Model-Based Approaches for the Gnda

**D.1 INTRODUCTION**

Modeling and simulation are useful when

• the system/architecture performance is very important;

• the system/architecture is too complex to intuitively assess performance; and

• significant time and resources are required to improve performance.

The GNDA meets all of these conditions. Mathematical models have been used in many domains to support system/architecture design, performance evaluation, and resource allocation decision making. The purpose of this chapter is to present the potential for GNDA mathematical models to describe the architecture, evaluate the effectiveness, and support resource allocation decision making to increase GNDA effectiveness.

**D.2 RATIONALE FOR GNDA MODELING**

Mathematical models are developed for many different reasons. For example, sometimes models are derived as compact and precise statements of basic truths (e.g., physics). Sometimes models are created to explore the logical consequences of alternative conjectures about how certain systems behave (e.g., population biology). Sometimes models are employed to summarize statistical information about the past to create forecasts of the future (e.g., macroeconomics). And sometimes models are constructed to provide a framework for better decision making (e.g., operations research).

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Appendix D
Model-Based Approaches for the Gnda
D.1 INTRODUCTION
Modeling and simulation are useful when
• the system/architecture performance is very important;
• the system/architecture is too complex to intuitively assess perfor-
mance; and
• significant time and resources are required to improve performance.
The GNDA meets all of these conditions. Mathematical models have
been used in many domains to support system/architecture design, perfor-
mance evaluation, and resource allocation decision making. The purpose of
this chapter is to present the potential for GNDA mathematical models to
describe the architecture, evaluate the effectiveness, and support resource
allocation decision making to increase GNDA effectiveness.
D.2 RATIONALE FOR GNDA MODELING
Mathematical models are developed for many different reasons. For
example, sometimes models are derived as compact and precise statements
of basic truths (e.g., physics). Sometimes models are created to explore the
logical consequences of alternative conjectures about how certain systems
behave (e.g., population biology). Sometimes models are employed to sum-
marize statistical information about the past to create forecasts of the future
(e.g., macroeconomics). And sometimes models are constructed to provide
a framework for better decision making (e.g., operations research).
75

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76 APPENDIX D
In thinking about how to evaluate the effectiveness of something as
complicated as the GNDA, modeling has much to offer. First, by combin-
ing the detection characteristics of GNDA resources (e.g., sensors, human
agents) with the physical deployment of such resources, it is possible to
model the probability (and risk consequences) of nuclear material out of
regulatory control entering the United States. Constructing such models
serves the purpose of linking GNDA resource inputs and program activities
to the primary outcomes of interest—interdiction and the risk consequences
of failing to detect radiological or nuclear material. Second, such models
can help identify appropriate performance measures for evaluating the ef-
fectiveness of the GNDA by identifying (via model analysis) the key vari-
ables that are associated with maximal detection and minimal risk. Third,
models can help evaluate alternative hypotheses regarding effective GNDA
design by comparing the modeled detection and risk outcomes of compet-
ing resource deployments. And fourth, by attaching appropriate costs to
the different resources deployed, models can help identify the most efficient
resource deployment at various budget levels.
The approach to modeling suggested above, with its emphasis on link-
ages between deployment of available resources and principal system objec-
tives, has been and continues to be employed in support of major business
and military decisions. By way of example, the next section reviews some
applications of decision-oriented operations research modeling to selected
military problems with the hope of convincing the reader that similar
models could be developed to help evaluate the effectiveness of the GNDA.
D.3 EXAMPLES FROM ELSEWHERE
Modeling and simulation play an important role in defense analysis and
support to decision makers. Military planning models exist at several levels:
component, system, force structure (architectures), and campaigns. The
models are used for force mission planning and force structure planning.
For example, consider strategic airlift to support a military campaign.
Component models exist of aircraft airframes to estimate drag and fuel
consumption. System models exist to calculate the time to deliver a plane’s
cargo to a destination. Force structure models exist to calculate the time
to deploy a force (people and equipment) for a mission. Finally, campaign
models exist to determine the time to achieve the campaign objectives given
the force available and the potential actions of the adversary. For force
structure planning, the models are used to help determine the best mix of
aircraft (e.g., tactical and strategic) and an affordable amount of airlift
capability given the potential threats our nation might face on the strategic
planning horizon. In both cases, the models do not make decisions but,

