st: Multiple constraint satisfaction problem

[Sarah Dykstra <sarahdykst@gmail.com>]

Hello Statalist members -

I'm trying to calculate a lower / upper bound for possible number of
troops in each province in Afghanistan for each country which
contributed troops.

The pieces of information I have are listed below. For reference,
there are 5 regions and 34 provinces in Afghanistan, and ~30 countries
contributing troops, depending on the year.

1) The total number of troops per region
2) The total number of troops contributed by each country
3) The provinces to which a country contributed troops  (yes/no). Some
countries (usually those with the lowest troop levels) have no
information and for the purpose of our analysis, we're assuming they
can be placed anywhere.

A simplified example:

USA:     30,000 troops
Canada: 10,000 troops

Region 1: 25,000 troops
-----
Prov A: USA, Canada
Prov B: USA

Region 2: 15,000 troops
-------
Prov C: Canada
Prov D: USA


The strategy I have in mind involves creating a new dataset with an
observation for each block of 100 troops (in the simple example above,
there would be 300 USA obs and 100 Canada obs), merging on a randomly
generated id to a dataset with set up the same way for regions (250
obs for Region 1, etc) and crossing against provinces. This ensures
that the total # troops / country and troops / region constraints are
always satisfied. We'll then drop any scenarios which don't satisfy
the last condition, the province assignments for each country. After X
iterations, we'll take the lowest and highest # of troops per country
and province as our lower and upper bounds.

Any estimates on the time it would take to run a program like this?
Any suggestions for a more efficient strategy in Stata?

Thanks!

Sarah Dykstra
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