Math 319
Homework 5: NonLinear Programming
#1: Facility Location
Suppose we want to locate an airstrip somewhere in the desert
where airplanes can land to drop off food aid, which will be trucked
to various refugee camps.
The camps are located and populated as
follows:
x
y
population
30
0
11 thousand people
300
20
20 thousand people
0
45
10 thousand people
60
60
13 thousand people
The # of trips to each camp is proportional to the camp population.
There are no roads for the trucks to usethey will drive straight
from the airport to the camps.
a) Formulate an NLP to minimize the total travel distance for
the trucks (using math notation, not yet in Excel).
b) Solve it using Excel.
Hint: I get an objective function value
around 6204.5 at optimality (not accounting for truck round trips).
c) Is the optimal solution the same as the weighted average
of the camps' locations?
Compare both the location and the total cost.
d) (optional) Does the optimal location change if you don't
bother to take the square roots when computing the distances?
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 '08
 staff
 Math, Operations Research, Linear Programming, Optimization, Logistic function, Logistic map

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