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APPENDIX D 77
rather, they inform the analysts, strategic planners, and decision makers.
Additional examples can be found within the report.
D.4 GNDA-SPECIFIC CONCERNS
Any focused modeling application must be responsive to the specifics
of the system under study. This is certainly true of the GNDA. As discussed
elsewhere in this report, the GNDA is a three-layered architecture—the in-
ternal (or domestic) layer, the U.S. border layer, and the international layer.
Responsibility for each layer rests with different agencies. It is therefore
convenient to think about detection/interdiction and risk consequences as
a function of GNDA activities and resource deployments within each of
these three layers first, and then use the layer-specific analyses to create an
overall model for the GNDA.
The GNDA does not have a centrally managed budget. Rather, each of
the agencies that participates in the GNDA determines which of its activities
qualify as GNDA-related, what resources are devoted to those activities,
and how much they cost. These determinations are historical in nature,
that is, “after-the-fact” estimates of how much money was spent on various
GNDA activities. Although these agency contributions have been totaled
to produce what looks like the total GNDA budget, there is no prospec-
tive procedure that determines how much money the government allocates
to the GNDA. The GNDA thus operates under what could be called an
best-effort budget. This is important to note, because in thinking about the
GNDA, it may not be possible to optimally allocate the resources of this
best-effort budget across different activities in a way that would change the
contributions of participating agencies to the overall budget. This does not
imply that modeling optimal GNDA resource allocation is without purpose,
however, because the gap between extant and optimal resource allocation
will provide a measure of the cost of operating the GNDA in the manner
chosen.
Another GNDA-specific concern is that the risks the system is trying to
minimize (nuclear materials out of regulatory control entering the United
States) derive in the main from the actions of intelligent adversaries such
as terrorists or hostile states. If such adversaries are intent upon attacking
the United States with nuclear or radiological materials, then surely they
will adapt their behavior given changes in GNDA resource deployments
to better achieve their goals. There are different choices possible for how
such adaptive behavior should be modeled. Traditional game theory models
adopt a “worst case” viewpoint that essentially grants adversaries perfect
foresight, while less pessimistic approaches presume that potential attackers
know some things but not others about GNDA activities (or know about
resource deployments of different assets with different probabilities). None

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78 APPENDIX D
of these frameworks are comparable to the “human vs. nature” models
that characterize risk analysis for naturally occurring threats such as floods,
earthquakes, or epidemics, for example, and so it is important to think hard
about the adversarial nature of the risks that the GNDA seeks to mitigate.
D.5 POTENTIAL MODELING APPLICATIONS FOR THE GNDA
In the section that follows the committee develops some simple exam-
ples for the purpose of illustrating insights that one can gain from modeling
and, at a basic level, some of the thought processes involved. It is not meant
to provide a complete set of models that should be developed. Later, we
discuss the availability of and need for more advanced modeling methods
to help evaluate the GNDA.
D.5.1 Descriptive Modeling
The first task when modeling any system is to understand the basic rela-
tionships among inputs, processes, and outputs. Such models are descriptive
in nature, are meant to help understand how the system in question actually
works, and also serve as building blocks for downstream decision-oriented
models that address resource allocation or other issues.
In thinking about the GNDA, one set of descriptive models would
seek to answer the following basic question: Given a particular physical
deployment of agents and sensors in a particular setting (e.g., a port, border
crossing, along a highway), what is the likelihood that the entry of nuclear
or radiological material out of regulatory control into the area of interest
would be detected? As an extremely simple example, suppose that each
of n sensors is capable of detecting a threat with probability p, and that
detection is independent across sensors. Then the probability that a threat
would be detected via the deployment of n sensors would equal 1 – (1 – p)n,
a graph of which appears in Figure D-1 the assumption that each sensor
detects with probability 0.2.
D.5.2 Sensor Quality
One of the Domestic Nuclear Detection Office’s (DNDO’s) missions is
to develop new sensor technologies (see DNDO acting director’s statement
to Congress in July 2012).1 Once we have a descriptive model, we use the
model as a tool to evaluate potential new sensor capabilities by assessing
the impact on the system performance measure, probability of detection, of
1 The written statement from Dr. H.A. Gowadia, DHS, provided July 26, 2012 can be ac-
cessed at http://homeland.house.gov/sites/homeland.house.gov/files/Testimony-Gowadia.pdf.

