacity planning and to help improve infrastructureresilience. Within this context, the following objectives are set for this re-search project:1. To formulate the fire management plans in the context of infrastructureinterdependencies.2. To develop a resource allocation and dynamic scheduling algorithm foremergency response during multiple fire incidents.3. To develop an economic efficiency model and incorporate it within thedecision-making process.4. To develop a methodology for evaluating the impact of resource allo-cation decisions on infrastructure resilience.5. To formulate the fire management problem as an optimization problemand provide a solution algorithm for this problem.6. To study the impact of human factors during fire incidents for improv-ing the overall efficiency.1.4 Thesis ContributionsThe main contributions of this thesis are summarized as follows:1. Development and implementation of a resource allocation and dynamicscheduling algorithm for emergency response during multiple fire inci-dents.122. Introduction of a methodology for evaluating the impact of infrastruc-ture interdependencies on firefighting operations.3. Evaluation of the impact of resources allocation decisions during fireincidents on infrastructure resilience.4. Development of an economic efficiency model to evaluate direct andindirect losses during emergency responses.5. Development of a planning model for capacity investment in firefight-ing resources.1.5 Thesis OrganizationThis thesis is organized as follows:Chapter 1 introduces the main focus of the thesis and discusses themotivation for the research project and its objectives.Chapter 2 describes the developed system and provides a detailed casestudy of multiple fire incidents in a large petrochemical complex.Chapter 3 applies the developed system to allocate resources to mini-mize economic losses resulting from fires. Linear and none-linear damagefunctions are considered. Finally, the human performance factor is discussedand evaluated.Chapter 4 provides a description of the capacity planning problem ina fire department. The concept of C+NVC is presented. This concept isincorporated within the developed system to determine the most efficientfire management plans.13Chapter 5 describes the resilience of infrastructure systems under fireincidents. The developed system is used to evaluate the impact of resourcesallocation decisions during fire incidents for improving infrastructure re-silience.Chapter 6 summarizes the contributions of this thesis and makes recom-mendations for future studies.14Chapter 2System Development2.1 IntroductionThis chapter presents the development of a fire management decision sup-port system for assisting fire managers in making efficient decisions. Thissystem relates suppression operation costs to the reduction in expected dam-ages. It is assumed that the goal of fire managers is to minimize the totalcost which consists of the fire operational costs and the net damage. Themain functions of the proposed system are: (a) resources allocation opti-mization: this includes damage and economic impact analysis, optimizationof resources allocation and scheduling decisions during fire incidents, (b)manpower capacity planning: this includes making decisions on planningof manpower management over long-term planning and evaluating the costand consequences of alternative plans, and (c) improving resilience of inter-dependent infrastructure systems: this includes the evaluation of resilienceof infrastructure systems and making effective decisions to strengthen re-15Figure 2.1: Overall architecture of the proposed FMDSS.silience. These functions are covered separately in Chapters 3 to 5.Figure 2.1 presents the overall architecture of the proposed fire man-agement decision support system. It has four main components: (i) a firesimulation model for modelling fire behavior and evaluation of fire damage,(ii) Infrastructure Interdependencies Simulator (i2Sim) for evaluating the in-teraction among critical infrastructure systems, (iii) an economic model forevaluating both operational costs (pre-suppression and suppression costs)and damage (direct and indirect losses), and (iv) an optimization agent forminimizing the sum of management costs and net damage.The above main components are described in sections 2.2 through 2.5.Finally, Section 2.6 describes a case study that is used throughout this thesisto show the effectiveness of the various functions of the developed system.162.2 Fire Simulation ModelThis section describes the fire simulation model. The objective of this modelis to assess the damage level produced by fires. In order to evaluate thedamage, we first introduce a fire severity measure to estimate fire duration.This measure relates the required number of firefighters to the estimatedfire suppression time. Secondly, a damage function is used to associate thefire duration with a particular level of damage. These are described in moredetail in the following subsections.2.2.1 Fire Severity MeasureThe fire simulation model starts with a definition of the Fire Severity Mea-sure (FSM). This measure is used to describe the severity of fire. Examplesof potential severity measures include fire duration, peak fire temperature,fuel load, heat release rate, etc. [55], [56]. Although these measures of fireseverity are often closely related, there is no standard quantitative measureof fire severity [57]. In this thesis, FSM is defined as the total man-hoursneeded to control a fire. This number can be estimated with the help offirefighting experts. A large FSM value means that a large number of fire-fighters is required to suppress the fire. For a given fire, different resourcesallocation decisions can be made and each decision may result in differentfire durations which in turn results in different FSM values.Fire duration has a strong positive correlation with damage and can forma basis for design decisions. Thus the fire damage, d(T ), can be expressedas a function of the fire duration time T . The fire duration time can be17calculated by:T = FSMi∑nj xij(2.1)whereFSMi is the severity measure of fire in is the total number of fire stationsxij is the total number of firefighters assigned to fire i from fire stationj during the suppression process.To capture the dynamics of fire, the damage assessment table, Table 2.1,can be used to map the fire duration time into five damage levels. Theselevels are: 1) minimal damage, 2) low damage, 3) intermediate damage, 4)high damage, and 5) excessive damage. During simulation, the expecteddamage level can change over time in the increasing direction. For example,the level of damage in a burning building can change from low damage tointermediate, but not in the opposite direction. Also, each level of damageis associated with the repair or reconstruction period of time, as shown inTable 2.1. For example, if the fire suppressed and resulting level of damageis intermediate, then the recovery time is estimated to be three months.2.2.2 Damage FunctionIn general, damage functions increase with the magnitude of the extremeevent such as a flood or a fire, and eventually exhibit saturation [58]. Here,18Color Code Level of damage Recovery time DescriptionGreen Minimal Minimal No damage but light maintenance isrequired for safety.Blue Low 1 MonthHeavy maintenance is required andsome equipment repair services areneeded.Yellow Intermediate 3 Months May cause minor damage and someequipment needs replacement.Orange High 6 Months May cause major damage requiringshort-term reconstruction.Red Excessive 12 Months May cause significant damage andlarge reconstruction effort is required.Table 2.1: Damage assessment table.Figure 2.2: Illustration of the damage function.a two-piece linear damage function is assumed with this form:d(T )lin =TTCif T < TC1 if T ≥ TC(2.2)whereTC is the time for the fire damage to reach 100%. This function isillustrated in Figure 2.2.19The assumptions in the damage functions are conservative since the levelof damage is influenced by several other factors such as wind speed anddirection and fuel type and load. The case of considering non-linear damagecurves are discussed in section i2Sim Modeling and Simulation FrameworkUnderstanding how interconnected infrastructure systems behave when sub-jected to external events such as fires remains a major challenge for emer-gency responders. Also, an effective emergency response requires considera-tion of the interactions among the multiple layers of an effective emergencyresponse: decision layer, damage layer, finance layer, and production layer.In order to understand this behavior, simulations can be used to model theinteractions between these dissimilar systems.The infrastructure interdependencies simulator (i2Sim) introduced byMarti [3] provides a simulation framework that captures the interactionsamong these systems. i2Sim has been used in modeling infrastructure sys-tems in different emergency response applications [59], [60], [61], [60]. Inthis thesis, i2Sim is selected for five main reasons: (i) the ability to choosethe global simulation objective (e.g., economic, environmental or security),(ii) the ability to simulate and produce reasonable results even when data islimited, (iii) the ability to simulate multiple infrastructure interdependencies(e.g., water, power and oil), (iv) the ability to simulate the effects of resourceallocation decisions in real time, and (v) the ability to integrate other simu-lators and assess the impacts of decisions made in one infrastructure on theother.20The simulator provides an environment for representing multiple inter-dependent infrastructure systems. To capture the interactions among thesesystems, i2Sim defines a common ontology based on a cell-channel approach.The i2Sim ontology is described in the following section.2.3.1 i2Sim OntologyThe i2Sim ontology is based on a cell-channel approach. It represents thefunctionality of each cell using input-output relationships. The i2Sim com-ponents are defined as follow:• Cell (Production Unit): A cell is used to model system componentssuch as hospitals, electrical substations and water stations.• Token (Resource): A token represents the resources that circulate through-out the system, such as, electricity, water or gas.• Channel (Transportation Unit): A channel carries the tokens fromone cell to another. They represent the relationships between thesystem components. Examples include roads, transmission lines andwater pipes.• Distributor (Control Unit): Distributor is a decision point where ac-tions can be taken to allocate the resources.• Aggregator (Control Unit): Aggregator is another decision point. Itcombines two outputs of the same token into one channel.• Physical Mode: Physical Mode (PM) represents the level of physicaldamage of the cells or channels.21• Resource Mode: Resource Mode (RM) represents the availability of in-put resources to the cells.• Sources: These are the producers of the external tokens. Sources repre-sent infrastructure systems that are not included in the i2Sim model.• Reservoirs: These are the storage elements in the i2Sim model.• Sinks: These are the components that send internal tokens to outside thei2Sim model.