Cost of Equity in Homeland Security Resource Allocation in the Face of a Strategic Attacker

Hundreds of billions of dollars have been spent in homeland security since September 11, 2001. Many mathematical models have been developed to study strategic interactions between governments (defenders) and terrorists (attackers). However, few studies have considered the tradeoff between equity and efficiency in homeland security resource allocation. In this article, we fill this gap by developing a novel model in which a government allocates defensive resources among multiple potential targets, while reserving a portion of defensive resources (represented by the equity coefficient) for equal distribution (according to geographical areas, population, density, etc.). Such a way to model equity is one of many alternatives, but was directly inspired by homeland security resource allocation practice. The government is faced with a strategic terrorist (adaptive adversary) whose attack probabilities are endogenously determined in the model. We study the effect of the equity coefficient on the optimal defensive resource allocations and the corresponding expected loss. We find that the cost of equity (in terms of increased expected loss) increases convexly in the equity coefficient. Furthermore, such cost is lower when: (a) government uses per‐valuation equity; (b) the cost‐effectiveness coefficient of defense increases; and (c) the total defense budget increases. Our model, results, and insights could be used to assist policy making.     

Efficient Allocation of Resources for Defense of Spatially Distributed Networks Using Agent‐Based Simulation

This article presents ongoing research that focuses on efficient allocation of defense resources to minimize the damage inflicted on a spatially distributed physical network such as a pipeline, water system, or power distribution system from an attack by an active adversary, recognizing the fundamental difference between preparing for natural disasters such as hurricanes, earthquakes, or even accidental systems failures and the problem of allocating resources to defend against an opponent who is aware of, and anticipating, the defender's efforts to mitigate the threat. Our approach is to utilize a combination of integer programming and agent‐based modeling to allocate the defensive resources. We conceptualize the problem as a Stackelberg “leader follower” game where the defender first places his assets to defend key areas of the network, and the attacker then seeks to inflict the maximum damage possible within the constraints of resources and network structure. The criticality of arcs in the network is estimated by a deterministic network interdiction formulation, which then informs an evolutionary agent‐based simulation. The evolutionary agent‐based simulation is used to determine the allocation of resources for attackers and defenders that results in evolutionary stable strategies, where actions by either side alone cannot increase its share of victories. We demonstrate these techniques on an example network, comparing the evolutionary agent‐based results to a more traditional, probabilistic risk analysis (PRA) approach. Our results show that the agent‐based approach results in a greater percentage of defender victories than does the PRA‐based approach.     

Resource Allocation in Integrated Preoperational and Operational Management of Natural Hazards

The management of natural hazards occurring over a territory entails two main phases: a preoperational —or pre-event—phase, whose objective is to relocate resources closer to sites characterized by the highest hazard, and an operational —during the event—phase, whose objective is to manage in real time the available resources by allocating them to sites where their intervention is needed. Obviously, the two phases are closely related, and demand a unified and integrated treatment. This work presents a unifying framework that integrates various decisional problems arising in the management of different kinds of natural hazards. The proposed approach, which is based on a mathematical programming formulation, can support the decisionmakers in the optimal resource allocation before (preoperational phase) and during (operational phase) an emergency due to natural hazard events. Different alternatives of modeling the resources and the territory are proposed and discussed according to their appropriateness in the preoperational and operational phases. The proposed approach can be applied to the management of any natural hazard and, from an integration perspective, may be particularly useful for risk management in civil protection operations. An application related to the management of wildfire hazard is presented.     

基于随机理论的多项目资源配置模型及应用研究

为解决多项目管理中共享资源配置问题,在对信息环境下企业资源特点研究的基础上,应用随机理论确定了企业资源多项目并行配置时的资源等效效率和效率转换系数,由此建立了资源配置效率模型,通过对其数学方程的分析给出了相应的算法.运用该模型和算法,通过实例分析实现了资源的合理配置.     

