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.     

Defender–Attacker Decision Tree Analysis to Combat Terrorism

We propose a methodology, called defender–attacker decision tree analysis, to evaluate defensive actions against terrorist attacks in a dynamic and hostile environment. Like most game‐theoretic formulations of this problem, we assume that the defenders act rationally by maximizing their expected utility or minimizing their expected costs. However, we do not assume that attackers maximize their expected utilities. Instead, we encode the defender's limited knowledge about the attacker's motivations and capabilities as a conditional probability distribution over the attacker's decisions. We apply this methodology to the problem of defending against possible terrorist attacks on commercial airplanes, using one of three weapons: infrared‐guided MANPADS (man‐portable air defense systems), laser‐guided MANPADS, or visually targeted RPGs (rocket propelled grenades). We also evaluate three countermeasures against these weapons: DIRCMs (directional infrared countermeasures), perimeter control around the airport, and hardening airplanes. The model includes deterrence effects, the effectiveness of the countermeasures, and the substitution of weapons and targets once a specific countermeasure is selected. It also includes a second stage of defensive decisions after an attack occurs. Key findings are: (1) due to the high cost of the countermeasures, not implementing countermeasures is the preferred defensive alternative for a large range of parameters; (2) if the probability of an attack and the associated consequences are large, a combination of DIRCMs and ground perimeter control are preferred over any single countermeasure.     

A Decision Framework for Managing Risk to Airports from Terrorist Attack

This article presents an asset‐level security risk management framework to assist stakeholders of critical assets with allocating limited budgets for enhancing their safety and security against terrorist attack. The proposed framework models the security system of an asset, considers various threat scenarios, and models the sequential decision framework of attackers during the attack. Its novel contributions are the introduction of the notion of partial neutralization of attackers by defenders, estimation of total loss from successful, partially successful, and unsuccessful actions of attackers at various stages of an attack, and inclusion of the effects of these losses on the choices made by terrorists at various stages of the attack. The application of the proposed method is demonstrated in an example dealing with security risk management of a U.S. commercial airport, in which a set of plausible threat scenarios and risk mitigation options are considered. It is found that a combination of providing blast‐resistant cargo containers and a video surveillance system on the airport perimeter fence is the best option based on minimum expected life‐cycle cost considering a 10‐year service period.     

突发事件情景下的中国战略石油储备应对策略研究

本文基于动态规划模型,模拟分析了不同突发事件下(自然灾害、局部武装冲突、金融危机等)我国战略石油储备的应对策略,以期最小化国家战略石油储备总成本。本文在成本函数中增加了突发事件造成的宏观经济损失,并用月度决策代替了已有相关研究的年度决策,使模拟结果更贴近实际。模型结果表明:突发自然灾害情景下,最优策略是先快速释放约12～36百万桶原油,来平抑油价、缓解供应短缺;金融危机情景下,最优策略是先趁油价高位抛售一定的储备(约6～18百万桶),然后当油价低位时快速补仓,但最大补仓量最好不要超过总储备能力的77%,来降低总的储备成本;局部武装冲突的情景下,最优策略是持续快速的释放约36～77百万桶原油,以保障石油供应安全。     

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.     

Robust allocation of a defensive budget considering an attacker's private information

Attackers' private information is one of the main issues in defensive resource allocation games in homeland security. The outcome of a defense resource allocation decision critically depends on the accuracy of estimations about the attacker's attributes. However, terrorists' goals may be unknown to the defender, necessitating robust decisions by the defender. This article develops a robust-optimization game-theoretical model for identifying optimal defense resource allocation strategies for a rational defender facing a strategic attacker while the attacker's valuation of targets, being the most critical attribute of the attacker, is unknown but belongs to bounded distribution-free intervals. To our best knowledge, no previous research has applied robust optimization in homeland security resource allocation when uncertainty is defined in bounded distribution-free intervals. The key features of our model include (1) modeling uncertainty in attackers' attributes, where uncertainty is characterized by bounded intervals; (2) finding the robust-optimization equilibrium for the defender using concepts dealing with budget of uncertainty and price of robustness; and (3) applying the proposed model to real data.     

