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Re: [Help-glpk] optimisation problem

From: Andrew Makhorin
Subject: Re: [Help-glpk] optimisation problem
Date: Wed, 19 Jul 2006 07:49:13 +0400

> 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 
> area. 
> 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 

You can try writing it in GNU MathProg (a subset of AMPL supported
by GLPK).

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