[Help-glpk] Constraint relaxation

[esma mehiaoui]

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

Esma