• Modifier (Affecter): Amodifier represents the external information thatis received as input into cells, channels, distributors and aggregators.For each cell, there is one output (product) and one or more inputs(resources). The operating state of each cell is influenced by the availabilityof the tokens (resources), the level of the PM (physical damage of the cell)and modifiers (external information) that are received as input into the cell.Figure2.3 shows the possible operating states of cells and channels. The PMare discretized into five possible color-coded levels. The five color-codedlevels are red=0%, orange=25%, yellow=50%, blue=75% and green=100%.2.3.2 i2Sim ModelsThe i2Sim components can be used to model multiple dissimilar infrastruc-ture systems. Infrastructure system components are defined as cells andthe connections between them, such as transmission lines and oil pipelines,which are defined as channels. Resources and services, such as oil, water and22Physical ModeCellChannelFigure 2.3: Conceptual cell and channel models [3].power, which are defined as tokens that move between cells (i.e., throughchannels). The relationship between the inputs and the output is predefinedby a function which describes the operation of the cell. This function is alsoknown as a lookup table or Human Readable Table (HRT). The operabilityof the cells is determined by the minimum available resources. An exampleof an HRT representing an Emergency Room (ER) in a hospital is shownin Figure 2.4. In this example, the operability of the unit is 50% due to thelack of water. At this level, the ER can treat only 10 patients per hour. Inour case study, we use the HRT function to simulate the operability of thepetrochemical plants.The combinations of cells and channels in the i2Sim model set up a math-ematical formulation of the relationships between infrastructure systems. Asystem of discrete time equations is created, which is solved simultaneouslyfor all components at every time step along the timeline to find the operatingpoint of each production cell. [3, 62]23Figure 2.4: An example a Human Readable Table (HRT) for an Emer-gency Room (ER) [3].The interaction between these systems can be captured using the i2Simsimulation layers. Figure 2.5 shows the basic i2Sim simulation layers. Theexchange of information between these layers is performed through the mod-ifiers. The availability of this information assists emergency responders toevaluate feasibility or effectiveness of different response plans to reduce therisk to life and property in the event of an emergency.2.4 Optimization AgentFinding optimal decisions to control the behavior of interdependent infras-tructure systems is crucial during extreme events. In some critical situations,the dynamics of the systems are not completely predictable and it is nec-essary to quickly find new optimal actions as incidents evolve. Simulationgives decision makers the opportunity to evaluate the options for action. Anoptimization agent, based on Reinforcement Learning (RL), is developed tooptimize the global objective by dynamically assigning firefighting units to24Production CellPhysical ModeICT ModeDistributorPhysical Layer(substations, pipes, hospitals)Damage Assessment Layer(flood, earthquake, sensors)Strategic Decisions Layer(organizations, policies, procedures)ICT Layer(data, voice, video)Figure 2.5: i2Sim simulation layers [3].the most critical fire. This agent is integrated with the i2Sim model and thefire simulation model.2.4.1 Reinforcement LearningRL is a machine learning technique which involves learning by taking actionsin a trial-and-error manner. It consists of an agent, a finite set of states S,a set of available actions A, and a reward function R. The agent is thelearner and the decision maker and everything it interacts with is called theenvironment.Unlike supervised learning methods such as neural networks which re-quire training data with input and expected output, RL can learn directlyfrom the interaction between the agent and its environment. By interacting25with its environment, the RL agent learns to map its current state to thebest action (state-action pair) to maximize long-term rewards [63]. A keyadvantage of the RL paradigm is in its ability to deal with delayed rewardsituations [64]. This makes it suitable for emergency response operations,where rewards are often obtained a long time after the action. For example,the impact of a fire suppression plan will not be apparent immediately, butrather at some point in the future. RL has been applied successfully to a widerange of problems in a variety of disciplines, including scheduling in sensornetworks [65], resource allocation in business process management [66], opti-mal allocation resource in water resource management systems [67], learninguser behavior in social networks [68], and spacecraft payload processing [69].RL has five main components [63]:1. An agent represents the learner and the decision maker that interactswith the environment.2. A policy is a function which defines the behavior of the agent. Itdetermines the proper action to take at each time-step based on thestate the agent is in.3. A reward function maps each state-action pair to a scalar value andreward, so that the performance can be evaluated in a mathematicalequation.4. A value function calculates the accumulated reward over time of aspecific state-action pair. The agent’s goal is to maximize the collectedrewards it receives over time.265. A model of the environment represents the system which the agentinteract with.A common algorithm for solving RL problems is Temporal DifferenceLearning (TD). The TD algorithm is described in the following section.2.4.2 Temporal Difference Learning (TD)TD is the reinforcements learning algorithm that is most successful andbroadly applied algorithm to RL problems [63]. TD methods apply a valuefunction that estimates the future reward for taking a particular action ina state. These methods can be classified based on the approach they followin search of the optimal action policy: on-policy and off-policy methods.In on-policy methods, the agent follows a policy to explore the envi-ronment. Simultaneously, the agent tries to find the optimal policy thatmaintains exploration of possible actions. In other words, the policy thatis being optimized is also used to explore the environment. An exampleof this type of methods is the State-Action-Reward-State-Action (SARSA)algorithm. On the other hand, in off-policy methods, the agent has two dif-ferent polices: a behavior policy and an estimation policy. The agent learnsthe estimation policy from the actions performed by the behavior policy. Anexample of this type of methods is the Q-learning algorithm [63].Both methods can find the optimal policies. The main difference betweenthese methods is in the speed of convergence. The on-policy methods haveshown faster convergence than the off-policy methods in different fields ofapplication [70, 71].During extreme events, such as fires, response time is critical. With this27kind of situation, on-policy methods can help to assist emergency respondersto optimize the allocation of limited resources. In this thesis, SARSA isutilized in our decision-making process.2.4.3 SARSA AlgorithmSARSA is a learning algorithm for sequential decision making that learnsthe value of applying an action in any state. In its simplest form, SARSAis defined by the following equation [63]:Q(st,at)←Q(st,at)+α[rt+1+γQ(st+1,at+1)−Q(st,at)], (2.3)whereat: is the action taken at time tst: is the state assumed at time trt+1: is the reward at time t+1Q(st,at): is the learned state-action value function at time t0 ≤ γ ≤ 1: is a discount factor, which determines the importance of fu-ture rewards0 ≤ α ≤ 1: is the learning rate, where a factor of 0 will make the agentnot learn anything, while a factor of 1 would make the agent considers onlythe most recent information.The goal of the agent is to learn a policy pi that maximizes the rewardover the agent’s lifetime. This policy maps the current state s into the mostdesirable action a to be performed in s:28Figure 2.6: Reinforcement Learning (RL) learning model.pi = {(s,a) | s ∈ S,a ∈A} (2.4)The desirability of each state-action pair can be represented by a valuefunction, Q:Q : S×A→R (2.5)At each interaction with the environment, the agent observes the environ-ment’s state st ∈ S. Then, it selects an action at ∈ A(st), where A(st) isthe set of all possible actions at state st. After taking an action, the agentmoves to a new state st+1 and receives from the environment a reward rt+1.The value function Q(s,a) is then updated based on in Equation 2.3. Thisprocedure continues and the agent adjusts its policy until either the optimalassignment is reached or the stopping criteria is met.292.4.4 Reinforcement Learning (RL) ModelFigure 2.6 shows the proposed RL model. It consists of an agent, a finiteset of states S, a set of available actions A, and a reward function R. Theagent is the learner, and the decision maker and everything it interacts withis called the environment. The objective of the agent is to minimize the costof business interruption.A state s ∈ S contains the PM and RM values in the i2Sim model.For example, the state list for two simultaneous fire incidents at two dif-ferent locations (x and y) is formatted as (PMx,RMx,PMy,RMy), wherePM and RM reflect the physical state and the functionality of each cell.As mentioned in section 2.3, PM and RM are discretized into five lev-els. Therefore, the total number of states considering two fire incidents is(number of PM for location1)×(number of RM for location1)×(number ofPM for location2)× (number of RM for location2).The set A of possible actions which can be taken when in a state s ∈S consists of available resources that can be assigned. If it is assumedthat the number of available resources is 100 firefighters, this enables theformation of 20 units of five firefighters each. Based on the number of fireincidents, the fire simulation model creates a list of possible actions fromA= {0,20,40,60,80,100}. For example, the available actions for each statein two simultaneous fire incidents are {(0,20), (0,40), (0,60), (0,80), (0,100),(20,0), (20,20). . . }, corresponding to a total of 21 actions.The reward r is based on the output of the economic model. It representsthe total value of all products produced by all production units (cells) in30the i2Sim model. More details on how to calculate this value are providedin the following sections.The agent begins learning by sensing the current state st of the modeledsystem reflected by the physical and resource modes of the i2Sim model.It then searches for the best action at (action with the highest reward onthat state) in a look-up. This table stores state-action pairs (s,a) and theircurrent Q-values, Q(s,a). Table 2.2 shows a look-up table sample. TheQ-values are initialized randomly. Upon performing the best action, thesystem transitions to state st+1 and receives a reward r. Next, the agentupdates Q(s,a) based on Equation 2.3. After consecutive runs, the agentlearns the best path with the help of the learned state-action value Q.(state, action) Q(state,action)(1,1,1,1,0,20) 51(1,1,1,2,0,40) 620(1,1,1,3,40,60) 422(1,1,1,4,0,80) 911(1,1,1,5,20,0) 1(1,1,2,1,40,60) 37(1,1,2,2,50,50) 8156. . . . . .. . . . . .