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APPENDIX D
DetecƟon Probability 79
1
0.9
0.8
DetecƟon Probability
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 2 4 6 8 10 12
Number of Sensors
FIGURE D-1 Detection Probability as a function of the number of deployed sen-
sors. This is an illustration of diminishing returns, in that doubling the number of
sensors increases the detection probability by less than a factor of 2. The model is
perhaps the simplest that can be envisioned, but the important point is to see how
a model links inputs (the number of sensors) to outputs (in this case the probability
of detection). D-1, editable
Figure
the extant systems with potential sensor improvements. Returning to our
sensor system model, above, with a probability of detection of 0.2, suppose
we want to assess the of system capability improvement of increasing the
probability of detection to 0.3 or 0.4. Suppose the system goal was a prob-
ability of detection of 0.8. How many of each sensor would be required to
achieve the goal?
To achieve a system probability of detection of 0.8, we would require
eight of the P = 0.2 sensors, five of the P = 0.3 sensors, and about three of
the P = 0.4 sensors. The model in Figure D-2 is very simple; it is intended
to show how a model links inputs (the number of sensors and sensor per-
formance) to outputs (in this case the probability of detection).
D.5.3 False Positive Versus False Negative Errors
When we model sensors we need to consider false negative and false
positive errors. For GNDA, a false negative error is the probability of not
detecting nuclear or radioactive material when it is present; that is, the
sensor does not alarm when threat material is present (also called a missed
detection or a false negative). A false positive error is the probability of a

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80 APPENDIX D
FIGURE D-2 Detection Probability as a function of the number of deployed sensors
of varying performance. Like Figure D-1, this figure illustrates diminishing returns,
but more rapidly for the better-performing sensors.
false detection; that is, the sensor indicates detection when the material is
not present in sufficient quantity. While GNDA is primarily concerned with
minimizing false negative errors for preventing the illicit transport of nu-
clear or radiological material, false positive errors can significantly increase
the detection cost and impose a burden on the organization whose vehicle
or container created the a false detection. Unfortunately, false positive and
false negative errors cannot be simultaneously reduced. For example, if we
lower the detection threshold to reduce the probability of missing a valid
detection (a false negative error), we increase the probability of false detec-
tion (false positive errors).
The number of false positive errors can be significant for low-preva-
lence events. A numerical example can help to illustrate the magnitude. Let
T and NT be the presence or absence of, respectively, the nuclear/radioac-
tive materials that could be a threat. Let D and ND refer to the probability
that the sensor detects (alarms) or does not detect the material (does not
alarm).
Suppose we are provided the data in Table D-1. The detection prob-
abilities seem to be quite high. The probability of a false negative error is
0.01 and the probability of a false positive error is 0.05. Suppose that 1 in

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APPENDIX D 81
Table D-1 Numerical Example Illustrating the Magnitude of False
Negative and False Positive Errors for a Low-Prevalence Event
False Negative False Positive
P(D | T] P(ND | T] P(ND | NT] P(D | NT] P[T]
Sensor 0.99 0.01 0.95 0.05
where
D = detect
ND = not detect (Type I)
T = threat present
NT = no threat present
P(D | T) = probability of detecting a potential threat
P(ND | T) = probability of not detecting a potential threat (a false negative error)
P(ND |NT) = probability of not detecting a non-threat (not alarming on a non-threat)
P(D |NT) = probability of detecting a non-threat (a false alarm error)
100,000 inspections contains the threat material. 2 Given we have a detec-
tion, what is our probability that we found the threat material?
This calculation can be done with Bayes’ Law; however, we will use a
simpler calculation. Suppose there are 10,000,000 inspections. On average,
there would be 100 inspections that find the threat material. The sensor
would properly detect 99 of these and miss 1. However, of the 9,999,900
inspections without the threat material, 5 percent of the time or 499,995
detections would be false positives. Therefore, for any given detection, the
probability of having the threat material would be only 0.02 percent [99/
(99 + 499,995)].
D.5.4 Resource Allocation Given Extant GNDA Capabilities
As discussed earlier, the GNDA functions with a best-effort budget that
precludes efficient resource allocation and substitution; yet, within agen-
cies or jurisdictions of different agencies participating in the GNDA, some
flexibility is possible. Continuing with our simple example, suppose that a
geographic area is subdivided into two zones A and B, and the participat-
ing GNDA agency is trying to decide how many of its 10 sensors it should
deploy in zone A versus zone B. From current intelligence assessments, the
agency believes that if an adversary were to attempt to bring illicit nuclear
or radiological material into the area of interest, there is a conditional prob-
ability a that entry would occur in zone A and a complementary conditional
probability b = 1 – a that entry would occur in zone B. This being the case,
if the agency deployed n sensors in zone A and 10 – n sensors in zone B,
2 In an actual modeling study, this value would be determined by intelligence estimates.

