A question about emp

Hi everybody,

I try to model multistage stochastic programming model. I get an error which is
=C*** emp.info line 1402: Unknown uel: i
=C*** emp.info line 1402: Cannot find (random) variable or equation p in model.
How can I solve this problem? I add model to attachment. I appreciate your help and time.

Thanks in advance,

Nazmi


Attachments-297/Untitled_1.gms

Nazmi,

This error is caused by the last three lines of your emp.info file:

stage 2 y(‘2’) d(‘2’) p(i,‘2’) s(‘2’) inv(‘2’) Bal_eq(‘2’) Sales_eq1(‘2’) Sales_eq2(‘2’)
stage 3 y(‘3’) d(‘3’) p(i,‘3’) s(‘3’) inv(‘3’) Bal_eq(‘3’) Sales_eq1(‘3’) Sales_eq2(‘3’)
stage 4 y(‘4’) d(‘4’) p(i,‘4’) s(‘4’) inv(‘4’) Bal_eq(‘4’) Sales_eq1(‘4’) Sales_eq2(‘4’)

You cannot use p(i,‘2’) here. You need to write out all possibilities. So you can replace your $onput … $offput section by this one:

put / “stage 1 y(‘1’) inv(‘1’) Bal_eq(‘1’)”;
put / "stage 2 y(‘2’) d(‘2’) “;
loop(i, put p.tn(i,‘2’) ’ ');
put " s(‘2’) inv(‘2’) Bal_eq(‘2’) Sales_eq1(‘2’) Sales_eq2(‘2’)”;
put / "stage 3 y(‘3’) d(‘3’) “;
loop(i, put p.tn(i,‘3’) ’ ');
put " s(‘3’) inv(‘3’) Bal_eq(‘3’) Sales_eq1(‘3’) Sales_eq2(‘3’)”;
put / "stage 4 y(‘4’) d(‘4’) “;
loop(i, put p.tn(i,‘4’) ’ ');
put " s(‘4’) inv(‘4’) Bal_eq(‘4’) Sales_eq1(‘4’) Sales_eq2(‘4’)”;

However, please note that there is a bigger issue with your model. As I can see it, you have 18 independent random variables, each with 1000 possible outcomes. This will result in 1000^18 scenarios which is just too big to be handled.
Is this really what you had in mind or did you actually want to have just 1000 scenarios? If this is the case, you should define your random variables as joint random variables instead of independent random variables. For more information please look for “jrandvar” in the “Stochastic Programming (SP) with EMP” documentation, which you can find in your installation folder or here:

http://www.gams.com/dd/docs/solvers/empsp/index.html

Best regards,
Lutz


On 1/30/2015 2:51 AM, Nazmi Åžener wrote:

Hi everybody,

I try to model multistage stochastic programming model. I get an error
which is
=C*** emp.info line 1402: Unknown uel: i
=C*** emp.info line 1402: Cannot find (random) variable or equation p in
model.
How can I solve this problem? I add model to attachment. I appreciate
your help and time.

Thanks in advance,

Nazmi


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Lutz Westermann LWestermann@gams.com
GAMS Development Corporation GAMS Software GmbH
1217 Potomac St. NW, P.O. Box 40 59
Washington DC, 20007, USA 50216 Frechen, Germany
Fon/Fax: +1 202 342-0180/1 Fon/Fax: +49 221 949-9170/1
http://www.gams.com


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Hi Nazmi,

In these lines, you should not put the set index along with the parameters, i.e., instead of writing p(i,‘2’) you should write p(‘1’,‘2’) or p, etc.

stage 2 y(‘2’) d(‘2’) p(i,‘2’) s(‘2’) inv(‘2’) Bal_eq(‘2’) Sales_eq1(‘2’) Sales_eq2(‘2’)
stage 3 y(‘3’) d(‘3’) p(i,‘2’) s(‘3’) inv(‘3’) Bal_eq(‘3’) Sales_eq1(‘3’) Sales_eq2(‘3’)
stage 4 y(‘4’) d(‘4’) p(i,‘2’) s(‘4’) inv(‘4’) Bal_eq(‘4’) Sales_eq1(‘4’) Sales_eq2(‘4’)

