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[Help-glpk] Constraint relaxation

From: esma mehiaoui
Subject: [Help-glpk] Constraint relaxation
Date: Wed, 6 Mar 2013 15:38:44 +0000 (GMT)

Dear All,
In my MILP formulation I need to define binary variables from integer variables, more precisely:
i have two sets: set1={1,2,3} and set2={5,6,7} than i define in set1 exactly one value for each i in set2 and this value could be the same for other elements in set2.
s.t. C1{i in set2}: sum{j in set1} X[i,j] =1; 
Then i define a variable for each element in set2 that specifies the chosen value from set1.
s.t. C2{i in set2}: Y[i] = sum{j in set1} X[i,j] * j ;
Now my problem is how to define binary variables that indicate if Y[i] is greater, lower or equal to Y[j] for i,j in set2.
I declare a binary variable order[i,j] such that:
1) if Y[i]>Y[j] then order[i,j] = 1 and order[j,i] =0
2) if Y[i]<Y[j] then order[i,j] = 0 and order[j,i] =1
3) if Y[i]=Y[j] then order[i,j] = 0 and order[j,i] =0
I did not find any possible relaxation for this using big M. Could someone help me ?
Best regards

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