Ever since 9/11, there has been concern about the possibility of attacks on commercial airliners. In particular, man-portable air defense systems (MANPADS)—such as shoulder-launched missiles—have been used in aircraft attacks in Baghdad, Iraq, and Kenya. In this exercise, we will look at a model for evaluating the use of countermeasures against MANPADS on U.S. commercial aircraft. Even though relatively little is known about the effects of a possible attack, there is some available information, enough to make an effort to address this problem. Below you will find information that can be used to create a simple model. Specifications, Parameters, and Inputs:

1. Time horizon: 10 years. That is, we will consider the possibility of an attack over the next 10 years.

2. Decision: To use countermeasures or not. The specific type of countermeasure is not specified, but it is safe to say that it is probably an electronic device; such devices have been used by the U.S. military against infrared-guided missiles.

3. Uncertainties. Whether countermeasures are used or not, there are four uncertainties. Probabilities are shown in the tables below.

a. Attempt/No attempt. Will there be an attempted attack on a U.S. aircraft over the next 10 years? For this model, we will consider only the possibility of one attempt in ten years.

b. Interdiction/No interdiction. If there is an attempt, will it be interdicted (rendered harmless) or not?

c. Hit/Miss. If there is an attempt that is not interdicted, will the missile hit the aircraft or not?

d. Fatal crash/safe landing. If there is an attempt, not interdicted, that hits the aircraft, will the aircraft crash or be able to land safely?

Probabilities of uncertain events given no countermeasures.

If countermeasures are employed, they could be more or less effective in a variety of ways. We will model the extent to which countermeasures reduce each of the probabilities shown above:

Effectiveness of countermeasures. These are percentage reductions in the probabilities above when countermeasures are used.

4. Consequences. We will consider five different kinds of consequences:

We will value lives lost and false alarms in terms of dollars:

For simplicity, assume that all dollar values are present values, so you can ignore discounting.

Finally, some outcomes that do not involve a crash may result in an economic loss—a loss smaller than if a crash had occurred. We will model two such cases as percentages of the loss in case there is a crash:

All other outcomes (no attack, or an attempt that is successfully interdicted) result in no cost, except the cost of countermeasures if they are used.

Build a decision tree to model this problem. The basic decision is whether to adopt countermeasures. Be sure to use good modeling practice: in the tree or in any formulas, use cell references to any input or constant. This will make it possible to perform sensitivity analysis on the inputs.

The preceding inputs are actually pretty soft, and it will be important to perform sensitivity analysis to understand how changes in them might impact the decision. Can you tell anything about which inputs might have the most impact on the expected costs of the alternatives?
 
 
 
 
 

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P(Attempt) 0.50 P(Interdiction I attempt)* P(Hit I attack, no countermeasures) P(Crash | Hit) 0.05 0.80 0.25 *The probablity of interdiction given an atempt. P(Attempt) 0.50 P(Interdiction I attempt)* P(Hit I attack, no countermeasures) P(Crash | Hit) 0.05 0.80 0.25 *The probablity of interdiction given an atempt.