On Friday, January 30, 2015 at 8:54:03 AM UTC+1, Nazmi wrote:

Hi everybody,

I try to model multistage stochastic programming model. I get an error which is
=C*** emp.info line 1402: Unknown uel: i
=C*** emp.info line 1402: Cannot find (random) variable or equation p in model.
How can I solve this problem? I add model to attachment. I appreciate your help and time.

Thanks in advance,

Nazmi


To unsubscribe from this group and stop receiving emails from it, send an email to gamsworld+unsubscribe@googlegroups.com.
To post to this group, send email to gamsworld@googlegroups.com.
Visit this group at http://groups.google.com/group/gamsworld.
For more options, visit https://groups.google.com/d/optout.

Hi Lutz,

Thanks for your quick response. I only want to try more than one indice random variables in MSSP. Scenario number isn’t important. I tried your solution but I got these errors which is listed below.


*** Identifier or number expected, saw Ch = / Id = “”
*** Error processing empinfo file
*** Problem in getObjects
*** Failure calling solver: DE (rc=1)

Best Regards,
Nazmi

Date: Fri, 30 Jan 2015 03:40:17 -0500
From: lwestermann@gams.com
To: gamsworld@googlegroups.com
Subject: Re: A question about emp

Nazmi,

This error is caused by the last three lines of your emp.info file:

stage 2 y(‘2’) d(‘2’) p(i,‘2’) s(‘2’) inv(‘2’) Bal_eq(‘2’)
Sales_eq1(‘2’) Sales_eq2(‘2’)
stage 3 y(‘3’) d(‘3’) p(i,‘3’) s(‘3’) inv(‘3’) Bal_eq(‘3’)
Sales_eq1(‘3’) Sales_eq2(‘3’)
stage 4 y(‘4’) d(‘4’) p(i,‘4’) s(‘4’) inv(‘4’) Bal_eq(‘4’)
Sales_eq1(‘4’) Sales_eq2(‘4’)

You cannot use p(i,‘2’) here. You need to write out all possibilities.
So you can replace your $onput … $offput section by this one:

put / “stage 1 y(‘1’) inv(‘1’) Bal_eq(‘1’)”;
put / "stage 2 y(‘2’) d(‘2’) “;
loop(i, put p.tn(i,‘2’) ’ ');
put " s(‘2’) inv(‘2’) Bal_eq(‘2’) Sales_eq1(‘2’) Sales_eq2(‘2’)”;
put / "stage 3 y(‘3’) d(‘3’) “;
loop(i, put p.tn(i,‘3’) ’ ');
put " s(‘3’) inv(‘3’) Bal_eq(‘3’) Sales_eq1(‘3’) Sales_eq2(‘3’)”;
put / "stage 4 y(‘4’) d(‘4’) “;
loop(i, put p.tn(i,‘4’) ’ ');
put " s(‘4’) inv(‘4’) Bal_eq(‘4’) Sales_eq1(‘4’) Sales_eq2(‘4’)”;

However, please note that there is a bigger issue with your model. As I
can see it, you have 18 independent random variables, each with 1000
possible outcomes. This will result in 1000^18 scenarios which is just
too big to be handled.
Is this really what you had in mind or did you actually want to have
just 1000 scenarios? If this is the case, you should define your random
variables as joint random variables instead of independent random
variables. For more information please look for “jrandvar” in the
“Stochastic Programming (SP) with EMP” documentation, which you can find
in your installation folder or here:

http://www.gams.com/dd/docs/solvers/empsp/index.html

Best regards,
Lutz

On 1/30/2015 2:51 AM, Nazmi Åžener wrote:

Hi everybody,

I try to model multistage stochastic programming model. I get an error
which is
=C*** emp.info line 1402: Unknown uel: i
=C*** emp.info line 1402: Cannot find (random) variable or equation p in
model.
How can I solve this problem? I add model to attachment. I appreciate
your help and time.