(5,5,5,5,20,80) 422Table 2.2: Look-up table sample.2.5 Economic Efficiency ModelEconomic efficiency of fire management can be defined as the ability toallocate limited resources in a way that minimizes the sum of management31costs and net damage. A formalization of this concept was introduced inthe early 1916s by Headley [72] and Lovejoy (1916) [73]. It was assumedthat increasing the cost of management (pre-suppression, suppression) woulddecrease the fire induced damage. Sparhawk (1925) [74] formulated thisconcept into the Least Cost Plus Loss (LC+L) model. The objective ofthis model is to find an optimal pre-suppression (protection plan) cost. Themodel has been investigated and improved over time into the Cost-Plus-Net-Value Change C+NVC model [75], [76] and [4].In the (C+NV C) model, the cost (C) sums all firefighting expenditures,such as purchasing equipment and wages for firefighting crews, as illustratedin Figure2.7. The net value change (NV C) include both direct and indi-rect losses induced by fire. The direct losses are the losses incurred due tothe immediate effects of fires. The indirect losses are the losses related toa cascade of effects of fires due to functional or physical interdependence.Theoretically, as the fire operation costs increase, the net fire damage isexpected to decrease [48]. The result of this analysis is a U-shape function,with a minimum point that represents the optimum fire management pro-gram (i.e P* in Figure2.7). For a given level of pre-suppression cost, themost efficient fire program is achieved where the summation of suppressioncost and net value change is minimized.In this thesis, we used the C+NVC model to evaluate both strategic andoperational planning decisions faced by decision makers in a fire department.The strategic planning, which we refer to as the strategic capacity planning,involves making decisions about manpower management over a long-termtime line. Over the strategic time frame, the fire department must plan32Figure 2.7: Illustration of the C+NVC model [4].for recruiting to meet desired staffing levels. The objective is to find themost efficient fire management program by minimizing the summation ofthe fire operation costs (C) and net fire damage (NV C). This minimizationproblem can be represented mathematically as:MIN: C + NVC=T∑t=1(Ct+NV Ct), (2.6)whereCt: fire operation costs (manpower and equipment) in period tNV Ct: net loss due to fires in period tT : planning periods33Operational planning deals with the allocation and scheduling of a lim-ited number of resources. Operational planning differs from strategic plan-ning in that for operational planning the manpower capacity is consideredfixed which means that the cost component of C+NVC is not the incre-mental cost between the different programs. As a result, the objective is todevelop efficient allocation and scheduling strategies that minimize net firedamage NVC.The net fire damage NVC can be expressed as the net loss in the valueof the overall production level. Mathematically, it can be calculated bysubtracting the value of the production level of all products pre-fire fromthe value of production level of all products post-fire. Different allocationstrategies can be evaluated using the following equation:NVC=n∑i=1m∑j=1(Q1ij−Q2ij)Vj (2.7)whereQ1: production without firesQ2: production with firesn: number of production unitsm: number of product categoriesVj : market value of product j342.6 Case StudyIn order to evaluate the effectiveness of the proposed FMDSS, a case studyof multiple fire incidents in a large petrochemical complex was conducted.This case study is based on real data and aims at optimizing firefightingresource management while considering operational and strategic decisions.2.6.1 Petrochemical IndustryAll experimental results in this thesis use a petrochemical complex as a casestudy for this research, for the following reasons. Firstly, the petrochemi-cal industry is considered to be one of the most important basic industries.Petrochemicals are derived from oil and natural gas and incorporated intoa great variety of products in the food industry, medical industry, textileindustry, plastic industry, and fertilizer industry. The petrochemical indus-try is a major contributor to the growth of the world economy. In 2011,the global petrochemicals market was valued at $472.06 US billion and isexpected to reach $791.05 billion by 2018. The global petrochemicals con-sumption is expected to reach 627.51 US million tonnes by 2018 [77].Secondly, the operation of petrochemical plants involves very complexprocesses of physical and chemical reactions. These processes often require awide variety of extreme operating conditions at high temperatures and pres-sures and other complex technical operations. Due to the large amounts offlammable gases and liquids involved, the petrochemical industry is contin-uously exposed to the risk of fires, explosions and other accidents. One ofthe safety measures to reduce this risk is to restrict the storage of flammablematerials. Therefore, petrochemical plants are most often grouped together35into a single complex to transport products immediately into pipelines. Asthe number of plants located in the complex increases, benefits increase dueto increase in efficiency, close access to specialized suppliers and reduction intransportation costs. On the other hand, any additional plant may decreasethe overall safety of the complex [78].Thirdly, the petrochemical industry is increasingly characterised by ahigh degree of physical interdependence. An interruption in one plant canbe extremely disruptive to the operation in one or more other plants. Thisphenomenon is called the "domino effect". Although the domino effect hasbeen reported in the technical literature since 1947, there is no agreed def-inition of what constitutes domino effects in the context of accidents inindustrial plants [79]. Khan and Abbasi [80] defined domino effect as "achain of accidents, or situations when a fire, explosion, missile or toxic loadgenerated by an accident in one unit in an industry causes secondary andhigher order accidents in other units".In this thesis, we generalize the definition of the domino effect by includ-ing any distractions in production generated by a primary accident in oneor more plants. Also, we consider the bidirectional effects of accidents byincluding the economic impacts on both the consumers’ side and the produc-ers’ side. For example, if Plant A supplies Plant B with its raw materials,any interruption in the production process of Plant A could result in aninterruption in Plant B. Conversely, if any interruption in the productionprocess of Plant B occurs, Plan A might suspend its operation.362.6.2 Case Study DataThe case study considered in this thesis is an industrial city that has a largepetrochemical complex. This complex consists of 12 petrochemical plants.Each plant produces one or more petrochemical products as listed in Table3.1.The industrial city has 300 firefighters (100 firefighters per shift) forming20 units deployed to five fire stations, where each station has four firefightingunits. Two simultaneous fire incidents, Fire 1 and Fire 2, were simulatedin Plant 10 and Plant 4, respectively. We assume that Fire 1 requires 600man-hours to be suppressed, while Fire 2 requires only 200 man-hours. Itis assumed that this type of accident occurs once every ten years.The simulations involved 15 hours of concurrent suppression operationsfor the two fire incidents. New assignments of the firefighting units weredetermined every hour.2.6.3 Example of Interdependence in a PetrochemicalcomplexEach plant in a petrochemical complex requires raw materials for produc-tion. Oil refinery and upstream plants supply raw materials to productionplants. The relationship between the plants can be expressed according totheir position in the production chain as primary producer, primary con-sumer, secondary consumer, and tertiary or higher-order consumer. Theprimary producers are the plants that do not receive their raw materialsfrom other plants, mainly they receive raw materials from oil refinery. Theother plants receive some of their raw materials from primary producers and37Figure 2.8: An example of interdependencies and relations betweenpetrochemical plants.may supply other plants with raw materials or export. Due to this inter-dependence, a single disruption to an upstream plant can impact the entirecomplex.Using this criterion, Figure 2.8 presents an example of interdependenceand the relations between the petrochemical plants during the productionprocess. Plant 4 is an example of a primary producer because it receives itsraw materials, Methane and Butane, from the oil refinery. It supplies Plant3 and Plant 8 (primary consumers) with Methanol. Plant 7 and Plant 12are considered as secondary consumers because they receive some of theirraw materials from primary consumers, Plant 3 and Plant 8. Plant 12 canbe also described as a tertiary consumer because it receives Ethylene froma secondary consumer, Plant 7.During the operation process, any disruption in the production processin Plant 4 can lead to a shutdown in the production process in primaryconsumers, Plant 3 and Plant 8. This shutdown has a domino effect that38spreads to all secondary and tertiary consumers, Plant 7 and Plant 12.Furthermore, any disruption to a secondary consumer (e.g., disruption inPlant 7) might suspend the production process in the primary producer,Plant 4, and all primary consumers, Plant 3 and Plant 8. As a result of this,other secondary consumers, Plant 12, suspends its operation due to lack ofraw materials.The previous example illustrates the high level of interdependence be-tween petrochemical plants that need to be considered when developingemergency response plans.2.6.4 General AssumptionsWhile this thesis has focused its attention on the fire managements decisionsin line with the expected losses, the following assumptions were made in thecase study:1. No humans were in danger during the incidents, otherwise saving themwould have been the highest priority.2. The environmental impact, such as toxicity, was not taken into ac-count.3. All the plants had the same level of flammability.4. No other organizations (e.g., police and ambulance services) were in-volved.5. The wind speed and wind direction were the same in both fire inci-dents.396. During multiple-fire incidents, there has to be a minimum numberof firefighting units to be allocated to each incident because of thepresence of explosive chemicals in the petrochemical industry.7. All the plants have the same level of fire safety over the planningperiod.2.7 ConclusionIn this chapter, we discussed the development of a fire management de-cision support system. The system estimates the damage associated withfire incidents, calculates the economic loss resulting from the damage andthen provides the optimal assignment of the available firefighting units. Akey novel addition is the consideration of infrastructure interdependenciesin the decision making process. The joint optimization of the number ofassigned firefighting units and the estimated damage significantly reducesthe economic loss.A detailed case study of multiple fire incidents in a large petrochemi-cal complex is described. The case study is used throughout this thesis tostudy the issues of resource allocation, capacity planning, and improvinginfrastructure resilience. Chapter 3 applies the developed system to allocateresources to minimize economic losses resulting from multiple-fire incidents.Linear and non-linear damage functions are considered. In chapter 4, thedeveloped system is used to evaluate the impact of hiring decisions on ef-fectiveness of firefighting operations. Chapter 5 describes the resilience ofinfrastructure systems under fire incidents. The developed system is used40to evaluate the impact of resource allocation decisions during fire incidentson improving infrastructure resilience.41Name Product Ton/yearPlant 1 Methanol 1,007,400Butanediol 75,000Plant 2 Poly Propylene 438,000Plant 3 MTBE (methyl tertiary-butyl ether) 613,200Poly