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82 DetecƟon Probability APPENDIX D
0.8
0.7
DetecƟon Probability
0.6
0.5
0.4
0.3
0.2
0.1
0
0 2 4 6 8 10
Number of Sensors in Zone A
FIGURE D-3 Detection probability as a function of the number of sensors allocated
to zone A (n) for the case where a = 0.3 (and b = 0.7) and P = 0.2.
Figure D-3, editable
then detection upon entry would occur with probability a[1 – (1 – P)n] +
b[1 – (1 – P)10 – n]. A graph of this detection probability as a function of
the number of sensors allocated to zone A (n) appears in Figure D-3 for the
case where a = 0.3 (and b = 0.7) and, as before, P = 0.2. The key feature of
this graph is that the probability of detection is highest when three sensors
are placed in zone A and seven in zone B, which results in an overall detec-
tion probability of 70 percent. Clearly there are many ways of deploying
the 10 sensors. This example shows how it is possible that even under the
best-effort budget of extant resources it is possible to think about different
deployments to improve the likelihood of detection or cost-effectiveness.
Cost-effectiveness is usually defined as the incremental (additional)
cost required to achieve an incremental unit of performance. Operational-
izing cost-effectiveness requires a measure (or measures) of effectiveness,
and a costing model for the level of performance (effectiveness) that can
be reached at different resource levels. To illustrate, consider the previous
example that shows how to best allocate 10 sensors between two zones.
Suppose that each sensor cost $100k/year to operate, so in total, $1M/year
is being spent, and suppose also that there is one infiltration attempt per
year. To maximize cost-effectiveness in this case means to minimize the cost
per detected infiltration, which of course is achieved by maximizing the
probability of detection. The example shows that placing three sensors in
zone A and seven in zone B maximizes detection probability at 70 percent,
thus, the cost per detected event equals $1M/.7 = $1.43 million per case de-

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APPENDIX D 83
tected. Any other allocation would have a lower detection probability and
thus a higher cost per detected event. For example, putting eight sensors in
zone A and two in zone B would yield a detection probability of 0.5 and
thus a cost per detected event of $1M/.5 = $2M. Clearly the first allocation
is more cost-effective than the second.
Estimating the cost-effectiveness of the entire GNDA is a challenging
task, because it requires determining (or more likely modeling) the cost and
the effectiveness of alternative allocations of GNDA resources. Nonetheless,
the principle is the same as in the simple example above.
D.5.5 Sensitivity Analysis
In many modeling applications, we may not be certain of the expert
data, especially if the experts do not have a large number of historical in-
cidents to assess. Suppose in our previous example, the intelligence analyst
believed the probability of attack in zone A (a) could be 0.3 to 0.5. We can
easily use our model to assess how sensitive our model is to that input data.
Figure D-4 shows the sensitivity of the probability of detection to the
intelligence analysis assumption about the probability of attack in zone A
versus zone B.
FIGURE D-4 Detection probability in two-zone, 10-sensor example illustrating the
sensitivity of detection probability to intelligence estimates of probability of attack
within a particular zone.