Thanks in advance,

Nazmi


You received this message because you are subscribed to the Google
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Lutz Westermann LWestermann@gams.com
GAMS Development Corporation GAMS Software GmbH
1217 Potomac St. NW, P.O. Box 40 59
Washington DC, 20007, USA 50216 Frechen, Germany
Fon/Fax: +1 202 342-0180/1 Fon/Fax: +49 221 949-9170/1
http://www.gams.com


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Nazmi,

To be sure that we both ran the same thing, I attached the complete modified version of your model. That runs for me without the error you described (but gives an error saying that the scenario tree is too big). If you still see “your error” with this file, the reason might be an old GAMS version? I ran the most recent one (GAMS 24.4.1, http://www.gams.com/download/ ).

Best regards,
Lutz


On 1/30/2015 4:41 AM, Nazmi Åžener wrote:

Hi Lutz,

Thanks for your quick response. I only want to try more than one indice
random variables in MSSP. Scenario number isn’t important. I tried your
solution but I got these errors which is listed below.

*** Identifier or number expected, saw Ch = / Id = “”
*** Error processing empinfo file
*** Problem in getObjects
*** Failure calling solver: DE (rc=1)

Best Regards,
Nazmi

Date: Fri, 30 Jan 2015 03:40:17 -0500
From: lwestermann@gams.com
To: gamsworld@googlegroups.com
Subject: Re: A question about emp

Nazmi,

This error is caused by the last three lines of your emp.info file:

stage 2 y(‘2’) d(‘2’) p(i,‘2’) s(‘2’) inv(‘2’) Bal_eq(‘2’)
Sales_eq1(‘2’) Sales_eq2(‘2’)
stage 3 y(‘3’) d(‘3’) p(i,‘3’) s(‘3’) inv(‘3’) Bal_eq(‘3’)
Sales_eq1(‘3’) Sales_eq2(‘3’)
stage 4 y(‘4’) d(‘4’) p(i,‘4’) s(‘4’) inv(‘4’) Bal_eq(‘4’)
Sales_eq1(‘4’) Sales_eq2(‘4’)

You cannot use p(i,‘2’) here. You need to write out all possibilities.
So you can replace your $onput … $offput section by this one:

put / “stage 1 y(‘1’) inv(‘1’) Bal_eq(‘1’)”;
put / "stage 2 y(‘2’) d(‘2’) “;
loop(i, put p.tn(i,‘2’) ’ ');
put " s(‘2’) inv(‘2’) Bal_eq(‘2’) Sales_eq1(‘2’) Sales_eq2(‘2’)”;
put / "stage 3 y(‘3’) d(‘3’) “;
loop(i, put p.tn(i,‘3’) ’ ');
put " s(‘3’) inv(‘3’) Bal_eq(‘3’) Sales_eq1(‘3’) Sales_eq2(‘3’)”;
put / "stage 4 y(‘4’) d(‘4’) “;
loop(i, put p.tn(i,‘4’) ’ ');
put " s(‘4’) inv(‘4’) Bal_eq(‘4’) Sales_eq1(‘4’) Sales_eq2(‘4’)”;

However, please note that there is a bigger issue with your model. As I
can see it, you have 18 independent random variables, each with 1000
possible outcomes. This will result in 1000^18 scenarios which is just
too big to be handled.
Is this really what you had in mind or did you actually want to have
just 1000 scenarios? If this is the case, you should define your random
variables as joint random variables instead of independent random
variables. For more information please look for “jrandvar” in the
“Stochastic Programming (SP) with EMP” documentation, which you can find
in your installation folder or here:

http://www.gams.com/dd/docs/solvers/empsp/index.html

Best regards,
Lutz

On 1/30/2015 2:51 AM, Nazmi Åžener wrote:

Hi everybody,

I try to model multistage stochastic programming model. I get an error
which is
=C*** emp.info line 1402: Unknown uel: i
=C*** emp.info line 1402: Cannot find (random) variable or equation
p in
model.
How can I solve this problem? I add model to attachment. I appreciate
your help and time.

