Re: Constraint for: If x>0 then y=1

[Bob Pay]

Hi

try this, maybe it helps:

x < M y

x> y

if x is positive, second is not considered, and from first, for example x =10, 10 < M y ,and in result, y must be 1 to meet constraint.

if x = 0, then first constrain is not considered, but second constrain, 0 > y, as y is binary, it takes value 0.

I am not sure about it.

you can check H.P Williams book, Model Building for more details.

On Mon, Oct 29, 2012 at 8:46 PM, JapanGo <markus...@googlemail.com> wrote:

Hello GAMS community,

I am trying to find a constraint solution for the case:

if x>0 then y=1
where x is a positive integer variable and y is a binary variable.
Thus in cases where x=0 also y=0

I tried several combination (including big M, -y, (1-y) formulations etc.) but do not get to the wanted result. Maybe it is not possible with a single constraint, but needs two?

Would be great to get your opinions on it. Thanks!

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Babak Saleck Pay
M.Sc
Socio-Economic System Engineering
Group of Industrial Engineering
University of Tehran
Tehran,Iran

www.babaksp.com

[Destin Zed]

JapanGo,

Modification to Bob's formulation.

y >= EPSILON*x
y <= x

If x equals 10, then y >= EPSILON and y <= 10 which forces y to have only a value of 1. On the other hand, if x is zero, y >= 0 and y <= 0 which forces y to be 0.

I hope this works for you.

Destin

[Destin Zed]

But that is non-linear!

On Thu, Nov 15, 2012 at 1:42 PM, HJW Vermue <hjwv...@gmail.com> wrote:

Regardless of what I wrote before, I obviously meant y>=min(x,1), as that does fulfill the requirements stated.

On Tuesday, October 30, 2012 10:59:33 AM UTC+1, JapanGo wrote:

Hello Destin,
hello Babak,

thanks to both of you. The adaption of Destin made it work.
As a feedback to the community: One can also model the constraint with big M:
yM >= x
y <= x

To view this discussion on the web visit https://groups.google.com/d/msg/gamsworld/-/5QkqUvVb-ZkJ.

[Guangjian Liu]

发自我的 iPad

在 2012-11-15，20:42，HJW Vermue <hjwv...@gmail.com> 写道：

Regardless of what I wrote before, I obviously meant y>=min(x,1), as that does fulfill the requirements stated.

On Tuesday, October 30, 2012 10:59:33 AM UTC+1, JapanGo wrote:

Hello Destin,
hello Babak,

thanks to both of you. The adaption of Destin made it work.
As a feedback to the community: One can also model the constraint with big M:
yM >= x
y <= x


Am Dienstag, 30. Oktober 2012 10:22:47 UTC+1 schrieb Destin Zed:

To view this discussion on the web visit https://groups.google.com/d/msg/gamsworld/-/5QkqUvVb-ZkJ.

[Sina Zabihi]

hello dears
maybe this constrains help you
y>=epsilon*x
y<=big M*x