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84 APPENDIX D
D.5.6 Intelligent Adversary
The example above treated the behavior of a terrorist as not reacting
to GNDA actions to deploy sensors within zones A or B the same way one
thinks of a weather forecast—there is a 30 percent chance of rain, and by
the way, there is a 30 percent chance that illicit nuclear materials will be
smuggled into zone A. Perhaps a more realistic approach is to recognize
that if terrorists (or operatives from a rogue state) are intent upon bringing
nuclear material into the country for the purpose of mounting an attack,
such operatives are likely to have studied our defensive posture so that they
can commit to a plan that is, from their vantage point, most likely to suc-
ceed. To see how such models can be constructed, suppose that the sensors
in question are overt and easily observed (as is the case in large ports, for
example). Then, from the defenders’ point of view, the worst case is that
the terrorists know how many sensors are allocated to zone A versus zone
B. In this game, the terrorists seek to minimize the chance that they will
be detected. Thus, given any split of the sensors between zones A and B
and assuming the terrorists are aware of the split, the terrorists will choose
the zone with the lowest probability of detection, and the chance that the
defender would detect entry reduces to the chance of detection in the zone
with the fewest sensors.
If four or fewer sensors are deployed in zone A, then the terrorists will
select zone A, but if six or more sensors are deployed in zone A, the ter-
rorists will select zone B. The result that is best for the government, and
at the same time worst for the terrorists, is to place five sensors in each
zone. This serves to equalize the likelihood that the illicit materials will be
detected; it is 67 percent in either zone (see Figure D-5) . With this result,
it does not matter if the terrorists select to infiltrate zone A or zone B (or
if they choose to flip a coin to choose between A and B). This turns out to
be a much more general proposition—when defending against intelligent
adversaries, worst-case analysis requires defenders to minimize the ter-
rorists’ maximum probability of success (or more generally the expected
risk consequences of terrorist success including, for example, morbidity,
mortality, economic, and political damage). To achieve this, defenders must
equalize the payoffs to the terrorists across their various options. Achiev-
ing such equalization in payoffs produces a certain robustness, in that the
likelihood and consequences of terrorist success are fixed no matter what
the terrorists decide to do.
Again, to understand why this result must be correct, note that if the
different terrorist options produce different payoffs, then just as in our ex-
ample with zone A and zone B, terrorists will gravitate toward their most
attractive option, which will be more rewarding to them (and damaging
to us) than what can be achieved from equalizing the payoffs. Worst-case
defense also provides a certain level of comfort when thinking about terror-

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APPENDIX D
DetecƟon Probability 85
0.8
0.7
DetecƟon Probability
0.6
0.5
0.4
0.3
0.2
0.1
0
0 2 4 6 8 10
Number of Sensors in Zone A
FIGURE D-5 Detection probability for the two-zone, 10-sensor example when an
adversary has knowledge of resource allocation.
ism, because if it turns out that the terrorists are not as smart as imagined
Figure D-4, editable
(i.e., they cannot see our defenses perfectly and hence cannot choose opti-
mally themselves), then whatever results actually occur will be less severe
than conjectured in the modeling analysis.
However, for defenders to take advantage of terrorists’ lack of infor-
mation requires “knowing just what they don’t know” (see Section 4.2
within the main body of the report). In the two-zone example above, if
the defenders strongly believed that terrorists were likely to attack zone A
with probability 0.3 and hence placed three sensors in A and seven in B,
the defenders would think (from the analysis in the second example) that
they would detect with probability 70 percent. But if the defenders were
wrong in their assessment, smart terrorists would choose to infiltrate zone
A, which contains only three sensors, with certainty (e.g., using insider in-
formation), so the probability of detection would shrink below 50 percent.
D.5.7 Extension to Risk Consequences and Randomization Defense
To illustrate how the ideas above extend beyond the probability of de-
tection to risk consequences, consider Table D-2. For simplicity we presume
that there are only four defensive agents (which could be human agents,
sophisticated sensors, or both working together) to defend zones A and B.
The table reports expected casualties in zone A or B as a function of the

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86 APPENDIX D
TABLE D-2 Extension to Risk Consequences
# Units at A Casualties(A) Casualties(B) Terrorist Attacks
0 32 6 A
1 16 7 A
2 8 9 B
3 4 12 B
4 2 16 B
number of units (or defensive agents) deployed to zone A, along with the
choice made by an intelligent terrorist. The terrorist, who observes the
allocation and concludes that the best the defender seems able to do is to
allocate two agents to each zone, would induce an attack in zone B with
an expected nine casualties.
This seems inconsistent with the previous example where we argued
that the defender should seek to equalize the attackers’ payoffs across the
choices they face; in the present example, after allocating two agents to each
zone, the attackers would expect eight casualties in A and nine in B, hence
their decision to attack B. Is it possible for the defenders to do better? The
answer is yes, and randomization provides the key. Suppose that instead
of committing two agents to defend each of zone A and B, the defender
randomized with probability 0.9 that two agents are assigned to zone A and
two to zone B, and with probability 0.1 that one agent is assigned to A but
three to B. As illustrated in the decision tree (Figure D-6), this randomiza-
tion equalizes the expected casualties in zones A and B to 8.8, a modest
reduction over the fixed deployment of two agents to each zone.
Should zone A be attacked, the expected casualties equal 0.9 × 8 + 0.1
× 16 = 8.8, whereas if zone B is attacked, expected casualties are given by
0.9 × 9 + 0.1 × 7, which again equals 8.8. Randomization is thus a pow-
erful mechanism for defending against strategic attackers. We note that
randomization is already employed in homeland defense: U.S. Air Marshals
are randomly rotated across flights, while defensive patrols at Los Angeles
Airport are also randomized to better defend against terrorist attacks (Jain
et al., 2010).
D.5.8 Resource Allocation Modeling
In the examples above, the allocation decisions faced by defenders all
involved the placement of different numbers of otherwise equivalent sensors
or agents in different zones. Recall that such examples were motivated by

