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[Help-glpk] optimisation problem

From: Mullen Michael (IE)
Subject: [Help-glpk] optimisation problem
Date: Tue, 18 Jul 2006 18:48:07 +0100

I am trying to solve the following optimisation problem using GLPK and
Matlab( linked by GLPKmex). Is there an easy way to formulate and solve
this problem.

The Problem is as follows:

m is the number of candidate base station sites such that S=1 to m
n is the number of test points such that set of test points I= 1 to n
Y(j) is a decision variable, 1 if a base station is installed in j for
j is element of S , 0 otherwise
X(i,j) is 1 if test point i is assigned to Base station j, 0 otherwise.
C(j) is the cost of the installation of the base station
G(i,j) is the propagation factor of the radio link between test point
1, 1<=i<=n and a candidate site j,i<=j<=m

Using a pseudo random number generator, each candidate site j and each
TP i is assigned a position with uniform distribution in the service

Minimize the overall cost and get the minimum number of base stations
required to cover the service area.
I think a basic model is :

min sum{j}C(j)*Y(j) + sum{i,j}X(i,j)/G(i,j)

subject to

sum{j}X(i,j)=1, i element of I
X(i,j)<=Y(j), i element of I, j element of S

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