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Indicator Constraints
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arush  
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  More options Aug 2, 7:51 pm
Newsgroups: sci.op-research
From: arush <arushgad...@gmail.com>
Date: Sat, 2 Aug 2008 16:51:46 -0700 (PDT)
Local: Sat, Aug 2 2008 7:51 pm
Subject: Indicator Constraints
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I need to impose the following constraints :

  over(i) = 1 --------> y(i) >= 1
  over(i) = 0 --------> y(i) <= 0
  under(i) = 1 ------> y(i) <= -1
  under(i) = 0 -------> y(i) >= 0

over(i) , under(i) are binary variables. y(i) is a integer variable.

Thanks
Arush.


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Rob Pratt  
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  More options Aug 2, 8:54 pm
Newsgroups: sci.op-research
From: "Rob Pratt" <Rob.Pr...@sas.com>
Date: Sat, 2 Aug 2008 20:54:14 -0400
Local: Sat, Aug 2 2008 8:54 pm
Subject: Re: Indicator Constraints
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"arush" <arushgad...@gmail.com> wrote in message

news:7d9032c0-b4a6-42f7-b9b0-c465fad6b189@l42g2000hsc.googlegroups.com...

>I need to impose the following constraints :

>  over(i) = 1 --------> y(i) >= 1
>  over(i) = 0 --------> y(i) <= 0
>  under(i) = 1 ------> y(i) <= -1
>  under(i) = 0 -------> y(i) >= 0

> over(i) , under(i) are binary variables. y(i) is a integer variable.

> Thanks
> Arush.

If y has bounds ymin and ymax, then the following will work:

1 - y <= M_1 * (1 - over)
y - 0 <= M_2 * over
y + 1 <= M_3 * (1 - under)
0 - y <= M_4 * under

where

M_1 = 1 - ymin
M_2 = ymax
M_3 = ymax + 1
M_4 = -ymin

Rob Pratt


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