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APPENDIX D 87
E(Casualties)
2 Agents to A 90.0%
8
Attack A Expect
8.8 Casualties
1 Agent to A 10.0%
16
Target Choice
2 Agents to A 90.0%
9
Attack B Expect
8.8 Casualties
1 Agent to A 10.0%
7
FIGURE D-6 Decision tree illustrating that randomization equalizes the expected
casualties in zones A and B to 8.8.
Figure D-5, editable
the idea that within a given jurisdiction, some lead agency with fixed physi-
cal resources (such as agents or sensors) might still face some flexibility in
how to deploy those resources. To see how the same resource allocation
logic can apply when there are multiple resources with different unit costs
available for GNDA use, suppose that there are some number m of differ-
ent resource types (e.g., sensors with different costs and different sensitiv-
ity and specificity [equivalently different likelihoods of committing false
negative and false positive errors as discussed previously]), and that there
are also some number n of distinct detection or interdiction tasks (where
“task” could mean “detect a specific threat type” or “detect any threat in
a given geographical location”). Let xij denote the number of units of type
i resources that are allocated to task j. We refer to xij as decision variables
because assigning numbers to such variables is equivalent to deciding how
many type i resources to allocate to task j. If cij represents the cost of allo-
cating one unit of resource i to task j, then cijxij is the cost of this particular
decision. Summing cijxij over all i (between 1 and m) and j (between 1 and

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88 APPENDIX D
n) then yields the total cost of making all decisions that allocate resources
to tasks. Presumably this sum cannot exceed the total budget available for
the set of tasks under consideration. Also, because we are dealing with
physical resources, each of the decision variables xij must be nonnegative,
while there are likely additional constraints governing the total number of
resources available by type. A proposed resource allocation plan as implied
by assigned numerical values of the decision variables is said to be feasible if
its total cost resides within the available budget and if no other constraints
on resource availability are violated.
Now, in similar spirit to the simple models discussed earlier, the likeli-
hood of interdicting an attempted infiltration with nuclear material out of
regulatory control (or more generally the expected risk consequences of any
terrorist infiltration plan) can be estimated using more complex models.
Models that allow for the behavior of intelligent adversaries can also be
developed. Again, the goal of such models is to produce a set of resource
allocation decisions that are likely to lead to good (if not optimal) GNDA
outcomes.
Now, recall our earlier discussion of GNDA’s best-effort budget. Op-
timal resource allocation as suggested by models of the form above could
result in radically different suggestions for how to best allocate the total
amount of money spent on GNDA activities. Using these same models in
descriptive mode—that is, setting the decision variables equal to the values
implied by current GNDA operations—provides an immediate basis for
comparison: for the same total amount of money spent, how much better
would optimal resource allocation perform than current practice? Equiva-
lently, what is the penalty paid for operating the GNDA in its current “pure
participation” mode when compared with the protection offered from
optimally disbursing the total GNDA budget? What loss in the likelihood
of detection (or other risk consequences) results from forcing the GNDA
to operate under a best-effort budget as opposed to rationally allocating a
fixed central budget?
This logic can also be applied to the GNDA’s three layers—each of
the domestic, border, and international layers has an associated best-effort
budget that equates to the total amounts spent by all participating agencies
in layer-specific GNDA activities. How might the prospects for detection
and risk reduction improve if each of these budgets was centrally allocated?
And, thinking across these layers, how much further could system perfor-
mance improve if the amounts allocated to each layer were allowed to vary
(e.g., across detection or transportation modalities) so as to maximize safety
from the threat of nuclear or radiological terrorism?