Propylene 1,500,000Isopentene 1,460Plant 4 Methanol 963,600MTBE (methyl tertiary-butyl ether) 1,007,400Isopentane 5,256Plant 5 Polyethylene 744,600Ethylene Glycol 1,489,200Plant 6 Ammonia 438,000Ethyl hexanol 171,550Urea 700,800Plant 7 Ethylene 2,102,400Propylene 1,314,000Butene 1,752,000Plant 8 Ethylene 1,051,200Sodium Hydroxide 175,200Ethylene Dichloride 3,066,000Plant 9 Fertilizer 4,818,000Plant 10 Methanol 3,285,000Plant 11 Ethylene 1,314,000Mono-ethylene Glycol 569,400Diethylene Glycol 613,200Plant 12 Ethylene 700,000Propylene 87,600Polyethylene 1,095,000Table 2.3: List of the petrochemical plants and their products coveredby this case study.42Chapter 3Resources Allocation andScheduling DuringMultiple-Fire Incidents3.1 IntroductionDuring fire incidents, the main duty of firefighters (after saving lives) is tominimize the incidents’ losses. According to Hall [9], the total cost of a fireis defined as the losses the fire causes, directly and indirectly, plus the costof provisions to mitigate these losses. The US NFPA reported that in 2011,the estimated fire-related economic loss was $14.9 US billion. These lossesinclude both property damage (direct losses) and business interruption (in-direct losses). Also, the report shows that 65% of the business interruptioncost ($9.7 US billion) was caused by fires in industrial properties [9]. Due43to the difficulty in pre-calculating the indirect losses, the current firefightingpractices target the fires with larger size to reduce property damage. How-ever, the analysis of the fires showed a low correlation between the propertydamage cost and the business interruption cost [9]. In many cases, the costof business interruption far exceeds its direct property loss. Hall [9] stated,“Sometimes, though, it can be difficult to determine what the true net lossdue to business interruption is.” In the method developed in this chapter,the indirect losses, resulting from business interruption, will be estimatedand then used as a significant factor in allocating the firefighting resources.In this study, we use propose a methodology to optimize the allocationprocess of firefighting resources in multiple-fire incidents. This methodol-ogy utilizes the concept of infrastructure interdependencies in evaluating theeconomic impact of the incidents. It consists of three main parts. The firstpart uses infrastructure interdependency modeling to represent the interac-tions among different systems. The second part uses economic modeling toevaluate the economic impact of the fire incidents. The third part deter-mines the assigned number of firefighting units using an optimization agentbased on the RL algorithm. The proposed methodology can be used beforethe fire occurs, for training and planning, during the fire for optimizing theresponse or after the fire, for evaluating suppression strategies.The proposed resource allocation methodology is presented in Section3.2. After that, we examine four different fire suppression methods in Section3.4. Also, we discuss the impact of considering different non-linear damagefunctions. Then, we evaluate the human performance factor on the resourceallocation decision in Section 3.4.2. Finally, a conclusion is presented in44Section Resource Allocation and SchedulingMethodologyIn terms of the operation planning of fire management systems, allocatingand scheduling available resources is one of the most challenging decisionsduring multiple fire incidents. The direct and indirect economic losses in-duced by fires should be carefully considered. Thus, it is extremely im-portant to minimize the overall economic losses by optimally allocating andscheduling firefighting units to each fire. In this section, we use the developedsystem, described in Chapter 2, to propose a methodology for the optimalallocation of firefighting resources during suppression operation. Figure 3.1shows the main steps of the proposed methodology.The proposed methodology starts by generating fire incident scenariosusing the fire simulation model. These scenarios can be single or multiplefire incidents. After evaluating the required number of firefighters for eachfire, the fire duration time is calculated by Equation 2.1. Using a damagefunction, the fire duration time is mapped into five Physical Modes (PMs)described previously in Section 2.3.1, which form the input to the i2Simmodel. Figure 3.2 shows how fire duration is mapped to physical modesusing a simplified (linear) damage function.Next, i2Sim simulates the effects of resources allocation decisions overtime. The production of each cell is degraded according to the damage as-sessed by the fire simulation model described in Section 2.2. Simultaneously,i2Sim simulates the functionality of the interdependent cells and computes45Figure 3.1: Resource allocation methodology.the outputs of all the production facilities. These outputs become the inputto the economic model, which calculates the estimated losses based on mar-ket prices. The output of the economic model is the economic loss associatedwith the current operating state of the cells.The last step of the methodology is the determination of the optimal al-46Figure 3.2: Mapping between fire duration and Physical Mode(PM).location decisions. The optimization agent uses the economic loss as rewardor penalty. The objective of the agent is to learn the optimal decision forassigning firefighters that minimizes the economic losses experienced in thelong run.47Name Product Ton/year Raw Martials Ton/year SourcePlant 4 Menthol 959,000 Methane 210,240,000 Oil refineryMTBE 985,000 Butane 876,000 Oil refineryPlant 6 Ammonia 459,900 Methane 150,000 Oil refineryEthyl Hexanol 171,550 Propylene 300,000 Plant 7Urea 693,500Plant 7 Ethylene 2,000,000 Ethylene Dichloride 3,248,500 Plant 8Propylene 1,000,000 Sodium Hydroxide 204,400 Plant 8Butane 2,000,000 Propane 2,007,500 Oil refineryMethane 2,007,500 Oil refineryEthane 1,000,000 Oil refineryTable 3.1: Sample Data Format3.3 Case Study Modeling3.3.1 Data DescriptionThe case study described in Section 2.6 considers an industrial city. The cityencompasses an area of about 100 square kilometres and has a petrochemicalcomplex consisting of 12 chemical plants. Theses plants produce 28 differentpetrochemical products. These materials are transported through pipelinesbetween the plants. The petrochemical complex is modeled based on realdata. Sample data for three plants is shown in Table 3.1. The first columnrepresents the plant name. The second and the third columns show theproducts and their annul production (Ton/year), respectively. The fourthand the fifth columns show the raw martials and their total quantity con-sumed per year (Ton/year), respectively. The last column shows the sourceof each raw material which can be a product of another plant or receiveddirectly from the oil refinery.483.3.2 i2Sim ModelThe first step to build the i2Sim model is to define the production cells. Re-call that an i2Sim production cell takes one or more inputs and produces anoutput based on the defined HRT function as described in Section 2.3.Eachplant is presented by one or more production cells based on the number ofoutput products. For example, we use two production cells to model Plant4 and use three production cells to model Plant 7. Figure 3.3 shows theproduction cells used to model Plant 7.Figure 3.3: Plant 7 production cells.In total, we need 28 production cells to model the entire complex. Table3.2 shows the number of production cells used to model each plant.The second step is to create the HRT tables for the production cells. TheHRT tables model the input-output relationship in i2Sim cells as described49Name Number ofproductsNumber of usedproduction cellsPlant 1 2 2Plant 2 2 2Plant 3 1 1Plant 4 3 3Plant 5 2 2Plant 6 3 3Plant 7 3 3Plant 8 3 3Plant 9 1 1Plant 10 1 1Plant 11 3 3Plant 12 3 3Table 3.2: Number of used production Section 2.3. Table 3.3 shows the HRT table for Ethylene productioncell in plant 7. The first column represents the operability level of theproduction cell. This level ranges from 0 to 100 %, where 0 % indicates nofunctionality and 100 % indicates full functionality. Each level is associatedwith a particular amount of production as shown in the second column.There are two factors that can influence the plant functionality. One is theavailability of the necessary resources (plant inputs) required to operate theplant, which are listed in the 3rd to the 5th column. The second factor isthe the physical integrity of the plant, which is given in the last column.50OperabilityPlant output(Product)Plant inputs(Raw materials) PhysicalintegrityEthylene[Tons/hour]Ethy. Dich.[Tons/hour]Sod.Hydroxid[Tons/hour]Propane[Tons/hour]Methane[Tons/hour]Ethane[Tons/hour]100% 240 350 20 230 230 100 100%75% 180 262.5 15 172.5 172.5 75 75%50% 120 175 10 115 115 50 50%25% 60 87.5 5 57.5 57.5 25 25%0% 0 0 0 0 0 0 0%Table 3.3: HRT table for Ethylene production cell in Plant 7.51The third step is to identify the i2Sim sources model the external tokens.As described in Section 2.3, sources represent infrastructure systems that arenot included in the i2Sim model. In this case study, we use sources to modelthe tokens produced by the oil refinery. Seven sources are used to model theproduction of the following tokens: Methane, Ethane, Propane, Propene,Butane, Butene and Benzene. Figure 3.4 shows the sources that used tomodel the oil refinery.Figure 3.4: Oil refinery sources.52The next step is to determine the distributors, the aggregators and thesinks. The distributors are the allocation units in the i2Sim model. Eachdistributer has one input and multiple outputs of the same token type. Inthis case study, we use 14 distributers to distribute 14 petrochemical prod-ucts among the plants. Also, we have 13 different petrochemical martials tobe aggregated in one channel for each one. We use 13 aggregators to com-bine two similar products into one channel. The last stage of the productionprocess in this case study is the export which is modeled as a sink. Sinksare the components that send internal tokens to outside the i2Sim model.The last step of modelling the case study is to connect all the i2Simcomponents via channels. Figure 3.5 shows the i2Sim model for the petro-chemical complex.53Figure 3.5: The i2Sim model for the petrochemical complex.543.4 Results and DiscussionIn this section, we consider applying four different allocation methods tothe case study. Next, we examine the case of non-linear damage functions.Two non-linear damage functions are considered to evaluate fast and slowdamage development. Finally, we extend the model to include the impactof human performance factors on firefighting operations. The most criticalhuman performance factor in firefigting effectiveness is the degradation ofperformance under stressful mental and physical conditions.We tested four different allocation methods (operational plans) as listedin Table 3.4. Methods 1 and 2 represent "business as usual" actions duringa multiple-fire incident, which means allocating firefighting units based onfire size and giving more units to larger fires. In method 3, fires are treatedequally regardless of their size or their criticality. Method 4 corresponds toa situation where the allocation and scheduling process of fire resources isbased on economic evaluation of losses.Method Methodology Description ObjectiveMethod 1 70%-30% 70% to the large fire,30% to the other fire. Suppress large fire firstMethod 2 60%-40% 60% to the large fire,40% to the other fire. Suppress large fire firstMethod 3 50%-50% 