equation with positive variable either equal to 0 or above 4

GAMS
1

Hi everybody,
i’m sorry to bother you. I have a question about my GAMS model. I would like to add a constraint in a farming model. Basically farmer has to allocate crops to area. I would like for a specific crop to add a constraint such as "if the farmer want to cultivate this crop he cannot grow less than 4 ha otherwise he cannot grow it.
I don’ know how to write this down…may be somebody could give me an hand ? I tried this:

Eq1… X(“crop”) * BV =e= 0 ;
Eq2… X(“crop”) =g= 4 * (1-BV);

BV is a binary variable.

But it didn’t work.

Thank you in advance for your help.

Regards.

Pc

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2

Pcho:



Search for ”Semi-continuous Variable”



Arne


\

Arne Stolbjerg Drud

ARKI Consulting & Development A/S

Bagsvaerdvej 246A, DK-2880 Bagsvaerd, Denmark

Phone: (+45) 44 49 03 23, Fax: (+45) 44 49 03 33, email: adrud@arki.dk



From: gamsworld@googlegroups.com [mailto:gamsworld@googlegroups.com] On Behalf Of pcho
Sent: Wednesday, November 27, 2013 3:07 PM
To: gamsworld@googlegroups.com
Subject: equation with positive variable either equal to 0 or above 4



Hi everybody,

i’m sorry to bother you. I have a question about my GAMS model. I would like to add a constraint in a farming model. Basically farmer has to allocate crops to area. I would like for a specific crop to add a constraint such as "if the farmer want to cultivate this crop he cannot grow less than 4 ha otherwise he cannot grow it.

I don’ know how to write this down…may be somebody could give me an hand ? I tried this:



Eq1… X(“crop”) * BV =e= 0 ;

Eq2… X(“crop”) =g= 4 * (1-BV);



BV is a binary variable.



But it didn’t work.



Thank you in advance for your help.



Regards.



Pc

–
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3

Hi pcho,

I believe this will work:

Eq2… X(“crop”) =g= 4 * BV;

That is: given that he is producing, BV=1, then X (‘crop’) is greater than 4.



Yonas



From: gamsworld@googlegroups.com [mailto:gamsworld@googlegroups.com] On Behalf Of pcho
Sent: 27. november 2013 15:07
To: gamsworld@googlegroups.com
Subject: equation with positive variable either equal to 0 or above 4



Hi everybody,

i’m sorry to bother you. I have a question about my GAMS model. I would like to add a constraint in a farming model. Basically farmer has to allocate crops to area. I would like for a specific crop to add a constraint such as "if the farmer want to cultivate this crop he cannot grow less than 4 ha otherwise he cannot grow it.

I don’ know how to write this down…may be somebody could give me an hand ? I tried this:



Eq1… X(“crop”) * BV =e= 0 ;

Eq2… X(“crop”) =g= 4 * (1-BV);



BV is a binary variable.



But it didn’t work.



Thank you in advance for your help.



Regards.



Pc

–
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4

Hi Pc,

You can try big-M Reformulation:

Eq1… X(“crop”) =l= M*(1-BV) ;
Eq2… -X(“crop”) =l= M*(1-BV) ;
Eq3… X(“crop”) - 4 =l= M * (1-BV) ;
Eq4… 4 - X(“crop”) =l= M * (1-BV) ;

where M is sufficiently large parameter.

Regards,
Dylan

在 2013年11月27日星期三UTC+8下午10时07分06秒，pcho写道：

Hi everybody,
i’m sorry to bother you. I have a question about my GAMS model. I would like to add a constraint in a farming model. Basically farmer has to allocate crops to area. I would like for a specific crop to add a constraint such as "if the farmer want to cultivate this crop he cannot grow less than 4 ha otherwise he cannot grow it.
I don’ know how to write this down…may be somebody could give me an hand ? I tried this:

Eq1… X(“crop”) * BV =e= 0 ;
Eq2… X(“crop”) =g= 4 * (1-BV);

BV is a binary variable.

But it didn’t work.

Thank you in advance for your help.

Regards.

Pc

–
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5

Pc,

Sorry for my mistake, the formulation should be:

Eq1 … X(“crop”) =l= MBV ;
Eq2… -X(“crop”) =l= MBV ;
Eq3… 4 - X(“crop”) =l= M*(1-BV) ;

If BV=1 that the farmer plants the crop, X(“crop”)>=4, otherwise X(“crop”)=0. This reformulation helps to linearize the model that is easier to be solved.

Regards,
Dylan

在 2013年11月27日星期三UTC+8下午10时07分06秒，pcho写道：

Hi everybody,
i’m sorry to bother you. I have a question about my GAMS model. I would like to add a constraint in a farming model. Basically farmer has to allocate crops to area. I would like for a specific crop to add a constraint such as "if the farmer want to cultivate this crop he cannot grow less than 4 ha otherwise he cannot grow it.
I don’ know how to write this down…may be somebody could give me an hand ? I tried this:

Eq1… X(“crop”) * BV =e= 0 ;
Eq2… X(“crop”) =g= 4 * (1-BV);

BV is a binary variable.

But it didn’t work.

Thank you in advance for your help.

Regards.

Pc

–
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6

Use this

X(“crop”) =L=4+BV *1000;
X(“crop”) =G=4+(BV-1) *1000;

So if there is no selection BV =0, then
first equation will be X(“crop”) =L=4
while secound will be X(“crop”) =G=4-10000,

And if BV =1 then
X(“crop”) =L=1004
X(“crop”) =G=4

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