Linearize if statement in MILP constraint

Question

I am trying to solve an optimization problem in which one of the constraints is : x*y=0, where x and y are decision variables and only x or y can be positive. In other words, if x!=0 then y=0 and if y!=0 then x=0. Please help

score 0 · Accepted Answer · answered Oct 07 '21 at 13:03

0

Assumption: x and y are nonnegative
Infer upper-bounds UB_x and UB_y for x, y
Introduce new boolean variable b
Add constraints:
```
x <= (1-b) * UB_x
y <= b * UB_y
```

answered Oct 07 '21 at 13:03

sascha

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how to define the UB_x and the UB_y? – amal nammouchi Oct 07 '21 at 19:43
You must limit them a-priori building your model. Those are constants. – sascha Oct 07 '21 at 19:50

Linearize if statement in MILP constraint

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