50% to each fire. Treat all fire accidents equallyMethod 4 Optimized Assign units based onoptimization technique. Suppress fires to minimize lossesTable 3.4: Allocation methods.Simulations were carried out for the four fire allocation methods men-55tioned above. Each method produces a different assignment sequence offirefighting units to each fire. The simulation results are shown in Table3.5. The first column shows the simulating time in hour. The last columnreports the results obtained by the proposed the FMDSS. It shows the dy-namic allocation of the firefighting units between the two fires, Fire 1 andFire 2. U represents the number of allocated firefighting units to each fire.T represents the required man-hour to suppress each fire.As shown in Table 3.5, the proposed FMDSS, Method 4, was able torecognize the critical fire and suppress both fires with minimum time com-pared to the other allocation methods. Also, the results show that Method1 is the worst decision, since it requires the longest suppression time.In order to evaluate the economic impact of using the four allocationmethods, we evaluate the annual production income of the petrochemicalcomplex. Using i2Sim, we simulates the functionality of the petrochemicalcomplex and compute the outputs of all the production cells. The annualproduction income of the complex is calculated using the market value ofthese outputs, which is $28,703 US million. Upon comparing this incomelevel with the income after the two fires are suppressed, it is clear that thedecision based on economic evaluation (Method 4) achieves the minimumeconomic loss.56Time (h)Method 1 Method 2 Method 3 Method 4Fire 1 Fire 2 Fire 1 Fire 2 Fire 1 Fire 2 Fire 1 Fire 2U T U T U T U T U T U T U T U T1 14 600 6 200 12 600 8 200 10 600 10 200 4 600 16 2002 14 530 6 170 12 540 8 160 10 550 10 150 4 580 16 1203 14 460 6 140 12 480 8 120 10 500 10 100 12 560 8 404 14 390 6 110 12 420 8 80 10 450 10 50 20 500 0 X5 14 320 6 80 12 360 8 40 20 400 0 X 20 4006 14 250 6 50 20 300 0 X 20 300 20 3007 14 180 6 20 20 200 20 200 20 2008 20 110 0 X 20 100 20 100 20 1009 20 10 0 X 0 X 0 X10 0 X1112131415X: Fire suppressed.Table 3.5: Results for the resource allocation methods (U: no. units; T: fire timer).57Figure 3.6 shows that the total economic loss in Method 4 was just $558US million compared with $3,525 US million for Method 1, $1,236 US millionfor both Method 2 and Method 3. It is worth noting that the total economicloss when no action is taken is a massive $ 21,006 US million.Method 1 Method 2 Method 3 Method 4 No action02,0004,0006,0008,00010,00012,00014,00016,00018,00020,00022,000Allocation MethodsTotal Losses ($ Millions)Figure 3.6: Total losses of different allocation methods.3.4.1 Damage FunctionsAs we mentioned in Section 2.2.2, the level of damage is influenced by severalfactors such as wind speed and direction, and fuel type and load. The moreconvex the damage function, the faster the damage level increases. The moreconcave this function, the slower the damage level grows. In this sectionwe evaluate the proposed methodology considering slow and fast damagegrowth.58Two non-linear damage functions are used to describe slow and fast dam-age growth. We assume the form of the damage function for slow damagegrowth as a square root form d(T )sqrt, where:d(T )sqrt =( TTC )1/2 if T < TC1 if T ≥ TC(3.1)For fast damage growth, we assume the form of the damage function asa quadratic form d(T )quad, where:d(T )quad =( TTC )2 if T < TC1 if T ≥ TC(3.2)Both functions define level of damage as a function of the time duration ofthe fire. Figure 3.7 illustrates the difference between the damage functionsin terms of damage level related to fire duration time. The first case (a)represents the linear damage function described in Section 2.2.2. Case (b)and (c) represent the slow damage growth (square root function) and fastdamage growth (quadratic function), respectively.Figure 3.8 shows the results of applying these damage functions to thepetrochemical complex case study. These results show that the proposedmethodology, Method 4 (as described in Section 3.3), is capable of achievingthe minimum economic losses regardless of the damage function being used.The results also show that Method 1 is the worst decision with the largestamount of economic losses.As expected, the faster damage growth results in more economic loss.59Figure 3.7: Illustration of the difference between different damagefunctions showing level of damage as a function of time durationof fire for (a) Equation 2.2, linear function reflecting a constantrate of fire damage growth; (b) Equation 3.1, non-linear damagefunction reflecting fast damage growth; and (c) Equation 3.2,non-linear damage function reflecting slow damage growth.In the case of the slow growth damage function, the economic losses are theminimal compared to the other damage functions. Slow damage growth al-lows firefighters the time to control the fire before significant damage occurs.Method 2, Method 3 and Method 4 yielded optimal minimal losses of $420million compared with $1,099 million for the business-as-usual, Method 1.In the case of the fast growth damage function, the economic lossesincrease for all the allocation methods, however, Method 4 maintains thebest performance compared to the others. Using Method 4, the resultingeconomic losses are $1,565 million compared with $3,853 million for theother methods.We conclude that the damage growth rate has a significant effect on thetime to control the fire and in the resulting economic losses. Also, regardlessof the damage growth rate, the proposed methodology is able to allocate60Method 1 Method 2 Method 3 Method 405001,0001,5002,0002,5003,0003,5004,000Allocation MethodsTotal Losses ($ Millions)Slow growthLinear growthFast growthFigure 3.8: Total losses of different allocation methods for three dam-age functions.resources efficiently to minimize the economic losses.3.4.2 Human Performance FactorIn this section, we study the effect of Human Performance (HP) on resourceallocation decisions during fire incidents. The most important human perfor-mance factor in firefighting effectiveness is the degradation of performanceunder stressful mental and physical conditions, such as heat, smoke andhydration.As we discussed in Section 2.2, each fire is described by its severity mea-sure, FSM. This measure estimates the required man-hours to suppress afire. For example, if a fire is described by FMS=100, then it means that al-locating 50 firefighters can suppress the fire in two hours and 100 firefighterscan suppress it in one hour. During a long suppression process, the perfor-61mance of the firefighters is degraded and the suppression process might takemore time.To study this factor, we extend the model described in Section 3.3 byconsidering the impact of the HP factor on the effectiveness of firefightingoperations. We apply the allocation methods in Table 3.4 to suppress twosimultaneous fire incidents, Fire 1 and Fire 2, occurring in Plant 10 andPlant 4, respectively. Fire 1 requires 600 man-hours to be suppressed, whileFire 2 requires only 200 man-hours. In order to consider the effect of theHP, we assume that during fire incidents, the firefighters’ performance dropsby 20% every three hours. Also, every eight hours a new shift replaces thecurrent one.Using the developed FMDSS in Chapter 2, the following cases are consid-ered in comparing the impact of the HP on the resources allocation decisions.• Case 1: represents the result obtained in Section 3.4.1 for the four allo-cation methods in Table 3.4 without consideration of the HP factor.• Case 2: represents the results obtained for these allocation methods withconsideration of the HP factor.Figure 3.9 shows the results of applying these allocation methods to thepetrochemical complex case study. In general, the results show that the HPfactor has a considerable impact in the total loss. Also, the results showthat the proposed methodology, Method 4, is more efficient than the otherthree methods.There are 24 different combinations of four allocation methods for eachof the three damage functions with and without the HP factor. Figure 3.10,62Method 1 Method 2 Method 3 Method 401,0002,0003,0004,0005,0006,0007,0008,0009,000Allocation MethodsTotal Losses ($ Millions)Slow growthLinear growthFast growthFigure 3.9: Total losses of different allocation methods for three dam-age functions considering the human performance factor.3.11, 3.12, and 3.13 correspond to Method 1, Method 2, Method 3 andMethod 4 (as described in Section 3.3), respectively. The results of thiscomparison indicate that the human performance factor has a significantimpact on the development of fire damage and also on the economic losses.The results in Figure 3.10 show that the total loss in Method 1 afterconsidering the HP factor increased by 126% to reach $1,236 US millionduring the fast growth fire. For the other allocation methods, the impactof this factor is in the same direction as on Method 1 but to a much lesserdegree.3.5 ConclusionIn this chapter, we use economic analysis to help fire managers determineappropriate responses during daily operations. We proposed a methodology63Slow growth Linear growth Fast growth01,0002,0003,0004,0005,0006,0007,0008,0009,000Damage FunctionsTotal Losses ($ Millions)Case 1Case 2Figure 3.10: Comparison of total losses of Method 1 between Case 1,neglecting the human performance factor, and Case 2, consid-ering the human performance optimize the allocation process of firefighting. The concept of infras-tructure interdependencies is incorporated into the decision making process.The proposed methodology estimates the damage associated with a givenfire scenario, calculates the economic losses resulting from the damage, andthen provides the optimal assignment of available firefighters.Different damage functions are considered to investigate different typesof damage behaviour. Also, we evaluate the human performance factorthat influences the firefighting operations. By considering these factors, theresults show that optimizing jointly the number of assigned firefighters withthe estimated damage reduces the economic losses greatly.In the next chapter, we extend the study of the human factor to evaluatethe potential benefits and consequences of alternative manpower planning64Slow growth Linear growth Fast growth05001,0001,5002,0002,5003,0003,5004,000Damage FunctionsTotal Losses ($ Millions)Case 1Case 2Figure 3.11: Comparison of total losses of Method 2 between Case 1,neglecting the human performance factor, and Case 2, consid-ering the human performance factor.decisions.65Slow growth Linear growth Fast growth05001,0001,5002,0002,5003,0003,5004,000Damage FunctionsTotal Losses ($ Millions)Case 1Case 2Figure 3.12: Comparison of total losses of Method 3 between Case 1,neglecting the human performance factor, and Case 2, consid-ering the human performance factor.Slow growth Linear growth Fast growth02004006008001,0001,2001,4001,600Damage FunctionsTotal Losses ($ Millions)Case 1Case 2Figure 3.13: Comparison of total losses of Method 4 between Case 1,neglecting the human performance factor, and Case 2, consid-ering the human performance factor.66Chapter 4Capacity Planning in theFire Department4.1 IntroductionFires are becoming more costly in terms of fire operational costs and eco-nomic losses (direct and indirect losses). The increased interdependenceof existing infrastructure systems makes economic losses induced by firesvery severe and difficult to predict. With a limited budget and resources,fire