Big-M reformulation

Hi GAMS wolrd,
I have a problem in reformulating equation constraints in a disjunctive model by Big-M reformulation.
When reformulating equations constraints, the only way I know is to introduce two inequalities. for example:
A(i) = B(j) reformulated as:

A(i) - B(j) =l= M*( 1-x(i,j) ) ;
B(j) - A(i) =l= M*( 1-x(i,j) ) ;
sum( i$(ord(i)<=I), x(i,j) ) =e= 1 ;

where x is binary variable.
Is there any way to reduce the number of equation and inequalities I have to use in Big-M reformulation?
Regards,
Dylan


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Hi, Dylan

Are both A(i) and B(j) variables?
In an affirmative case, can one of them be an upper bound for the other?

Regards,
Luiz Carlos.


On Sun, Sep 29, 2013 at 6:23 AM, Dylan Lan wrote:

Hi GAMS wolrd,
I have a problem in reformulating equation constraints in a disjunctive model by Big-M reformulation.
When reformulating equations constraints, the only way I know is to introduce two inequalities. for example:
A(i) = B(j) reformulated as:

A(i) - B(j) =l= M*( 1-x(i,j) ) ;
B(j) - A(i) =l= M*( 1-x(i,j) ) ;
sum( i$(ord(i)<=I), x(i,j) ) =e= 1 ;

where x is binary variable.
Is there any way to reduce the number of equation and inequalities I have to use in Big-M reformulation?
Regards,
Dylan


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Hi Luiz,
Yes, both A(i) and B(j) are variables.
But A(i) - B(j) could be positive or negative.
Regards,
Dylan

在 2013年9月30日星期一UTC+8上午1时50分06秒,luizcfs写道:

Hi, Dylan

Are both A(i) and B(j) variables?
In an affirmative case, can one of them be an upper bound for the other?

Regards,
Luiz Carlos.


On Sun, Sep 29, 2013 at 6:23 AM, Dylan Lan wrote:

Hi GAMS wolrd,
I have a problem in reformulating equation constraints in a disjunctive model by Big-M reformulation.
When reformulating equations constraints, the only way I know is to introduce two inequalities. for example:
A(i) = B(j) reformulated as:

A(i) - B(j) =l= M*( 1-x(i,j) ) ;
B(j) - A(i) =l= M*( 1-x(i,j) ) ;
sum( i$(ord(i)<=I), x(i,j) ) =e= 1 ;

where x is binary variable.
Is there any way to reduce the number of equation and inequalities I have to use in Big-M reformulation?
Regards,
Dylan


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Dylan,

Given your extra information about the variables, I can’t think anything different from your initial
formulation

regards,
Luiz Carlos.


On Mon, Sep 30, 2013 at 4:38 AM, Dylan Lan wrote:

Hi Luiz,
Yes, both A(i) and B(j) are variables.
But A(i) - B(j) could be positive or negative.
Regards,
Dylan

在 2013年9月30日星期一UTC+8上午1时50分06秒,luizcfs写道:

Hi, Dylan

Are both A(i) and B(j) variables?
In an affirmative case, can one of them be an upper bound for the other?

Regards,
Luiz Carlos.


On Sun, Sep 29, 2013 at 6:23 AM, Dylan Lan wrote:

Hi GAMS wolrd,
I have a problem in reformulating equation constraints in a disjunctive model by Big-M reformulation.
When reformulating equations constraints, the only way I know is to introduce two inequalities. for example:
A(i) = B(j) reformulated as:

A(i) - B(j) =l= M*( 1-x(i,j) ) ;
B(j) - A(i) =l= M*( 1-x(i,j) ) ;
sum( i$(ord(i)<=I), x(i,j) ) =e= 1 ;

where x is binary variable.
Is there any way to reduce the number of equation and inequalities I have to use in Big-M reformulation?
Regards,
Dylan


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Hi Luiz,
Thank you for your help, I would try different formulation.

Regards,
Dylan

在 2013年10月1日星期二UTC+8上午11时46分21秒,luizcfs写道:

Dylan,

Given your extra information about the variables, I can’t think anything different from your initial
formulation

regards,
Luiz Carlos.


On Mon, Sep 30, 2013 at 4:38 AM, Dylan Lan wrote:

Hi Luiz,
Yes, both A(i) and B(j) are variables.
But A(i) - B(j) could be positive or negative.
Regards,
Dylan

在 2013年9月30日星期一UTC+8上午1时50分06秒,luizcfs写道:

Hi, Dylan

Are both A(i) and B(j) variables?
In an affirmative case, can one of them be an upper bound for the other?

Regards,
Luiz Carlos.


On Sun, Sep 29, 2013 at 6:23 AM, Dylan Lan wrote:

Hi GAMS wolrd,
I have a problem in reformulating equation constraints in a disjunctive model by Big-M reformulation.
When reformulating equations constraints, the only way I know is to introduce two inequalities. for example:
A(i) = B(j) reformulated as:

A(i) - B(j) =l= M*( 1-x(i,j) ) ;
B(j) - A(i) =l= M*( 1-x(i,j) ) ;
sum( i$(ord(i)<=I), x(i,j) ) =e= 1 ;

where x is binary variable.
Is there any way to reduce the number of equation and inequalities I have to use in Big-M reformulation?
Regards,
Dylan


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