Thanks in advance,

Nazmi


You received this message because you are subscribed to the Google
Groups “gamsworld” group.
To unsubscribe from this group and stop receiving emails from it, send
an email to gamsworld+unsubscribe@googlegroups.com
.
To post to this group, send email to gamsworld@googlegroups.com
.
Visit this group at http://groups.google.com/group/gamsworld.
For more options, visit https://groups.google.com/d/optout.


Lutz Westermann LWestermann@gams.com
GAMS Development Corporation GAMS Software GmbH
1217 Potomac St. NW, P.O. Box 40 59
Washington DC, 20007, USA 50216 Frechen, Germany
Fon/Fax: +1 202 342-0180/1 Fon/Fax: +49 221 949-9170/1
http://www.gams.com


You received this message because you are subscribed to the Google
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For more options, visit https://groups.google.com/d/optout.



Lutz Westermann LWestermann@gams.com
GAMS Development Corporation GAMS Software GmbH
1217 Potomac St. NW, P.O. Box 40 59
Washington DC, 20007, USA 50216 Frechen, Germany
Fon/Fax: +1 202 342-0180/1 Fon/Fax: +49 221 949-9170/1
http://www.gams.com


Untitled_1.gms (2.44 KB)

Lutz,

Thanks for your quick response and kindness. I apologize for my rudeness. I explained myself with wrong words. The problem is that I copied without a punctuation. I run the model and I got same error with you. I use 24.1.3 version of gams because my license does not allow newer version from this version.

Date: Fri, 30 Jan 2015 05:08:13 -0500
From: lwestermann@gams.com
To: gamsworld@googlegroups.com
Subject: Re: A question about emp

Nazmi,

To be sure that we both ran the same thing, I attached the complete
modified version of your model. That runs for me without the error you
described (but gives an error saying that the scenario tree is too big).
If you still see “your error” with this file, the reason might be an old
GAMS version? I ran the most recent one (GAMS 24.4.1,
http://www.gams.com/download/ ).

Best regards,
Lutz

On 1/30/2015 4:41 AM, Nazmi Åžener wrote:

Hi Lutz,

Thanks for your quick response. I only want to try more than one indice
random variables in MSSP. Scenario number isn’t important. I tried your
solution but I got these errors which is listed below.

*** Identifier or number expected, saw Ch = / Id = “”
*** Error processing empinfo file
*** Problem in getObjects
*** Failure calling solver: DE (rc=1)

Best Regards,
Nazmi

Date: Fri, 30 Jan 2015 03:40:17 -0500
From: lwestermann@gams.com
To: gamsworld@googlegroups.com
Subject: Re: A question about emp

Nazmi,

This error is caused by the last three lines of your emp.info file:

stage 2 y(‘2’) d(‘2’) p(i,‘2’) s(‘2’) inv(‘2’) Bal_eq(‘2’)
Sales_eq1(‘2’) Sales_eq2(‘2’)
stage 3 y(‘3’) d(‘3’) p(i,‘3’) s(‘3’) inv(‘3’) Bal_eq(‘3’)
Sales_eq1(‘3’) Sales_eq2(‘3’)
stage 4 y(‘4’) d(‘4’) p(i,‘4’) s(‘4’) inv(‘4’) Bal_eq(‘4’)
Sales_eq1(‘4’) Sales_eq2(‘4’)

