Big M and Cplex

GAMS
1

Hi
I’m currently trying to run a simple VRPTW (with 30 nodes) gams code. it has Big M in one the equations as u can see:
eq7 (arc1(i,f),k)… s1(f,k)=g=s1(i,k) + t1(i,f) ;

The value of big M extremely effects the solver performance, for example when I set M, 100000000(9 zeros), gams couldnt find a feasible solution withing 3000secs. but a big M with 10 zeros, worked and I could get a feasible solution. the point is it seems this big M,doesnt work with all data sets. so what should I do???

I found this: http://www.gams.com/solvers/cpxindic.htm
so I changed my code to this one:

eq7(arc1(i,f),k)… s1(f,k)=g=s1(i,k) + t1(i,f);

model vrpcd /cost,eq2,eq3,eq4,eq52,eq7,eq8,eq8a,eq91/;
vrpcd.reslim= 3000 ;

option mip= cplex;

file fcpx Cplex Option file / cplex.opt /;
putclose fcpx ‘indic eq7(arc1(i,f),k)$x1(i,f,k) 1’ ;


vrpcd.OptFile = 1;

solve vrpcd using mip minimizing z;



but then I get this error:

Row ‘eq7(1.7.a)’ infeasible, all entries at implied bounds.
No solution exists.
problem is integer infeasible




can anyone help me with this plz?

–
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2

Hi
You should define big M like a parameter and it most be tight enough.
I suggest that you set the big M as sum((i,j),t(i,j)). It is the
summation of transportation time between all nodes.
Regards.
Hossein Karimi

On 10/18/12, Sarah shm wrote:

Hi
I’m currently trying to run a simple VRPTW (with 30 nodes) gams code. it
has Big M in one the equations as u can see:
eq7 (arc1(i,f),k)… s1(f,k)=g=s1(i,k) + t1(i,f) ;

The value of big M extremely effects the solver performance, for example
when I set M, 100000000(9 zeros), gams couldnt find a feasible solution
withing 3000secs. but a big M with 10 zeros, worked and I could get a
feasible solution. the point is it seems this big M,doesnt work with all
data sets. so what should I do???

I found this: http://www.gams.com/solvers/cpxindic.htm
so I changed my code to this one:

eq7(arc1(i,f),k)… s1(f,k)=g=s1(i,k) + t1(i,f);

model vrpcd /cost,eq2,eq3,eq4,eq52,eq7,eq8,eq8a,eq91/;
vrpcd.reslim= 3000 ;

option mip= cplex;

file fcpx Cplex Option file / cplex.opt /;
putclose fcpx ‘indic eq7(arc1(i,f),k)$x1(i,f,k) 1’ ;

vrpcd.OptFile = 1;

solve vrpcd using mip minimizing z;

but then I get this error:

Row ‘eq7(1.7.a)’ infeasible, all entries at implied bounds.
No solution exists.
problem is integer infeasible

can anyone help me with this plz?

–
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3

Thank you so much Hossein.
also the equation is this one: (I had forgotten to type the Big M part :smiley: )
eq7 (arc1(i,f),k)… s1(f,k)=g=s1(i,k) + t1(i,f)-M*(1-x1(i,f,k))

I’m gonna try ur idea now.
Do u know if it’s ok for CPLEX/GAMS to run the VRPTW code with 30 nodes for about 2000 seconds and still doesnt guarantee that the solution is optimal?
Thanks

On Saturday, October 20, 2012 9:50:58 AM UTC-7, hossein karimi wrote:

Hi
You should define big M like a parameter and it most be tight enough.
I suggest that you set the big M as sum((i,j),t(i,j)). It is the
summation of transportation time between all nodes.
Regards.
Hossein Karimi

On 10/18/12, Sarah shm wrote:

Hi
I’m currently trying to run a simple VRPTW (with 30 nodes) gams code. it
has Big M in one the equations as u can see:
eq7 (arc1(i,f),k)… s1(f,k)=g=s1(i,k) + t1(i,f) ;

The value of big M extremely effects the solver performance, for example
when I set M, 100000000(9 zeros), gams couldnt find a feasible solution
withing 3000secs. but a big M with 10 zeros, worked and I could get a
feasible solution. the point is it seems this big M,doesnt work with all
data sets. so what should I do???

I found this: http://www.gams.com/solvers/cpxindic.htm
so I changed my code to this one:

eq7(arc1(i,f),k)… s1(f,k)=g=s1(i,k) + t1(i,f);

model vrpcd /cost,eq2,eq3,eq4,eq52,eq7,eq8,eq8a,eq91/;
vrpcd.reslim= 3000 ;

option mip= cplex;

file fcpx Cplex Option file / cplex.opt /;
putclose fcpx ‘indic eq7(arc1(i,f),k)$x1(i,f,k) 1’ ;

vrpcd.OptFile = 1;

solve vrpcd using mip minimizing z;

but then I get this error:

Row ‘eq7(1.7.a)’ infeasible, all entries at implied bounds.
No solution exists.
problem is integer infeasible

can anyone help me with this plz?

–
“gamsworld” group.
To view this discussion on the web visit
https://groups.google.com/d/msg/gamsworld/-/3wN8mruktu8J.
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–
To view this discussion on the web visit https://groups.google.com/d/msg/gamsworld/-/jCzdn46honEJ.
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4

The answer depends on the data-set. Moreover, it relies on the model
complexity. I don’t know the precise answer of your question.

On 10/23/12, Sarah shm wrote:

Thank you so much Hossein.
also the equation is this one: (I had forgotten to type the Big M part :smiley: )
eq7 (arc1(i,f),k)… s1(f,k)=g=s1(i,k) + t1(i,f)-M*(1-x1(i,f,k))

I’m gonna try ur idea now.
Do u know if it’s ok for CPLEX/GAMS to run the VRPTW code with 30 nodes for

about 2000 seconds and still doesnt guarantee that the solution is optimal?
Thanks

On Saturday, October 20, 2012 9:50:58 AM UTC-7, hossein karimi wrote:

Hi
You should define big M like a parameter and it most be tight enough.
I suggest that you set the big M as sum((i,j),t(i,j)). It is the
summation of transportation time between all nodes.
Regards.
Hossein Karimi

On 10/18/12, Sarah shm > wrote:

Hi
I’m currently trying to run a simple VRPTW (with 30 nodes) gams code. it

has Big M in one the equations as u can see:
eq7 (arc1(i,f),k)… s1(f,k)=g=s1(i,k) + t1(i,f) ;

The value of big M extremely effects the solver performance, for example

when I set M, 100000000(9 zeros), gams couldnt find a feasible solution

withing 3000secs. but a big M with 10 zeros, worked and I could get a
feasible solution. the point is it seems this big M,doesnt work with all

data sets. so what should I do???

I found this: http://www.gams.com/solvers/cpxindic.htm
so I changed my code to this one:

eq7(arc1(i,f),k)… s1(f,k)=g=s1(i,k) + t1(i,f);

model vrpcd /cost,eq2,eq3,eq4,eq52,eq7,eq8,eq8a,eq91/;
vrpcd.reslim= 3000 ;

option mip= cplex;

file fcpx Cplex Option file / cplex.opt /;
putclose fcpx ‘indic eq7(arc1(i,f),k)$x1(i,f,k) 1’ ;

vrpcd.OptFile = 1;

solve vrpcd using mip minimizing z;

but then I get this error:

Row ‘eq7(1.7.a)’ infeasible, all entries at implied bounds.
No solution exists.
problem is integer infeasible

can anyone help me with this plz?

–
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