Dynamic Policies for Optimal LEO Satellite Launches

Low‐earth orbit satellite (LEO) systems continue to provide mobile communication services. The issue of cost containment in system maintenance is a critical factor for continued operation. Satellite finite life‐times follow a stochastic process, and since satellite replenishment cost is the most significant on‐going cost of operation, finding optimal launch policies is of paramount importance. This paper formulates the satellite launch problem as a Markovian decision model that can be solved using dynamic programming. The policy space of the system is enormous and traditional action space dominance rules do not apply. In order to solve the dynamic program for realistic problem sizes, a novel procedure for limiting the state space considered in the dynamic program is developed. The viability of the proposed solution procedure is demonstrated in example problems using realistic system data. The policies derived by the proposed solution procedure are superior to those currently considered by LEO system operators, and result in substantial annual cost savings.     

企业战略联盟风险防范体系的架构研究

在对企业战略联盟存在的风险及规避措施进行理论透析的基础上,给出了企业战略联盟伙伴选择机制的权值排序模型。提出了企业战略联盟的3种风险防范整合架构,并论述了三者之间的相关关系。最后通过实例对企业战略联盟伙伴选择机制的权值排序模型和风险防范整合体系进行了验证。     

Efficiency of Even Separation of Parallel Elements with Variable Contest Intensity

The article considers strategic defense and attack of a system that can be separated into parallel elements. The defender distributes its resource between separation and protecting the elements from outside attacks. The vulnerability of each element is determined by an attacker‐defender contest success function, which depends on a contest intensity that may increase or decrease through the separation process. The article determines criteria of separation efficiency for systems without performance redundancy and 1‐out‐of‐N and Q‐out‐of‐N systems with performance redundancy. For the systems with performance redundancy the cases of expected damage proportional to the probability that the demand is not met, and expected damage proportional to the unsupplied demand, are considered.     

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.     

Competition within the U.S. National Security Regime: A study of the U.S. Aerospace Defense Sector

This article examines the aerospace defense sector and the national export control regime within which U.S. corporations operate. While the U.S. federal government plays many roles in this industry, the focus here is on its role as regulator of defense exports from the United States. From this vantage point, ten case studies illustrate the difficulties faced by companies in this challenging environment, and highlight factors that lead to noncompliance with U.S. government regulations. Firm performance effects are investigated, including impacts on profits, share price, and reputation. The paper concludes with implications for international management practice and international business research that reflect realities in the aerospace defense sector.     

Strategic Cognition of Operations Executives

The nature of operations executives’ strategic cognition, as the antecedent to their choices about operations strategy, remains underexplored in the literature. This mixed‐methods study examines executives’ thinking about supply chain strategy through the lens of managerial cognition. Our qualitative study at a pharmaceutical distributor, which examined 25 executives’ outlook on the future of the turbulent U.S. healthcare sector and their suggestions for adapting the company's supply chain strategy to that future, suggests that an executive's strategic cognition can be defined by its regulatory focus—whether the executive envisions the future environment in terms of opportunities or threats—and the level of optimism in regards to the envisioned future. We propose a typology that predicts the strategic choices of operations executives based on four types of cognition: pioneering, pushing, protective, and provocative. It describes whether an executive's strategic choices target traditional or novel sources of revenue, and if they seek to influence either the firm's structure and practices or its environment. Our empirical test of the typology using quantitative data collected in a survey of senior operations executives supports the study's propositions associating three of the four types of cognition with their respective preferred strategic choices.     

Part II: Quantitative Evaluation of Choices Used in Setting Noncancer Chronic Human Health Reference Values Across Organizations

