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Re: [Help-glpk] 0-1 Integer Programming problem

From: François Galea
Subject: Re: [Help-glpk] 0-1 Integer Programming problem
Date: Mon, 25 Jul 2005 16:17:00 +0200
User-agent: Mozilla Thunderbird 1.0.2 (X11/20050602)


It is possible if C1 and C2 are nonnegative:

create a continuous 'max' variable, then for each possible (i,j) pair add a specific constraint:
C1*Xij + C2*Yij <= max

now, by solving min(max), you'll actually minimize the maximum C1*Xij + C2*Yij for all (i,j).


Gaurav Khanna a écrit :

I am trying to solve a 0-1 linear optimization problem
with linear constraints. I am explaining the problem i
am facing with a small example. lets say there are
three variables i am solving for Xij, Yij and Zij.
Each of the X,Y, and Z are indexed by i and j where i
varies from 1 to 10, j varies from 1 to 100. The
function f is defined as

f = (for all i  max( C1*Xij + C2*Yij)) and the goal
function is min(f) subject to a set of constraints on
Xij and Yij. Is this possible to do in GLPK.? The
reason i am asking this is because GLPK requires
entering the coeffecients for each of the terms in the
goal function .However, here i cant determine the
coefficients since my goal function which is to be
minimized is itself a maximum over multiple functions.


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François Galea
Equipe OPALE - Laboratoire PRiSM
Université de Versailles-Saint Quentin en Yvelines
45 av Etats-Unis F-78035 Versailles CEDEX
Tél. : +33 1 39 25 40 50

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