A non-linear program, truck stops and camps

[lcary]

I could use some help starting my homework.
The problem set up is as follows:

#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
300 20 20 thousand
0 45 10 thousand
60 60 13 thousand

(I can't seem to separate the x, y and pop column so that it looks neater- but all numbers in the first left column are the x values, the middle numbers are the y values and the numbers in the right column are the pop values (the ones in thousands)) The # of trips to each camp is proportional to the camp population.
There are no roads for the trucks to use--they 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).

I'm not sure where to start writing equations for a non linear program.

Any ideas?

 

[Valkarie]

One approach for this problem would be to formulate a nonlinear programming (NLP) problem that minimizes the total travel distance for the trucks. The objective function would be the sum of the distances between the airstrip and each of the refugee camps, multiplied by the population of each camp. The decision variables would be the coordinates of the airstrip (x and y).The objective function would be: Minimize Z = 11,000*d(x,y,30,0) + 20,000*d(x,y,300,20) + 10,000*d(x,y,0,45) + 13,000*d(x,y,60,60)Where d(x,y,a,b) represents the distance between the airstrip location (x,y) and the camp location (a,b). The constraints would be:-x ≥ 0 -y ≥ 0 This NLP problem can then be solved using an appropriate software package.