Originally posted by: SystemAdmin

In the part where I write the constraints, I am having some trouble making a summation.

The problem is the following:

Decision Variables:
Y_ij = 1 if link (i,j) is used by an active path, 0 otherwise
Xp1 = 1 if path 1 is used, 0 otherwise
Xp2 = 1 if path 1 is used, 0 otherwise
Xp3 = 1 if path 1 is used, 0 otherwise

The constraint I am trying to write is that if any of the paths Xp1, Xp2 or Xp3 = 1, then Y_ij = 1. Otherwise (if none of the paths = 1), Y_ij = 0.

I am trying to do this the following way:

sum(p in Paths) X[p] <= Y_ij

But if more than 1 path is used, then it gives me trouble because it makes it as:

Xp1 + Xp2 + Xp3 <= Y_ij

1 + 1 + 0 <= 1
2 <= 1
Error

Is there any way to make a binary sum, boolean sum, or XOR or something to make it so that if I have:

1 + 1 + 1 <= 1
1 <= 1

Thanks very much for your help!

Tomas.
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Originally posted by: UDOPS

You use a technique called a "big M" constraint. You assign a coefficient to Y that is very large, thus when all X are zero, Y may be zero, but when any or all X are one, then the right hand side will satisfy with Y equal to one.

You could either use a large number or possibly "infinity" in OPL?
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Originally posted by: SystemAdmin

Did you try using an implication:
(sum(p in Paths) X[p]>=0) => (Y_ij==1)

Tschau, Frank
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Originally posted by: SystemAdmin

To me it looks like you are looking for something like
forall(p in Paths) X[p] <= Y_ij
<code>
(*forall* instead of sum / if one the the x[p] is 1 y is 1 as well)

Dependent on the objective, you might add
Y_ij <= sum(p in Paths) X[p]
<code>
in order to force y to be 0 if all x are 0
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