A variable that can be zero or a non-zero range

[grandmoon]

Hi all,

We are trying to solve an optimization case and now face some problem. It is like follows: We have a variable (water flow at a valve); it can be either zero (when the valve is closed), or between 500-1500 m3/h (when it is open). In the beginning we took the flow as x1*x2, where x1 is binary and x2 is between 500 and 1500. But then SAS can't solve this non-linear thing with binary variable. How can I avoid this situation and linearize this?

Thanks.

[Ksharp]

Maybe you could try Genetic Algorithm .

Can you explain it more,and better post an example .

[RobPratt]

To model such a semi-continuous variable y, introduce a binary variable x and the following linear constraints:

• y >= 500*x
• y <= 1500*x

If x = 0, then y = 0.  If x = 1, then y is in [500, 1500].