Department of Homeland Security Bioterrorism Risk Assessment A Call for Change (2008) / Chapter Skim
Currently Skimming:
Appendix E: Optimizing Department of Homeland Security Defense Investments: Applying Defender-Attacker (-Defender) Optimization to Terror Risk Assessment and Mitigation
Appendix E: Optimizing Department of Homeland Security Defense Investments: Applying Defender-Attacker (-Defender) Optimization to Terror Risk Assessment and Mitigation
Pages 90-102
The Chapter Skim interface presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter.
Select key terms on the right to highlight them within pages of the chapter.
From page 90... ...
Our primary goal is to recommend investments in conducted an extensive bioterrorism risk-assessment exercise, a set of available defense options; each of these options referred to here as the Biological Threat Risk Assessment can reduce our vulnerability to terrorist attack, or enable (BTRA)
|
From page 91... ...
• Indices d ∈ D defense strategy, e.g., stockpile vaccines A and B, but not C a ∈ A attack alternative, e.g., release infectious agent V m ∈ M after-attack, mitigation activity, e.g., distribute vaccine A m ∈ Md mitigation activities enabled by defense option d, e.g., distribute vaccine A, distribute vaccine B d ∈ Dm defense strategies that enable mitigation activity m k ∈ K resource types used by mitigation activities, e.g., aircraft for distributing vaccine, personnel for administering vaccine • Data damaged,a expected damage if defense strategy d and attack alternative a are chosen, given no mitigation mitigated,a,m expected damage reduction of after-attack mitigation effort m, given investment strategy d and attack a (assumes additive reduction and ∑ mitigationd ,a, m ≤ damaged ,a) m rk,d total mitigation resource of type k available if defense strategy d is chosen qk,d,m consumption of mitigation resource k provided by defense option d for mitigation activity m
|
From page 92... ...
. tion term, over yd,m, subtracts from expected damage if a (We use the generic term "tree" to represent the sequence of mitigating effort has been enabled by the defense plan, and if defender and attacker decisions we model.
|
From page 93... ...
we Figure E-1 R01268, can use enumeration to probability distributions yields an objective function that bound the effect of this relaxation on the optimal objective measures "expected damage." function value. A "mixed attack strategy" means that the optimal at Solving MXM tacker decision includes multiple attacks and then we choose mitigation responses, and this results in some damage that Temporarily fixing w = w in MXM, we take the linear ˆ can only be estimated, and some part of that estimation can programming dual (hereafter referred to simply as "the dual")
|
From page 94... ...
Figure E.2 illustrates the generic relationship relating investment options to the ability to reduce expected damage from any terrorist attack before it is carried out, and/or TABLE E.2 Defensive investment options in each mitigate damage after an attack occurs. This is a complicated potential defense strategy.
|
From page 95... ...
Figure E.3 shows minimized maximum expected damage d00 10 10 10 d01 10 5 7 as a function of total defense budget, and Table E.5 summa d02 6 8 7 rizes the solutions for each budget break-point. For instance, d03 6 6 6 with a budget of 3, the optimal defense plan in MXM is to d04 4 3 5 choose defense option "d02." The terrorists' optimal attack d05 5 5 4 is a mixed strategy, with a probability of 0.50 of choosing (This table gives the values for damaged,a for MXM.
|
From page 96... ...
Because the defender's investment options here are discrete, each improvement appears as a staircase drop as soon as sufficient budget permits some new, improved cohort of investment defense options, i.e., a new defense strategy. The law of diminishing returns is evident: expected damage reduced by each budget dollar decreases as budget increases.
|
From page 97... ...
, can be repeated for any number of for which there is no conventional optimization method, into consecutive stages with continuous decision variables. The an equivalent "max-max" problem that is nothing more than final model obtained in this manner is a simple maximization a conventional linear program.
|
From page 98... ...
, but now the values of these mixed-strategy prob- We represent defensive investment strategy selection abilities will be prescribed by the optimization model: for simply, as we think realistic and politically palatable during the stage under control of the terrorists, these will represent this early phase of homeland security capital planning. We the worst-case mix of attack decisions the terrorists can de- anticipate that this will eventually mature to more closely vise; in the mitigation stage, under DHS control, these will resemble classic military capital planning (e.g., Brown et represent the best response to each of the attacker's possible al., 2004)
|
From page 99... ...
especially when there are defense options that do not directly However, every situation is different, and it is extremely reduce expected damage (i.e., damaged,a might be high hard to predict what the effect any given "secrecy policy" for those defenses) but that enable mitigation efforts that will have on the optimal outcome, much less on the actual are significantly more effective than those available under attacker behavior.
|
From page 100... ...
mately, the defender learns enough to declare that his best In theory, this could be achieved by setting a defender defense plan is (e-) optimal against the best possible attacker option d, and estimating the consequences of this action on plan, and attains a mathematical certificate of the quality of BTRA for each pure attacker response.
|
From page 101... ...
ditive nor separable between and among attacks, so we must rely on the simplified risk analysis we have. Accordingly, REFERENCES we endow each defense strategy with the number of defense investment options reflected in each BTRA path.
|
From page 102... ...
2004. Homeland Security Presidential Directive 10 Security Under Terrorist Threat," IEEE Transactions on Power Systems [HSPD-10]
|
Key Terms
This material may be derived from roughly machine-read images, and so is provided only to facilitate research.
More
information on Chapter Skim is available.