Set Covering Problem

GAMS
1

Hello All,



I need help with the problem below, I think the problem is in the equation “AgebtoPtoEnc…”



I’ll be very gratefully if someone could help me.



Best Regards

Víctor Ortíz






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  • TITLE Set Covering;



    Set i / i1*i6 / ;

Set k / k1*k6 / ;



Table d(i,k)



k1 k2 k3 k4 k5 k6

i1 1 1 0 1 0 0

i2 1 1 1 0 0 0

i3 0 1 1 0 0 1

i4 1 0 0 1 1 0

i5 0 0 0 1 1 1

i6 0 0 1 0 1 1 ;



Binary Variable Y(k);



Variables

z “Set Covering”



Equation AgebtoPtoEnc , Def_obj ;



AgebtoPtoEnc…



sum(k, Y(k)*d[i,k)) =g= 1 ;



Def_obj…



z =e= sum(k, Y(k));



Model setcovering / all / ;



Solve setcovering using mip minimizing z;



Display z.l, y.l ;

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2

Dear Victor,

Your equation AgebtoPtoEnc is not unique and depends on the set i, so you need to declare and define the equation in the following way:

…
Equation AgebtoPtoEnc(i), Def_obj;

AgebtoPtoEnc(i)… sum(k, Y(k)*d(i,k)) =g= 1 ;
…


Cheers,
Pedro



On Sat, Feb 16, 2013 at 10:04 PM, Victor Ortiz wrote:

Hello All,



I need help with the problem below, I think the problem is in the equation “AgebtoPtoEnc…”



I’ll be very gratefully if someone could help me.



Best Regards

Víctor Ortíz






\

  • TITLE Set Covering;



    Set i / i1*i6 / ;

Set k / k1*k6 / ;



Table d(i,k)



k1 k2 k3 k4 k5 k6

i1 1 1 0 1 0 0

i2 1 1 1 0 0 0

i3 0 1 1 0 0 1

i4 1 0 0 1 1 0

i5 0 0 0 1 1 1

i6 0 0 1 0 1 1 ;



Binary Variable Y(k);



Variables

z “Set Covering”



Equation AgebtoPtoEnc , Def_obj ;



AgebtoPtoEnc…



sum(k, Y(k)*d[i,k)) =g= 1 ;



Def_obj…



z =e= sum(k, Y(k));



Model setcovering / all / ;



Solve setcovering using mip minimizing z;



Display z.l, y.l ;

–
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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

The correct model is as following:

  • TITLE Set Covering;
    Set i / i1i6 / ;
    Set k / k1    k6 / ;
    Table d(i,k)
    k1 k2 k3 k4 k5 k6
    i1 1 1 0 1 0 0
    i2 1 1 1 0 0 0
    i3 0 1 1 0 0 1
    i4 1 0 0 1 1 0
    i5 0 0 0 1 1 1
    i6 0 0 1 0 1 1 ;
    Binary Variable Y(k);
    Variables
    z “Set Covering”
    Equation AgebtoPtoEnc(i) , Def_obj ;
    AgebtoPtoEnc(i)…sum(k, Y(k)*d(i,k)) =g= 1 ;
    Def_obj…z =e= sum(k, Y(k));
    Model setcovering / all / ;
    Solve setcovering using mip minimizing z;
    Display z.l, y.l ;

On 2/17/13, Victor Ortiz wrote:

Hello All,

I need help with the problem below, I think the problem is in the equation
“AgebtoPtoEnc…”

I’ll be very gratefully if someone could help me.

Best Regards

Víctor Ortíz

  • TITLE Set Covering;

Set i / i1*i6 / ;

Set k / k1*k6 / ;

Table d(i,k)

     k1       k2       k3       k4       k5       k6

i1 1 1 0 1 0 0

i2 1 1 1 0 0 0

i3 0 1 1 0 0 1

i4 1 0 0 1 1 0

i5 0 0 0 1 1 1

i6 0 0 1 0 1 1 ;

Binary Variable Y(k);

Variables

     z "Set Covering"

Equation AgebtoPtoEnc , Def_obj ;

AgebtoPtoEnc…

sum(k, Y(k)*d[i,k)) =g= 1 ;

Def_obj…

z =e= sum(k, Y(k));

Model setcovering / all / ;

Solve setcovering using mip minimizing z;

Display z.l, y.l ;

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4

Thank you Hossein Karim, Pedro Ramirez and Jose Quezada

The model is working correctly

Best regards
Víctor Ortíz

-----Mensaje original-----
De: gamsworld@googlegroups.com [mailto:gamsworld@googlegroups.com] En nombre
de hossein karimi
Enviado el: domingo, 17 de febrero de 2013 01:11 a.m.
Para: gamsworld@googlegroups.com
Asunto: Re: Set Covering Problem

The correct model is as following:

  • TITLE Set Covering;
    Set i / i1i6 / ;
    Set k / k1    k6 / ;
    Table d(i,k)
    k1 k2 k3 k4 k5 k6
    i1 1 1 0 1 0 0
    i2 1 1 1 0 0 0
    i3 0 1 1 0 0 1
    i4 1 0 0 1 1 0
    i5 0 0 0 1 1 1
    i6 0 0 1 0 1 1 ;
    Binary Variable Y(k);
    Variables
    z “Set Covering”
    Equation AgebtoPtoEnc(i) , Def_obj ;
    AgebtoPtoEnc(i)…sum(k, Y(k)*d(i,k)) =g= 1 ; Def_obj…z =e= sum(k, Y(k));
    Model setcovering / all / ; Solve setcovering using mip minimizing z;
    Display z.l, y.l ;

On 2/17/13, Victor Ortiz wrote:

Hello All,

I need help with the problem below, I think the problem is in the
equation “AgebtoPtoEnc…”

I’ll be very gratefully if someone could help me.

Best Regards

Víctor Ortíz

  • TITLE Set Covering;

Set i / i1*i6 / ;

Set k / k1*k6 / ;

Table d(i,k)

     k1       k2       k3       k4       k5       k6

i1 1 1 0 1 0 0

i2 1 1 1 0 0 0

i3 0 1 1 0 0 1

i4 1 0 0 1 1 0

i5 0 0 0 1 1 1

i6 0 0 1 0 1 1 ;

Binary Variable Y(k);

Variables

     z "Set Covering"

Equation AgebtoPtoEnc , Def_obj ;

AgebtoPtoEnc…

sum(k, Y(k)*d[i,k)) =g= 1 ;

Def_obj…

z =e= sum(k, Y(k));

Model setcovering / all / ;

Solve setcovering using mip minimizing z;

Display z.l, y.l ;

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5

Hello I am learning Gams and ı need help about this topic.
I dont know the “Equation AgebtoPtoEnc” code.
What is it used for?