Big M formulation of an if-then-else condition

 2 I have an if-then-else condition in one of my constraints and I read online that Big M formulation can actually convert the constraint into a linear one. So, I'd like to ask you guys if my formulation of the constraint is correct or wrong. subject to Phy {w in PHY, dns in DEMAND}: x_ns[w] := (if (x_S[dns, w] = 1 or x_P[dns, w] = 1 or x_M[dns, w] = 1 or x_I[dns, w] = 1) then (x_ns[w]) = 1 else (x_ns) = 0); Now the Big M formulation of the above constraint is as follows: 5 * x_ns - x_S - x_P - x_M - x_I >= 0 #(constraint 1) 1 * x_ns - x_S - x_P - x_M - x_I <= 0 #(constraint 2) Please let me know if this is correct or wrong. Also, I tried using an indicator constraint but I'm having some trouble with it as it always points me to the solution 0.0 Thank You asked 11 Jun '14, 10:26 crypto 67●2●7 accept rate: 0%

 4 I assume all variables are booleans. The second constraint is correct. For the first one, 4 instead of 5 would do it with a smaller big M. However, I would rather write the set of constraints instead: \begin{align} x_{ns} & \ge x_S\\ x_{ns} & \ge x_P\\ x_{ns} & \ge x_M\\ x_{ns} & \ge x_I \end{align} answered 11 Jun '14, 10:43 David 306●1●6 accept rate: 12% fbahr ♦ 4.6k●7●16 Yes, all variables are binary and also the constraint you've mentioned could be written but in the objective, what I do is sum up all x_ns' over the number of nodes. So, for every node I'd have only one x_ns. If I follow your formulation, I'm not sure how I can do that. Also do I need both the constraints in my formulation or only one of them would do? (11 Jun '14, 10:47) crypto What prevents you to replicate these set of constraints at every node ? I do not understand the relation with the objective function. (11 Jun '14, 12:48) David Sorry for the confusion there but when I tried your formulation it provided me the same result the big M formulation provided. Thanks a lot for the answer and I just wanted to implement it using an indicator constraint because the idea sounded cooler but it had a few problems of its own. I'm working on that one as well. So, thanks to your answer I now have three ways to implement the same constraint. Many thanks David (12 Jun '14, 03:12) crypto It is a must that any alternative solutions lead to the same optimal solution on small case, otherwise one of the formulation is wrong ! However, some formulations might be better than the other ones, and you will measure it when you do branch & cut. Roughly, you may close the gap much more faster with some formulations rather than others. (12 Jun '14, 05:31) David
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Asked: 11 Jun '14, 10:26

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Last updated: 12 Jun '14, 06:32

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