From 1997 to 2002, I worked on Ammunition Stockpile Planning
for the Canadian
Forces and the North Atlantic Treaty Organization (NATO).
I developed a computer program called the Marginal AnalysisStockpile Planning Program (MASPP). The
latest version of MASPP was 4.0 published in May 2001.
I used Monte Carlo
simulation to support my algorithmic method of calculating the probability of
destroying N targets with K shots from a guided weapon.
For example, if the single shot kill probability is 0.5 then
on average 5 targets would be killed every 10 shots. However, I proved that the probability of
killing all 5 five targets with 10 shots is only 0.623. Thus to have 95% confidence that all 5 targets will be destroyed, we would need at least 16 shots.
I used my algorithm to draw a curve of the relationship
between the number of shots fired and the probability of killing all the
targets. This curve demonstrated diminishing returns for firing more shots.
Thus, the problem was well-suited to a marginal analysis approach.
To demonstrate that this algorithm was correct, I ran a
Monte Carlo simulation of an individual
ammunition type against an individual target type. Then I matched the algorithm's probability density
and cumulative probability functions against the simulation's frequency and percentile
curves.
The stockpile planning problem that I examined involved many
different scenarios in which it was assumed that the stockpile needed to
be sufficiently large to handle one mid-intensity conflict and two “other than war”
conflicts in so-called "peacetime".
Each type of ammunition was assigned to destroy a certain
number of targets of each target type in each scenario. So if ammunition type 1 was assigned to three
types of targets in the three scenarios, we needed to compute nine cumulative
probability functions.
In MASPP 4.0, the convolution of these nine cumulative
probability functions was estimated using Monte Carlo
simulation. This method was very similar
to the one-on-one Monte Carlo simulation
described above. The only difference is
that I ran the one-on-one case for each scenario combination and for all
targets in each scenario within that scenario combination. Then I summed the
number of rounds required to obtain an individual trial. I ran 999 trials, then sorted the results to
obtain percentile approximations of the cumulative probability curves.
For each ammunition type, a cumulative probability function
was simulated. Then if we wanted to have 95% confidence of destroying all of
the targets in all of the scenarios, we would trace up the cumulative
probability functions until the 0.95 point is reached for all of the ammunition
types.
MASPP 4.0 was a good example of how Monte Carlo simulation and marginal analysis could be used together.