managers are faced with challenging decisions concerning how best toallocate resources, in terms of minimizing costs and keeping risks at an ac-ceptable level.In the previous chapter, we discussed the allocation and scheduling de-cisions of firefighting units during fire incidents. We showed how severalfactors, including human factors, are able to influence the decision-makingprocess. The human factor is not only significant at the operational level67planning, but also at the strategic planning level. The strategic planningincludes the most long- range decisions like capacity investment (e.g., in-creasing the number of firefighters).In this chapter, we propose an additional function to the developed sys-tem in Chapter 2 to investigate the impact of capacity planning decisionson the effectiveness of firefighting operations. The challenge to the deci-sion maker is to determine the most cost-effective plan in terms of reducingoverall cost. The developed system is used to identify the optimal numberof firefighters to be recruited to contain the fires and minimize damage. InSection 4.2, the proposed methodology to evaluate long-term planning de-cisions is presented. In Section 4.3 the proposed methodology is applied tothe case study of the petrochemical complex. Finally, concluding remarksare given in Section Proposed MethodologyIn this section, we use the developed system described in Chapter 2 to de-velop a manpower capacity planning methodology. The proposed method-ology evaluates the impact of hiring decisions on effectiveness of firefightingoperations. It incorporates the C+NVC concept described in Section 2.5to perform economic analysis to determine the most efficient strategic plan.The objective is to minimize the cost of fire by minimizing the sum of theoperation cost (C) and the net value change (NVC). The key question is:what is the optimal number of firefighters to be hired by minimizing theC+NVC objective function?Figure 4.1 illustrates the proposed manpower capacity planning method-68Figure 4.1: Proposed methodology to evaluate long-term planning de-cisions.69ology. The first step in the proposed methodology is the plan developmentwhich includes time frame and budget. The next step is to specify the re-quirements of the developed plan, such as an estimate of manpower to berecruited and trained, and the required equipment to be purchased such aswater pumps and fire trucks. The cost of these requirements represents thefire operation costs (C) in the C+NVC concept.In order to investigate the effectiveness of the developed plan, we usethe fire simulation model described in Section 2.2 to simulate multiple-firescenarios. These scenarios can be generated by simulation or taken fromhistorical data. For each scenario, different resource allocation decisions areevaluated to find the minimum economic losses. i2Sim and the optimizationagent described in Section 2.3 and 2.4 respectively are used to estimate theresulting physical damage and to calculate the expected economic losseswhich represents the net value change (NVC) part of the C+NVC concept.At this point, C+NVC can be calculated using the following equation:C+NV C =T∑t=1(LftCft+LqtCqt+NV Ct) (4.1)whereCft: cost of hiring one firefighter in period tLft: number of hired firefighters in period tCqt: cost of purchasing one unit of equipment in period tLqt: number of purchased one unit of equipment in period tNV Ct: net loss due to fires in period tT : control time (years)70This process is repeated for all alternative plans. Once all of the costsare calculated, a point of economic efficiency can be found where the sumof the operation cost (C) and the net value change (NVC) is minimized.In order to evaluate the effectiveness of each of plan, Equation 2.6 can berewritten as follows:MIN: C + NVC=T∑t=1(LftCft+LqtCqt+NV Ct), (4.2)The control time T for the decision analysis is usually based on thedecision maker’s interest in evaluating alternative strategic plans. In general,economic losses associated with large fire incident increase if longer controlperiods are considered.4.3 Results and DiscussionIn order to evaluate the effectiveness of the proposed methodology, ninestrategic planning scenarios are considered in this study as shown in Table4.1. Each plan has a number of firefighters to be hired and fire trucks topurchased over the planned period. It is assumed that the control period is10 years.Plan 1 is taken as the base case scenario where the number of firefightersis 300 (100 firefighters per shift) and the number of trucks is 20. Plan 2to Plan 9 represent alternative plans with an increase of 40% in the num-ber of firefighters over the base case for each plan. The annual cost ofhiring one firefighter is estimated to be $93,663 [81]. This cost includes71PlanningscenarioNumber offirefighters (Lf )Cost of hire(Cf )Number oftrucks (Lq)Cost of trucks(Cq)Total cost(C)Plan 1 300 $280,989,000 20 $14,000,000 $294,989,000Plan 2 420 $393,384,600 28 $19,600,000 $412,984,600Plan 3 540 $505,780,200 36 $25,200,000 $530,980,200Plan 4 660 $618,175,800 44 $30,800,000 $648,975,800Plan 5 780 $730,571,400 52 $36,400,000 $766,971,400Plan 6 900 $842,967,000 60 $42,000,000 $884,967,000Plan 7 1020 $955,362,600 68 $47,600,000 $1,002,962,600Plan 8 1140 $1,067,758,200 76 $53,200,000 $1,120,958,200Plan 9 1260 $1,180,153,800 84 $58,800,000 $1,238,953,800Table 4.1: Strategic planning scenarios costs (in US dollars).the personnel salary and benefits such as health and dental benefits, life in-surance, vacation and holiday time, average sick leave usage, uniforms andsafety equipment. The cost of purchasing a new industrial fully equippedfire truck is approximately $700,000. The last column in Table 4.1 depictsthe total cost (C) of each plan.To evaluate the expected economic loss NV C over the specified horizon,two simultaneous fire incidents, Fire 1 and Fire 2, were considered in Plant4 and Plant 10, respectively. We assume that Fire 1 requires 200 man-hoursto be suppressed, while Fire 2 requires 600 man-hours. To suppress thesefires, we use Method 4 described in Table 3.4.Each plan is evaluated by testing its performance for different fire damagegrowth functions, namely linear, square root and quadratic. The lineardamage function represents fire incidents that have a constant rate of damageover time. Details of the linear damage function were presented in Section2.2.2. The square root damage function represents all fire incidents that have721 2 3 4 5 6 7 8 9200400600800100012001400160018002000Planning ScenariosCost ($ Millions)Linear fire growthSlow fire growthFast fire growthFigure 4.2: C+NVC curves of three damage growth functions, linear,slow and fast.a slow rate of damage growth, as defined in Equation 3.1. The opposite isobserved with the quadratic damage function which represents fire incidentsthat have a fast rate of damage growth, as already defined in Equation 3.2.Figure 4.2 shows the obtained curves from the C+NVC model for thethree damage growth functions described in Section 3.4.1. The results in-dicate that the most efficient allocation of funding for hiring is achieved byplan 2 and plan 3 where the minimum of the C+NVC curves is reached.Compared to the base case (300 firefighters), the recommended increase inmanpower is from 300 to 540 firefighters for both fast and linear growthfires. This increase resulted in a saving of approximately $230 US million inlosses in cost of firefighters.Tables 4.2, 4.3 and 4.4 show a comparison of the strategic planningscenarios costs for different fire damage growth speeds. The last column in73Planning Scenario Cf Cq NV C C+NV C................... ($ Millions)...................Plan 1 $280 $14 $493.2 $787.2Plan 2 $393 $19 $164.7 $576.7Plan 3 $505 $25 $27.3 $557.3Plan 4 $618 $30 $27.3 $675.3Plan 5 $730 $36 $27.3 $793.3Plan 6 $842 $42 $27.3 $911.3Plan 7 $955 $47 $27.3 $1,029.3Plan 8 $1,067 $53 $27.3 $1,147.3Plan 9 $1,180 $58 $27.3 $1,265.3Table 4.2: Comparison of strategic planning scenario costs for lineardamage growth.each of these tables show C+NVC, the total fire operation costs and theexpected economic losses for different strategic plans.Table 4.2 shows that Plan 3 is the most cost effective plan for linearfire damage growth. Increasing the number of firefighters from 300 to 540reduces the total losses by 30% (from 787.2 to $ 557.3 US million). Wecan notice that NVC reached its minimum value at Plan 3. The increasein C+NVC value for Plan 4 through Plan 9 comes from the cost of morefirefighters.For slow fire damage growth, using Plan 2 can reduce the total lossesby 5% (from $458.7 to $439.3 US million) as shown in Table 4.3. The mostcost effective investment is to increase the number of firefighters from 300to 420 as shown in Table 4.3. Although Plan 4 is able to suppress both fireswithout any economic losses (NVC =0), its hiring cost is greater than the74Planning Scenarios Cf Cq NV C C+NV C................... ($ Millions)...................Plan 1 $280 $14 $164.7 $458.7Plan 2 $393 $19 $27.3 $439.3Plan 3 $505 $25 $27.3 $557.3Plan 4 $618 $30 $0 $648Plan 5 $730 $36 $0 $766Plan 6 $842 $42 $0 $884Plan 7 $955 $47 $0 $1,002Plan 8 $1,067 $53 $0 $1,120Plan 9 $1,180 $58 $0 $1,238Table 4.3: Comparison of strategic planning scenario costs for slowdamage growth.Planning Scenarios Cf Cq NV C C+NV C................... ($ Millions)...................Plan 1 $280 $14 $1,171.8 $1,465.8Plan 2 $393 $19 $1,171.8 $1,583.8Plan 3 $505 $25 $843.3 $1,373.3Plan 4 $618 $30 $843.3 $1,491.3Plan 5 $730 $36 $843.3 $1,609.3Plan 6 $842 $42 $843.3 $1,727.3Plan 7 $955 $47 $843.3 $1,845.3Plan 8 $1,067 $53 $843.3 $1,963.3Plan 9 $1,180 $58 $705.9 $1,943.9Table 4.4: Comparison of strategic planning scenario costs for fastdamage growth.75total losses in Plan 3. Because we are dealing with slow fires, Plan 4 throughPlan 9 are able to suppress both fires with no economic losses.In case of fast fire damage growth as shown in Table 4.4, Plan 3 canreduce the total losses by 9% (from $1,465.8 to $1,373.3 US million) byincreasing the number of firefighters to 540. The high values in NVC columnis due to the fast damage growth resulting from this type of fires.4.4 ConclusionThe methodology presented in this chapter has focused on integrating thecost of fire damage within strategic planning. The strategic plans deal withthe optimal budget allocation and the deployment or relocation of firefight-ing resources. The concept of the C+NVC was used to perform the economicanalysis to determine the most efficient strategic plan. i2Sim is used to modelthe infrastructure systems in order to understand and evaluate the net valuechange of goods and services due to the fires. The fire damages were eval-uated using three different damage functions. The results have shown thatthe proposed methodology can be used for more effective strategic planningand better daily scheduling and allocation decisions.In this chapter, we focused on human resources planning decisions fromthe fire departments’ point of view. Overall, the increasing interdependenceof infrastructure systems makes economic losses induced by extreme eventsvery severe and difficult to predict. We believe that methods like ours thataddress this problem will be a key component of future decisions supportsystems. In the next chapter, we change our perspective and observe theimpact that resource allocation decisions during emergency response have76on improving infrastructure resilience.77Chapter 5Improving Resilience ofInterdependentInfrastructure Systems5.1 IntroductionModern infrastructure systems, such as water, electrical power and