Is it possible to linearize these inequalities

GAMS
1

x1(m,j) * ( TI(m)-T(j) ) =g= 0 ;
x1(m,j) * ( T(j+1)-TO(m) ) =g= 0 ;
x2(m,j) * ( T(j+1)-TI(m) ) =g= 0 ;
x3(m,j) * ( TO(m)-T(j) ) =g= 0 ;
x1(m,j) +x2(m,j) +x3(m,j) =e= 1 ;

where x1, x2, x3 are binary variables. TI(m), TO(m) and T(j) are positive variables and greater than 30. T(j) are in descending order. TI(m)>=TO(m). All value of TI(m) and TO(m) can be found in T(j). The purpose of inequalities above is to use binary variables to recognize whether T(j) and T(j+1) are between TI(m) and TO(m).
Is it possible to linearize these inequalities

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2

Hi Dylan,

Check section 7.7 of this document:

http://www.aimms.com/aimms/download/manuals/aimms3om_integerprogrammingtricks.pdf


Cheers,
Pedro



On Wed, Aug 21, 2013 at 5:26 AM, Dylan Lan wrote:

x1(m,j) * ( TI(m)-T(j) ) =g= 0 ;
x1(m,j) * ( T(j+1)-TO(m) ) =g= 0 ;
x2(m,j) * ( T(j+1)-TI(m) ) =g= 0 ;
x3(m,j) * ( TO(m)-T(j) ) =g= 0 ;
x1(m,j) +x2(m,j) +x3(m,j) =e= 1 ;

where x1, x2, x3 are binary variables. TI(m), TO(m) and T(j) are positive variables and greater than 30. T(j) are in descending order. TI(m)>=TO(m). All value of TI(m) and TO(m) can be found in T(j). The purpose of inequalities above is to use binary variables to recognize whether T(j) and T(j+1) are between TI(m) and TO(m).
Is it possible to linearize these inequalities

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\

PEDRO JAVIER RAMÍREZ TORREALBA
Ingeniero Civil Eléctrico PUC
MSc en Ingeniería Eléctrica PUC
Londres, REINO UNIDO

Celular: +44-(0)75-8069-3119

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3

Hi Predo,
Oh, it is amazing, thank you very much for your help.
By the way, is this book named “AIMMS Modeling Guide”?.
Dylan


在 2013年8月21日星期三UTC+8下午5时06分17秒，PowerChile写道：

Hi Dylan,

Check section 7.7 of this document:

http://www.aimms.com/aimms/download/manuals/aimms3om_integerprogrammingtricks.pdf


Cheers,
Pedro



On Wed, Aug 21, 2013 at 5:26 AM, Dylan Lan wrote:

x1(m,j) * ( TI(m)-T(j) ) =g= 0 ;
x1(m,j) * ( T(j+1)-TO(m) ) =g= 0 ;
x2(m,j) * ( T(j+1)-TI(m) ) =g= 0 ;
x3(m,j) * ( TO(m)-T(j) ) =g= 0 ;
x1(m,j) +x2(m,j) +x3(m,j) =e= 1 ;

where x1, x2, x3 are binary variables. TI(m), TO(m) and T(j) are positive variables and greater than 30. T(j) are in descending order. TI(m)>=TO(m). All value of TI(m) and TO(m) can be found in T(j). The purpose of inequalities above is to use binary variables to recognize whether T(j) and T(j+1) are between TI(m) and TO(m).
Is it possible to linearize these inequalities

–
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\

PEDRO JAVIER RAMÍREZ TORREALBA
Ingeniero Civil Eléctrico PUC
MSc en Ingeniería Eléctrica PUC
Londres, REINO UNIDO

Celular: +44-(0)75-8069-3119

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4

Hi, GAMS world
I just found that I forgot to solute, sorry.

在 2013年8月21日星期三UTC+8下午12时26分13秒，Dylan Lan写道：

x1(m,j) * ( TI(m)-T(j) ) =g= 0 ;
x1(m,j) * ( T(j+1)-TO(m) ) =g= 0 ;
x2(m,j) * ( T(j+1)-TI(m) ) =g= 0 ;
x3(m,j) * ( TO(m)-T(j) ) =g= 0 ;
x1(m,j) +x2(m,j) +x3(m,j) =e= 1 ;

where x1, x2, x3 are binary variables. TI(m), TO(m) and T(j) are positive variables and greater than 30. T(j) are in descending order. TI(m)>=TO(m). All value of TI(m) and TO(m) can be found in T(j). The purpose of inequalities above is to use binary variables to recognize whether T(j) and T(j+1) are between TI(m) and TO(m).
Is it possible to linearize these inequalities

–
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5

Hello,

let’s say for the first inequality (after the expand of the parenthesis) you will have the following:
x1(m,j) *TI(m)

Introduce the next triplet of constraints:

TI1(m,j)+TI2(m,j)=E=TI(m)
T1(m,j)=L=TIu(m)*x1(m,j); TIu(m) is an upper bound of variable TI(m)
T2(m,j)=L=TIu(m)(1-x1(m,j));

and replace bilinear term x1(m,j) *TI(m) with T1(m,j).

Konstantinos Petridis

PhD Student

Τη Τετάρτη, 21 Αυγούστου 2013 7:26:13 π.μ. UTC+3, ο χρήστης Dylan Lan έγραψε:

x1(m,j) * ( TI(m)-T(j) ) =g= 0 ;
x1(m,j) * ( T(j+1)-TO(m) ) =g= 0 ;
x2(m,j) * ( T(j+1)-TI(m) ) =g= 0 ;
x3(m,j) * ( TO(m)-T(j) ) =g= 0 ;
x1(m,j) +x2(m,j) +x3(m,j) =e= 1 ;

where x1, x2, x3 are binary variables. TI(m), TO(m) and T(j) are positive variables and greater than 30. T(j) are in descending order. TI(m)>=TO(m). All value of TI(m) and TO(m) can be found in T(j). The purpose of inequalities above is to use binary variables to recognize whether T(j) and T(j+1) are between TI(m) and TO(m).
Is it possible to linearize these inequalities

–
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