基于未来效率的兼顾公平与效率的资源分配DEA模型研究——以各省碳排放额分配为例

根据需要实现的目标，评估各生产决策单元的投入产出效率及改进潜力，可以为资源分配提供重要参考。构建一个基于未来效率的兼顾公平与效率的资源分配DEA模型可以有效、灵活地解决该问题。该DEA模型首先根据历史数据计算每个生产决策单元过去各期的技术增长率，并预测各DMU未来的技术增长率，从而获得未来的生产前沿面。以此为基础，在九个硬性目标约束下，分三个步骤分别解决三个追求的软性目标：最大化期望总产出、最小化非期望总产出、最小化可变要素总投入。管理者不仅可以改变九个硬性目标的参数值，以及调整三个软性目标的优先顺序和软性目标参数值，进而形成各种兼顾效率与公平的资源分配方案。最后，运用该DEA模型评估了我国各省碳排放削减潜力，并形成了能够实现管理者期望目标的各省碳排放削减责任分配方案。     

Modeling the Cost Effectiveness of Fire Protection Resource Allocation in the United States: Models and a 1980–2014 Case Study

The estimated cost of fire in the United States is about $329 billion a year, yet there are gaps in the literature to measure the effectiveness of investment and to allocate resources optimally in fire protection. This article fills these gaps by creating data‐driven empirical and theoretical models to study the effectiveness of nationwide fire protection investment in reducing economic and human losses. The regression between investment and loss vulnerability shows high R² values (≈0.93). This article also contributes to the literature by modeling strategic (national‐level or state‐level) resource allocation (RA) for fire protection with equity‐efficiency trade‐off considerations, while existing literature focuses on operational‐level RA. This model and its numerical analyses provide techniques and insights to aid the strategic decision‐making process. The results from this model are used to calculate fire risk scores for various geographic regions, which can be used as an indicator of fire risk. A case study of federal fire grant allocation is used to validate and show the utility of the optimal RA model. The results also identify potential underinvestment and overinvestment in fire protection in certain regions. This article presents scenarios in which the model presented outperforms the existing RA scheme, when compared in terms of the correlation of resources allocated with actual number of fire incidents. This article provides some novel insights to policymakers and analysts in fire protection and safety that would help in mitigating economic costs and saving lives.     

Stochastic Optimal Control for Staffing and Backlog Policies in a Two‐Stage Customized Service Supply Chain

Motivated by an oilfield services industry case study, we investigate the dynamic behavior of customized service supply chains by developing a two‐stage serial staffing model. Each stage holds no finished goods inventory, but rather only backlogs that can be managed by adjusting staffing levels. We develop optimal control policies to balance backlog costs against hiring and firing personnel costs'assuming shared backlog information—under both centralized and decentralized control. We examine when there is sufficient economic incentive for two completely decentralized stages to begin: (1) to share backlog information without centralizing control, or (2) to completely centralize control. These switching points are determined by the relative service and personnel costs of the two stages. From these results, we show that decentralizing control in many cases does not materially worsen performance, so long as information is shared. Moreover, in some cases, even sharing information is of only marginal benefit.     

Modeling Arbitrary Layers of Continuous‐Level Defenses in Facing with Strategic Attackers

We propose a novel class of game‐theoretic models for the optimal assignment of defensive resources in a game between a defender and an attacker. Compared to the other game‐theoretic models in the literature of defense allocation problems, the novelty of our model is that we allow the defender to assign her continuous‐level defensive resources to any subset (or arbitrary layers) of targets due to functional similarity or geographical proximity. We develop methods to solve for equilibrium, and illustrate our model using numerical examples. Compared to traditional models that only allow for individual target hardening, our results show that our model could significantly increase the defender's payoff, especially when the unit cost of defense is high.     

Risk‐Cost‐Benefit Analysis for Transportation Corridors with Interval Uncertainties of Heterogeneous Data

Access management, which systematically limits opportunities for egress and ingress of vehicles to highway lanes, is critical to protect trillions of dollars of current investment in transportation. This article addresses allocating resources for access management with incomplete and partially relevant data on crash rates, travel speeds, and other factors. While access management can be effective to avoid crashes, reduce travel times, and increase route capacities, the literature suggests a need for performance metrics to guide investments in resource allocation across large corridor networks and several time horizons. In this article, we describe a quantitative decision model to support an access management program via risk‐cost‐benefit analysis under data uncertainties from diverse sources of data and expertise. The approach quantifies potential benefits, including safety improvement and travel time savings, and costs of access management through functional relationships of input parameters including crash rates, corridor access point densities, and traffic volumes. Parameter uncertainties, which vary across locales and experts, are addressed via numerical interval analyses. This approach is demonstrated at several geographic scales across 7,000 kilometers of highways in a geographic region and several subregions. The demonstration prioritizes route segments that would benefit from risk management, including (i) additional data or elicitation, (ii) right‐of‐way purchases, (iii) restriction or closing of access points, (iv) new alignments, (v) developer proffers, and (vi) etc. The approach ought to be of wide interest to analysts, planners, policymakers, and stakeholders who rely on heterogeneous data and expertise for risk management.     