trans-portation, become more and more interconnected and interdependent [82].Due to such interdependence, these systems are inherently vulnerable to dis-ruptions in other systems. Despite the fact that a lot of resources have beeninvested in prevention, not all incidents can be averted. Increasingly, theemphasis in emergency response has shifted from protection and preventiontowards preparedness and response [11]. This shift is realized by the conceptof resilience. The effectiveness of the emergency preparedness and response78plans has a high impact on infrastructure resilience.A resilient infrastructure is an infrastructure that can withstand sud-den disturbances with minimum disruption and recovers within acceptablelosses and time [83]. One way to improve resilience is to consider the effec-tiveness of the emergency preparedness and response plan. The effectivenessof emergency response plans includes prioritization of responses and optimalallocation of available limited resources.In this chapter, we propose a methodology to evaluate the impact of re-source allocation decisions during fire incidents in improving infrastructureresilience. This methodology focuses on two dimensions: system resource-fulness and system rapidity. The system resourcefulness is evaluated by theability to prioritize fire incidents and the optimality of mobilizing firefight-ing units. The system rapidity is evaluated by containing economic lossesin production and by minimizing the recovery time. This methodology canbe used for any type of natural or man-made hazards. It can also be usedfor other resource allocation problems in any interdependent environmentsuch as telecommunications, transportation, electric power grids, and watersupply systems. Section 5.2 of this chapter describes the problem formula-tion. Section 5.3 provides background information infrastructure Resilience.Section 5.4 presents the proposed methodology. Results and discussion areprovided in Section 5.5 and the conclusion is given in Section Problem FormulationThis research is mainly concerned with developing a methodology to evaluatethe impact of allocating firefighting units during fire incidents on infrastruc-79ture resilience. Once a fire alarm signal is received, the response mobilizationis started by dispatching firefighting units from the fire stations. Emergencyresponders must determine the optimal number of firefighters that shouldbe allocated to mitigate the potential disruptions resulting from extremeevents. The existing strong interdependence between infrastructure systemsremains a challenge in modeling the consequences of fire incidents. Becausesuch incidents and their cascading effects are becoming stronger, there is animportant need to evaluate this impact of the resources allocation processon infrastructure resilience.In the analysis of infrastructure systems and emergency response behav-iors, two major problem exist, namely:1. An infrastructure system, I, is a set of production units related to eachother, I = {P1,P2,P3, ...,Pn}, where Pn is the nth production unit, andn is the total number of production units. Given a set of fire incidents{f(P1),f(P2), ...,f(Pn)}, what is the impact on infrastructure systemI ?2. Given a set of firefighting units {u1,u2,u3, ...,uq}, where uq is the qthfirefighting unit, q is the total number of available firefighting units,and a desired level of resilience, R(I), what is the best allocationscheme of the available firefighting units during suppression time [0,TS ]such that Ts = {(u1,f(P1)), (u2,f(P2)), (u3,f(P2)), ...}, ∀ Ts ∈ [0,TS ]to maintain a desired resilience level, R(I)?These problems are discussed in the next section.805.3 Infrastructure ResilienceResilience was originally introduced as a property of systems by Holling in1973 [84]. Since that time, the concept of resilience has been studied in alarge number of disciplines such as ecology, psychology, sociology, economics,and engineering. Increasingly, resilience is recognized to be an important di-mension of the sustainability of infrastructure systems. Bruneau et. al. [85]emphasize that resilient systems reduce the probability of failure, the con-sequences of failure such as economic losses and the time for recovery.According to Bruneau, et. al. [85], there are four dimensions that canimprove resilience. These dimensions are as the following:• Robustness: The inherent strength or resistance in any system to with-stand a given level of stress or demand without degradation or loss offunctionality.• Redundancy: The ability of a system to satisfy the functional require-ments using alternate options, choices and substitutions in the eventof disruption, degradation or loss of functionality• Rapidity: The speed with which losses are overcome and safety, service-ability and stability are resumed.• Resourcefulness: The ability to identify problems, establish prioritiesand mobilize resources and services in emergencies to restore the sys-tem performance.Although many of these dimensions have been evaluated as technically-based functions of the physical system, quantifying resourcefulness, as a81property, remains challenging because it relies on human skills and theirabilities to respond and recover from disaster events [86]. The focus in thischapter is on two of these dimensions, resourcefulness and rapidity, thattrack the reaction during extreme events. The system resourcefulness isevaluated by the ability to prioritize fire incidents and the optimality inmobilizing firefighting units. The system rapidity is evaluated by containingeconomic losses in production and by minimizing the recovery time.Infrastructure resilience can be defined as the ability to reduce the mag-nitude and the duration of disruptive events [87]. Resilience, as a propertyof complex systems, can be measured in one of two ways: the amount ofdisturbance a system can withstand without changing its original state [84]and the time taken for a system to recover after a disturbance [88]. In thissense and after analyzing the literature, the definition provided by Cimel-laro et. al. in [86] has been adopted. Cimellaro et. al. define resilience (R)as [86]:“. . . a function indicating the capability to sustain a level of func-tionality or performance . . . over a period defined as the controltime (TLC) that is usually decided by owners, or society. . . ”Figure 5.1 shows a hypothetical system functionality curve after theeffects of an event, E. This figure provides a general overview of the timedependent system functionality and illustrates the important times duringsystem response. As expected, system functionality under the effects ofthe event degrades from the normal operating level. This functionality withrespect to the time of event occurrence can be divided into three stages: pre-82event (t < tE0), recovery time (tE0< t< tE0+TRE) and post-event (t > tE0+TRE). In the pre-event stage, the system operates under normal conditions.During the recovery period, the system operates under the influence of thehazard. In the post-event stage, the system returns to normal operation.Analytically, the resilience measure can be expressed by the followingequation [86]:R= 1TLC∫ t0E+TLCt0EQ(t)dt (5.1)whereQ(t) is the functionality of the systemt0E is the time of occurrence of event ETLC is the control time of the systemFigure 5.1: Graphical representation of resilience.83For infrastructure systems, the functionality can be expressed as eco-nomic losses in production. These losses include losses in production dueto a disturbance (direct losses) plus business interruptions due to degrada-tion in production (indirect losses). The analytical functionality Q(t) of theinfrastructure system can be expressed as follows:Q(t) = 100− [LD(t)+LID(t)] (5.2)whereLD is the direct losses functionLID is the indirect losses functionBoth direct losses and indirect losses functions are expressed as a per-centage of the total production.5.4 Proposed MethodologyIn this chapter, we use the developed system described in Chapter 2 toevaluate the impact of resource allocation decisions during fire incidents inimproving infrastructure resilience. Figure 5.2 depicts the proposed method-ology for assessing resilience of infrastructure systems.The methodology starts with identifying the severity of the fire incident.As discussed in Section 2.2, each fire is described by its severity. This mea-sure defines the required number of man-hours to suppress a fire. Based onthis information, emergency responders generate the allocation decisions ofthe available firefighting units. These decisions are evaluated by the damage84Figure 5.2: Flowchart describing the proposed methodology for as-sessing resilience of infrastructure systems.function described in Section 2.2. After each decision, the physical state ofthe infrastructure system components is evaluated using i2Sim described inSection 2.3. The impact of this damage is translated into recovery time TRE .At this point, the infrastructure performance can be evaluated before andafter the hazard. The functionality of this system Q is defined as the un-realized production (compared to nominal) due to inoperability which canbe calculated using Equation 5.2. Both direct and indirect losses can be85AllocationMethodPlant 10 Plant 4Level of damage Recovery time Level of damage Recovery timeMethod 1 High 6 months Intermediate 3 monthsMethod 2 High 6 months Low 1 monthMethod 3 High 6 months Low 1 monthMethod 4 High 6 months Minimul MinimulTable 5.1: Level of damage and recovery time for applied allocationmethods.measured through i2Sim’s cells’ output. The final step is to evaluate theresilience of the infrastructure system R using Equation Results and DiscussionThe methodology described above has been applied to the case study intro-duced in Section 2.6. Two simultaneous fire incidents, Fire 1 and Fire 2,were simulated in Plant 4 and Plant 10, respectively. We assume that Fire1 requires 200 man-hours to be suppressed, while Fire 2 requires 600 man-hours. Four allocation methods listed in Table 3.4 were used to evaluatethe impact of resource allocation decisions on the petrochemical complexresilience. For each method, the developed system evaluates the potentialdamage based on fire duration. The severity of this damage is reflectedinto a reduction in the production level and recovery time TRE . Recoverytime TRE given here is the time needed for repair and reconstruction as de-scribed in Table 2.1. A 1-years control period is chosen for evaluating thefunctionality of the petrochemical complex, TLC = 365 days.Figure 5.1 shows the resulting level of damage for each allocation methodand the associated recovery time. Figures 5.3, 5.4, 5.5 and 5.6 show the86functionality of the petrochemical complex using different allocation meth-ods. It can be seen that robustness is extremely high for Method 4 (Figure5.6), which represents the optimized allocation decision. Method 4 was ableto prioritize fire incidents and allocate more firefighters to the critical fire.Method 1, which represents the "business as usual" decision, recorded thelowest robustness at 55% as shown in Figure 5.3. It appeared that the rapid-ity of the complex was the same for all the allocation methods (180 days).The expected equivalent production losses for each allocation method areshown in the third column of Table 5.2, along with the recovery periodconsidering an observation period TLC of 365 days.0 50 100 150 200 250 300 350 400020406080100120daysFunctionality Q(t) [%]TRETLC45%Figure 5.3: Functionality the of the case study after multiple-fire