Environmental and public health organizations, including the World Health Organization (WHO) and the U.S. Environmental Protection Agency (USEPA), develop human health reference values (HHRV) that set “safe” levels of exposure to noncarcinogens. Here, we systematically analyze chronic HHRVs from four organizations: USEPA, Health Canada, RIVM (the Netherlands), and the U.S. Agency for Toxic Substances and Disease Registry. This study is an extension of our earlier work and both closely examines the choices made in setting HHRVs and presents a quantitative method for identifying the primary factors influencing HHRV agreement or disagreement.⁽¹⁾ We evaluated 171 organizational comparisons, developing a quantitative method for identifying the factors to which HHRV agreement (that is, when both organizations considering the same data set the identical HHRV values) is most sensitive. To conduct this analysis, a Bayesian belief network was built using expert judgment, including the specific science policy choices analysis made in the context of setting an HHRV. Based on a sensitivity of findings analysis, HHRV agreement is most sensitive to the point of departure value, followed by the total uncertainty factor (UF), critical study, critical effect, animal model, and point of departure approach. This analysis also considered the specific impacts of individual UFs, with the database UF and the subchronic‐to‐chronic UF being identified as primary factors impacting the total UF differences observed across organizations. The sensitivity of findings analysis results were strengthened and confirmed by frequency analyses evaluating which choices most often disagreed when the HHRV and the total UF disagreed.     

A Data‐Driven Approach to Assessing Supply Inadequacy Risks Due to Climate‐Induced Shifts in Electricity Demand

The U.S. electric power system is increasingly vulnerable to the adverse impacts of extreme climate events. Supply inadequacy risk can result from climate‐induced shifts in electricity demand and/or damaged physical assets due to hydro‐meteorological hazards and climate change. In this article, we focus on the risks associated with the unanticipated climate‐induced demand shifts and propose a data‐driven approach to identify risk factors that render the electricity sector vulnerable in the face of future climate variability and change. More specifically, we have leveraged advanced supervised learning theory to identify the key predictors of climate‐sensitive demand in the residential, commercial, and industrial sectors. Our analysis indicates that variations in mean dew point temperature is the common major risk factor across all the three sectors. We have also conducted a statistical sensitivity analysis to assess the variability in the projected demand as a function of the key climate risk factor. We then propose the use of scenario‐based heat maps as a tool to communicate the inadequacy risks to stakeholders and decisionmakers. While we use the state of Ohio as a case study, our proposed approach is equally applicable to all other states.     

Optimization of Cascade‐Resilient Electrical Infrastructures and its Validation by Power Flow Modeling

Large‐scale outages on real‐world critical infrastructures, although infrequent, are increasingly disastrous to our society. In this article, we are primarily concerned with power transmission networks and we consider the problem of allocation of generation to distributors by rewiring links under the objectives of maximizing network resilience to cascading failure and minimizing investment costs. The combinatorial multiobjective optimization is carried out by a nondominated sorting binary differential evolution (NSBDE) algorithm. For each generators–distributors connection pattern considered in the NSBDE search, a computationally cheap, topological model of failure cascading in a complex network (named the Motter‐Lai [ML] model) is used to simulate and quantify network resilience to cascading failures initiated by targeted attacks. The results on the 400 kV French power transmission network case study show that the proposed method allows us to identify optimal patterns of generators–distributors connection that improve cascading resilience at an acceptable cost. To verify the realistic character of the results obtained by the NSBDE with the embedded ML topological model, a more realistic but also more computationally expensive model of cascading failures is adopted, based on optimal power flow (namely, the ORNL‐Pserc‐Alaska) model). The consistent results between the two models provide impetus for the use of topological, complex network theory models for analysis and optimization of large infrastructures against cascading failure with the advantages of simplicity, scalability, and low computational cost.     

Topological Performance Measures as Surrogates for Physical Flow Models for Risk and Vulnerability Analysis for Electric Power Systems

Critical infrastructure systems must be both robust and resilient in order to ensure the functioning of society. To improve the performance of such systems, we often use risk and vulnerability analysis to find and address system weaknesses. A critical component of such analyses is the ability to accurately determine the negative consequences of various types of failures in the system. Numerous mathematical and simulation models exist that can be used to this end. However, there are relatively few studies comparing the implications of using different modeling approaches in the context of comprehensive risk analysis of critical infrastructures. In this article, we suggest a classification of these models, which span from simple topologically‐oriented models to advanced physical‐flow‐based models. Here, we focus on electric power systems and present a study aimed at understanding the tradeoffs between simplicity and fidelity in models used in the context of risk analysis. Specifically, the purpose of this article is to compare performance estimates achieved with a spectrum of approaches typically used for risk and vulnerability analysis of electric power systems and evaluate if more simplified topological measures can be combined using statistical methods to be used as a surrogate for physical flow models. The results of our work provide guidance as to appropriate models or combinations of models to use when analyzing large‐scale critical infrastructure systems, where simulation times quickly become insurmountable when using more advanced models, severely limiting the extent of analyses that can be performed.     