Cost‐Benefit Analysis for Optimization of Risk Protection Under Budget Constraints

Cost‐benefit analysis (CBA) is commonly applied as a tool for deciding on risk protection. With CBA, one can identify risk mitigation strategies that lead to an optimal tradeoff between the costs of the mitigation measures and the achieved risk reduction. In practical applications of CBA, the strategies are typically evaluated through efficiency indicators such as the benefit‐cost ratio (BCR) and the marginal cost (MC) criterion. In many of these applications, the BCR is not consistently defined, which, as we demonstrate in this article, can lead to the identification of suboptimal solutions. This is of particular relevance when the overall budget for risk reduction measures is limited and an optimal allocation of resources among different subsystems is necessary. We show that this problem can be formulated as a hierarchical decision problem, where the general rules and decisions on the available budget are made at a central level (e.g., central government agency, top management), whereas the decisions on the specific measures are made at the subsystem level (e.g., local communities, company division). It is shown that the MC criterion provides optimal solutions in such hierarchical optimization. Since most practical applications only include a discrete set of possible risk protection measures, the MC criterion is extended to this situation. The findings are illustrated through a hypothetical numerical example. This study was prepared as part of our work on the optimal management of natural hazard risks, but its conclusions also apply to other fields of risk management.     

A Case Study Evaluating the Risk of Infection from Middle Eastern Respiratory Syndrome Coronavirus (MERS‐CoV) in a Hospital Setting Through Bioaerosols

Middle Eastern respiratory syndrome, an emerging viral infection with a global case fatality rate of 35.5%, caused major outbreaks first in 2012 and 2015, though new cases are continuously reported around the world. Transmission is believed to mainly occur in healthcare settings through aerosolized particles. This study uses Quantitative Microbial Risk Assessment to develop a generalizable model that can assist with interpreting reported outbreak data or predict risk of infection with or without the recommended strategies. The exposure scenario includes a single index patient emitting virus‐containing aerosols into the air by coughing, leading to short‐ and long‐range airborne exposures for other patients in the same room, nurses, healthcare workers, and family visitors. Aerosol transport modeling was coupled with Monte Carlo simulation to evaluate the risk of MERS illness for the exposed population. Results from a typical scenario show the daily mean risk of infection to be the highest for the nurses and healthcare workers (8.49 × 10^?4 and 7.91 × 10^?4, respectively), and the lowest for family visitors and patients staying in the same room (3.12 × 10^?4 and 1.29 × 10^?4, respectively). Sensitivity analysis indicates that more than 90% of the uncertainty in the risk characterization is due to the viral concentration in saliva. Assessment of risk interventions showed that respiratory masks were found to have a greater effect in reducing the risks for all the groups evaluated (>90% risk reduction), while increasing the air exchange was effective for the other patients in the same room only (up to 58% risk reduction).     

An Approach for Optimal Allocation of Safety Resources: Using the Knapsack Problem to Take Aggregated Cost‐Efficient Preventive Measures

On the basis of the combination of the well‐known knapsack problem and a widely used risk management technique in organizations (that is, the risk matrix), an approach was developed to carry out a cost‐benefits analysis to efficiently take prevention investment decisions. Using the knapsack problem as a model and combining it with a well‐known technique to solve this problem, bundles of prevention measures are prioritized based on their costs and benefits within a predefined prevention budget. Those bundles showing the highest efficiencies, and within a given budget, are identified from a wide variety of possible alternatives. Hence, the approach allows for an optimal allocation of safety resources, does not require any highly specialized information, and can therefore easily be applied by any organization using the risk matrix as a risk ranking tool.     