in-cidents using Method 1.870 50 100 150 200 250 300 350 400020406080100120daysFunctionality Q(t) [%]TRETLC32%Figure 5.4: Functionality the of the case study after multiple-fire in-cidents using Method 2.0 50 100 150 200 250 300 350 400020406080100120daysFunctionality Q(t) [%]TRETLC32%Figure 5.5: Functionality the of the case study after multiple-fire in-cidents using Method 3.880 50 100 150 200 250 300 350 400020406080100120daysFunctionality Q(t) [%]TRETLC3.5%Figure 5.6: Functionality the of the case study after multiple-fire in-cidents using Method 4.Allocation Methods Recovery TimeTRE (days)Production Losses($ US Millions)ResilienceR(%)Method 1 180 $3,460 87.78%Method 2 180 $1,171 95.86%Method 3 180 $1,171 95.86%Method 4 180 $493 98.26%Table 5.2: Recovery time, losses and resilience of the case study fordifferent allocation methods (TLC = 365 days).The complex resilience value is calculated according to Equation 5.1 forcontrol time TLC . Figures 5.7, 5.8, 5.9 and 5.10 show the calculated resiliencefor Method 1, Method 2, Method 3 and Method 4, respectively.The resilience values are summarized in Table 5.2. For this case study,it is shown that the optimized allocation has the largest resilience value of8995.86%, when compared with the other three methods, and it is the leastlosses in production ($ 493 US million). However, if the common action(Method 1) is taken, the complex resilience is reduced to 87.78%, and theproduction losses increased drastically to $3,460 US million. For Method 2and Method 3, the resilience values were the same at 95.86% and productionlosses at $1,171 US million.This means that the optimizing resource allocation process during fireincidents improves the infrastructure resilience. We conclude that effec-tiveness of the emergency response plan has a high impact on improvinginfrastructure resilience.50 100 150 200 250 300 350 4005060708090100110120130140DaysFunctionality Q(t) [%]R=87.78%Figure 5.7: Resilience curve showing level of functionality of the casestudy over time for Method 1.9050 100 150 200 250 300 350 4005060708090100110120130140DaysFunctionality Q(t)[%]R=95.86%Figure 5.8: Resilience curve showing level of functionality of the casestudy over time for Method 2.50 100 150 200 250 300 350 4005060708090100110120130140DaysFunctionality Q(t)[%]R=95.86%Figure 5.9: Resilience curve showing level of functionality of the casestudy over time for Method 3.9150 100 150 200 250 300 350 4005060708090100110120130140DaysFunctionality Q(t) [%]R=98.26%Figure 5.10: Resilience curve showing level of functionality of the casestudy over time for Method 4.5.6 ConclusionIn this chapter, we proposed a methodology to evaluate the impact of re-source allocation decisions during fire incidents in improving infrastructureresilience. Resourcefulness and rapidity revolve around the ability to max-imize the utilization of available resources and to minimize the economiclosses by minimizing the recovery time.A case study of a petrochemical complex was used to explore the impactof allocating limited number of firefighters during multiple fire incidents. Weconclude that the decisions of allocating firefighting units are crucial for en-suring an acceptable level of production after suppression. Furthermore, thebest retrofit method to improve the resilience measure of any infrastructure92system should consider infrastructure interdependence for such decisions.The proposed methodology allows exploration of how different resourceallocation decisions affect infrastructure resilience. It can be used for anytype of natural or man-made hazards, which might lead to the disruption ofany infrastructure system. It can also be used for other resource allocationproblems in any interdependent environment such as telecommunications,transportation, electric power grids, and water supply systems.93Chapter 6ConclusionThis thesis focuses on the development of a decision support system forassisting emergency responders in making efficient decisions during extremeevents. The novelty consists of addressing infrastructure interdependenciesin firefighting operation. It formulates the fire management problem as anoptimization problems and provides solution algorithms for this problem.It also evaluates the impact of fire operation decisions on infrastructureresilience.The developed system can be used by fire department to minimize theeconomic losses during fire incidents. It incorporates economic analysiswithin the decision-making process and provides cost estimates for differentallocations methods. This can help decision-makers to better understandthe impact of their decision during emergency response.In addition, presenting the results of this research as economic impact,expressed in monetary values, can help to bridge the research gaps betweenindustry and academia. With results in this form, decision makers in indus-94tries would be better able to understand the value of academic research.In this chapter, we summarize our efforts to improve the emergency re-sponse decisions during fire incidents and present future research directions.6.1 Resource Allocation and Scheduling DuringMultiple-Fire IncidentsWe proposed and developed a methodology to evaluate resource allocationdecisions during multiple-fire incidents. The methodology uses infrastruc-ture interdependency modeling to evaluate the interactions among differentsystems. In this thesis, the economic impact of the fire incidents (direct andindirect losses) was evaluated to find an optimized allocation with minimumeconomic losses. Several factors such as fire damage growth rate and hu-man factors were studied to determine their effects on the decision-makingprocess. The developed methodology was elaborated and implemented in acase study of multiple-fire incidents in a petrochemical complex. Our resultsshow that the proposed methodology gives promising results to effectivelyimprove the resource allocation decisions in interdependent environments. Itperforms better than other allocation methods in terms of economic losses.6.2 Capacity Planning of Human ResourcesWe also presented a capacity planning methodology for fire managers toinvestigate the impact of hiring decisions on effectiveness of firefighting op-erations. In this thesis, we incorporated the concept on C+NVC to performan economic analysis to determine the most efficient strategic plans. i2Simis used to model infrastructure systems in order to understand and evaluate95the net value change of goods and services due to fire. The fire damagegrowth was evaluated using three different damage functions. The resultshave shown that the proposed methodology can be used for more effectivestrategic planning and better daily scheduling and allocation decisions.6.3 Improving Resilience of InterdependentInfrastructure SystemsFinally, we proposed a method to evaluate the impact of resource allocationdecisions during fire incidents in improving infrastructure resilience. Ourmethod focused on two dimensions of resilience: resourcefulness and rapid-ity. Resourcefulness was evaluated by the ability to prioritize fire incidentsand the optimality in scheduling firefighting units. Rapidity was evaluatedby minimizing economic losses and recovery time. The results showed thatincorporating these dimensions into fire fighting decisions has a high impacton improving infrastructure resilience.6.4 Future Research DirectionsIn this section we present some of the on-going research and possible exten-sions related to this thesis.6.4.1 Improvement to the Fire Damage AssessmentAccurate assessment of fire damage is essential for developing effective emer-gency response plans. The damage function developed in Section 2.2.2 usesa deterministic value estimated from fire duration. Predicting fire damageis a complex task and surrounded with considerable uncertainties. Some of96these uncertainties are due to uncontrollable factors such as weather, fireoccurrence, and fire severity. The fire damage function can be extended toconsider these uncertainties. It can be modelled using a discrete set of firescenarios each of which can occur with some known or estimated probability.6.4.2 Considering Multiple Owners During Multiple-FireIncidentsIn this thesis, a single owner of infrastructure systems was considered duringthe process of developing the emergency response plans. Multiple ownersof interdependent infrastructure systems make emergency repones decisionsduring multiple fire incidents more challenging, especially if the differentfire places are owned by different parties, and insured by different insurer.Further research is needed to study the situation of having multiple ownersduring multiple-fire incidents.6.4.3 Understanding the Impact of the Human FactorDuring Emergency ResponseThis thesis found that human performance has a direct impact on the ef-fectiveness of firefighting operations. Therefore, understanding firefightersbehaviour during the fire suppression process, and the impact on their phys-ical and mental performance, is another important area for future research.In general, there is a lack of data in human performance during emergencysituations [89]. Future research should explore human performance duringemergency conditions in harsh environments.976.4.4 Applications to Other Types of Emergency ResponseLastly, the developed system can be used as a decision support system forother disastrous events, such as floods, wildfire, machine failures, industrialaccidents and terrorist attacks. In addition, it can be used for interdepen-dent infrastructure risk and vulnerability analysis. Some examples of suchapplications are summarized below.• Wildfire Suppression: Wildfire is one of the most severe natural haz-ards in the world. The developed system in Chapter 2 can be furthermodified to optimize resources allocation for wildfire containment. Ge-ographic Information Systems (GIS) can be integrated to the devel-oped system to provide location information which can be used inevaluating the economic efficiency of alternative wildfire managementplans.• Evaluating Restoration Plans of Critical Services: During restora-tion after a natural disaster, engineers are faced with a large numberof theoretical possibilities of how critical services, such as electricalpower, can be restored. The proposed methodology in Chapter 5 canbe modified to develop restoration strategies and restoration plans.Different event scenarios can be modeled and their impact on the ser-vices provided by critical infrastructure systems can be assessed. Withthis knowledge, alternative restoration plans can be evaluated accord-ing to their ability to achieve rapid restoration of critical services.• Identifying and Ranking Critical Components: Identifying critical98components for infrastructure systems provides important input forvaluing infrastructure investments and managing risks. The developedsystem can be used to develop a model for risk analysis to identify andrank critical components. By using i2Sim to model interdependentinfrastructure systems, the consequences when components within thesystems fail to perform properly can be simulated. These consequencescan be evaluated by several factors, such as economic losses, affectedsites or degradation in performance. Then, the components can beranked based on its criticality.99Bibliography[1] K. Alutaibi, A. Alsubaie, and J. Martí, “Allocation and scheduling offirefighting units in large petrochemical complexes,” in InternationalConference on Critical Infrastructure Protection. 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