There is an integer linear programming problem with this constraint:
$$\left|X1 - X2\right|= 5\text{ or }10\text{ or }20$$
How it can be solved with adding auxiliary variable $y$?
Main problem is that "or" between $5$ and $10$ and $20$.
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Here is a tactic using 3 auxiliaries:
$$|X_1 - X_2| = 5y_1 + 10y_2 + 20y_3$$
$$y_1 + y_2 + y_3 = 1, all binary$$
Now you just need to model the left-hand-side, which isn't trivial.
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1$\begingroup$ You're quite close, actually. Just apply your approach to the constraint $$X_1-X_2 = -20~\text{or}~{-10}~\text{or}~{-5}~\text{or}~5~\text{or}~10~\text{or}~20$$ $\endgroup$Michael Grant– Michael Grant2015-03-23 16:34:19 +00:00Commented Mar 23, 2015 at 16:34