Obtaining the optimal fleet mix: A case study about towing tractors at airports

Planes do not have a reverse gear. Hence, they need to be towed by tractors when leaving the gate. Towing tractors differ with respect to investment as well as variable costs and plane type compatibility. We propose a model which addresses the problem of a cost minimal fleet composition to support towing service providers in their strategic investment decisions. The model takes into account a maximum lifetime, a minimum duration of use, an overhaul option and a sell option. In a case study with a major European airport (our cooperating airport) we generate a multi-period fleet investment schedule. Furthermore, we introduce a 4-step approach for demand aggregation based on flight schedule information. We analyze the impact of demand variation, flight schedule disruptions and cost structure on the optimal buy, overhaul and sell policy. The scenario analyses demonstrate the robustness of the investment schedule with respect to these factors. Ignoring the existing fleet, a green field scenario reveals saving potentials of more than 5% when applying this model.     

Schedule Recovery: Unplanned Absences in Service Operations*

The U.S. service sector loses 2.3% of all scheduled labor hours to unplanned absences, but in some industries, the total cost of unplanned absences approaches 20% of payroll expense. The principal reasons for unscheduled absences (personal illness and family issues) are unlikely to abate anytime soon. Despite this, most labor scheduling systems continue to assume perfect attendance. This oversight masks an important but rarely addressed issue in services management: how to recover from short‐notice, short‐term reductions in planned capacity. In this article, we model optimal responses to unplanned employee absences in multi‐server queueing systems that provide discrete, pay‐per‐use services for impatient customers. Our goal is to assess the performance of alternate absence recovery strategies under various staffing and scheduling regimes. We accomplish this by first developing optimal labor schedules for hypothetical service environments with unreliable workers. We then simulate unplanned employee absences, apply an absence recovery model, and compute system profits. Our absence recovery model utilizes recovery strategies such as holdover overtime, call‐ins, and temporary workers. We find that holdover overtime is an effective absence recovery strategy provided sufficient reserve capacity (maximum allowable work hours minus scheduled hours) exists. Otherwise, less precise and more costly absence recovery methods such as call‐ins and temporary help service workers may be needed. We also find that choices for initial staffing and scheduling policies, such as planned overtime and absence anticipation, significantly influence the likelihood of successful absence recovery. To predict the effectiveness of absence recovery policies under alternate staffing/scheduling strategies and operating environments, we propose an index based on initial capacity reserves.     

Mitigating the U.S. Drug Shortages Through Pareto‐Improving Contracts

Drug shortages have been a major challenge facing the US pharmaceutical industry and government in recent years. Although the problem has drawn tremendous attention from the government and media, limited academic research has been devoted to this problem, and few solutions have been proposed based on rigorous research. This study addresses the drug shortage problem from a supply chain perspective, a key aspect missing in the literature, and proposes to mitigate shortages through drug purchase contracts. By modeling the drug supply chain, we capture the objectives of various supply chain parties, and investigate Pareto‐improving contracts that mitigate drug shortages, improve drug manufacturer's and group purchasing organization (GPO)'s profits, and cut government spending and healthcare providers’ costs. We explore structural properties of key supply chain decisions and the Pareto‐improving contracts, and conduct scenario analysis with realistic industry data to evaluate shortage mitigation solutions. Our analysis shows that increasing drug prices only, a solution advocated by many, is not very effective in shortage mitigation. Price increases must be paired with strengthened failure‐to‐supply clauses (called the IPS approach) to achieve consistent and significant shortage reduction as well as Pareto improvement. Across all scenarios tested, a 30% price increase under IPS can lead to a minimum, average, and maximum shortage reduction of 25%, 53%, and 70%, respectively. Our analysis also shows the impacts of IPS on different parties in the supply chain and the impacts of various model parameters on shortage mitigation. The IPS approach rewards reliability of drug supply, which is in line with the FDA's strategic plan to reward quality, but is easier to achieve in this regulation‐based industry. Interactions with the government and industry practitioners indicate that IPS also challenges the current mindset in pharmaceutical contracting.