Health Risk Characterization of Chlorpyrifos Using Epidemiological Dose‐Response Data and Probabilistic Techniques: A Case Study with Rice Farmers in Vietnam

Various methods for risk characterization have been developed using probabilistic approaches. Data on Vietnamese farmers are available for the comparison of outcomes for risk characterization using different probabilistic methods. This article addresses the health risk characterization of chlorpyrifos using epidemiological dose‐response data and probabilistic techniques obtained from a case study with rice farmers in Vietnam. Urine samples were collected from farmers and analyzed for trichloropyridinol (TCP), which was converted into absorbed daily dose of chlorpyrifos. Adverse health response doses due to chlorpyrifos exposure were collected from epidemiological studies to develop dose‐adverse health response relationships. The health risk of chlorpyrifos was quantified using hazard quotient (HQ), Monte Carlo simulation (MCS), and overall risk probability (ORP) methods. With baseline (prior to pesticide spraying) and lifetime exposure levels (over a lifetime of pesticide spraying events), the HQ ranged from 0.06 to 7.1. The MCS method indicated less than 0.05% of the population would be affected while the ORP method indicated that less than 1.5% of the population would be adversely affected. With postapplication exposure levels, the HQ ranged from 1 to 32.5. The risk calculated by the MCS method was that 29% of the population would be affected, and the risk calculated by ORP method was 33%. The MCS and ORP methods have advantages in risk characterization due to use of the full distribution of data exposure as well as dose response, whereas HQ methods only used the exposure data distribution. These evaluations indicated that single‐event spraying is likely to have adverse effects on Vietnamese rice farmers.     

A Hybrid Methodology for Modeling Risk of Adverse Events in Complex Health‐Care Settings

In spite of increased attention to quality and efforts to provide safe medical care, adverse events (AEs) are still frequent in clinical practice. Reports from various sources indicate that a substantial number of hospitalized patients suffer treatment‐caused injuries while in the hospital. While risk cannot be entirely eliminated from health‐care activities, an important goal is to develop effective and durable mitigation strategies to render the system “safer.” In order to do this, though, we must develop models that comprehensively and realistically characterize the risk. In the health‐care domain, this can be extremely challenging due to the wide variability in the way that health‐care processes and interventions are executed and also due to the dynamic nature of risk in this particular domain. In this study, we have developed a generic methodology for evaluating dynamic changes in AE risk in acute care hospitals as a function of organizational and nonorganizational factors, using a combination of modeling formalisms. First, a system dynamics (SD) framework is used to demonstrate how organizational‐level and policy‐level contributions to risk evolve over time, and how policies and decisions may affect the general system‐level contribution to AE risk. It also captures the feedback of organizational factors and decisions over time and the nonlinearities in these feedback effects. SD is a popular approach to understanding the behavior of complex social and economic systems. It is a simulation‐based, differential equation modeling tool that is widely used in situations where the formal model is complex and an analytical solution is very difficult to obtain. Second, a Bayesian belief network (BBN) framework is used to represent patient‐level factors and also physician‐level decisions and factors in the management of an individual patient, which contribute to the risk of hospital‐acquired AE. BBNs are networks of probabilities that can capture probabilistic relations between variables and contain historical information about their relationship, and are powerful tools for modeling causes and effects in many domains. The model is intended to support hospital decisions with regard to staffing, length of stay, and investments in safety, which evolve dynamically over time. The methodology has been applied in modeling the two types of common AEs: pressure ulcers and vascular‐catheter‐associated infection, and the models have been validated with eight years of clinical data and use of expert opinion.     

Evaluation of Inhaled Versus Deposited Dose Using the Exponential Dose‐Response Model for Inhalational Anthrax in Nonhuman Primate,Rabbit, and Guinea Pig

The application of the exponential model is extended by the inclusion of new nonhuman primate (NHP), rabbit, and guinea pig dose‐lethality data for inhalation anthrax. Because deposition is a critical step in the initiation of inhalation anthrax, inhaled doses may not provide the most accurate cross‐species comparison. For this reason, species‐specific deposition factors were derived to translate inhaled dose to deposited dose. Four NHP, three rabbit, and two guinea pig data sets were utilized. Results from species‐specific pooling analysis suggested all four NHP data sets could be pooled into a single NHP data set, which was also true for the rabbit and guinea pig data sets. The three species‐specific pooled data sets could not be combined into a single generic mammalian data set. For inhaled dose, NHPs were the most sensitive (relative lowest LD₅₀) species and rabbits the least. Improved inhaled LD₅₀s proposed for use in risk assessment are 50,600, 102,600, and 70,800 inhaled spores for NHP, rabbit, and guinea pig, respectively. Lung deposition factors were estimated for each species using published deposition data from Bacillus spore exposures, particle deposition studies, and computer modeling. Deposition was estimated at 22%, 9%, and 30% of the inhaled dose for NHP, rabbit, and guinea pig, respectively. When the inhaled dose was adjusted to reflect deposited dose, the rabbit animal model appears the most sensitive with the guinea pig the least sensitive species.