You cannot use p(i,‘2’) here. You need to write out all possibilities.
So you can replace your $onput … $offput section by this one:

put / “stage 1 y(‘1’) inv(‘1’) Bal_eq(‘1’)”;
put / "stage 2 y(‘2’) d(‘2’) “;
loop(i, put p.tn(i,‘2’) ’ ');
put " s(‘2’) inv(‘2’) Bal_eq(‘2’) Sales_eq1(‘2’) Sales_eq2(‘2’)”;
put / "stage 3 y(‘3’) d(‘3’) “;
loop(i, put p.tn(i,‘3’) ’ ');
put " s(‘3’) inv(‘3’) Bal_eq(‘3’) Sales_eq1(‘3’) Sales_eq2(‘3’)”;
put / "stage 4 y(‘4’) d(‘4’) “;
loop(i, put p.tn(i,‘4’) ’ ');
put " s(‘4’) inv(‘4’) Bal_eq(‘4’) Sales_eq1(‘4’) Sales_eq2(‘4’)”;

However, please note that there is a bigger issue with your model. As I
can see it, you have 18 independent random variables, each with 1000
possible outcomes. This will result in 1000^18 scenarios which is just
too big to be handled.
Is this really what you had in mind or did you actually want to have
just 1000 scenarios? If this is the case, you should define your random
variables as joint random variables instead of independent random
variables. For more information please look for “jrandvar” in the
“Stochastic Programming (SP) with EMP” documentation, which you can find
in your installation folder or here:

http://www.gams.com/dd/docs/solvers/empsp/index.html

Best regards,
Lutz

On 1/30/2015 2:51 AM, Nazmi Åžener wrote:

Hi everybody,

I try to model multistage stochastic programming model. I get an error
which is
=C*** emp.info line 1402: Unknown uel: i
=C*** emp.info line 1402: Cannot find (random) variable or equation
p in
model.
How can I solve this problem? I add model to attachment. I appreciate
your help and time.

Thanks in advance,

Nazmi


You received this message because you are subscribed to the Google
Groups “gamsworld” group.
To unsubscribe from this group and stop receiving emails from it, send
an email to gamsworld+unsubscribe@googlegroups.com
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Visit this group at http://groups.google.com/group/gamsworld.
For more options, visit https://groups.google.com/d/optout.


Lutz Westermann LWestermann@gams.com
GAMS Development Corporation GAMS Software GmbH
1217 Potomac St. NW, P.O. Box 40 59
Washington DC, 20007, USA 50216 Frechen, Germany
Fon/Fax: +1 202 342-0180/1 Fon/Fax: +49 221 949-9170/1
http://www.gams.com


You received this message because you are subscribed to the Google
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For more options, visit https://groups.google.com/d/optout.


Lutz Westermann LWestermann@gams.com
GAMS Development Corporation GAMS Software GmbH
1217 Potomac St. NW, P.O. Box 40 59
Washington DC, 20007, USA 50216 Frechen, Germany
Fon/Fax: +1 202 342-0180/1 Fon/Fax: +49 221 949-9170/1
http://www.gams.com


To unsubscribe from this group and stop receiving emails from it, send an email to gamsworld+unsubscribe@googlegroups.com.
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Hello,
Please how can I access the emp.info file?
Thank you.
Tunde

On Friday, January 30, 2015 at 1:40:36 AM UTC-7, Lutz Westermann wrote:

Nazmi,

This error is caused by the last three lines of your emp.info file:

stage 2 y(‘2’) d(‘2’) p(i,‘2’) s(‘2’) inv(‘2’) Bal_eq(‘2’)
Sales_eq1(‘2’) Sales_eq2(‘2’)
stage 3 y(‘3’) d(‘3’) p(i,‘3’) s(‘3’) inv(‘3’) Bal_eq(‘3’)
Sales_eq1(‘3’) Sales_eq2(‘3’)
stage 4 y(‘4’) d(‘4’) p(i,‘4’) s(‘4’) inv(‘4’) Bal_eq(‘4’)
Sales_eq1(‘4’) Sales_eq2(‘4’)

You cannot use p(i,‘2’) here. You need to write out all possibilities.
So you can replace your $onput … $offput section by this one:

put / “stage 1 y(‘1’) inv(‘1’) Bal_eq(‘1’)”;
put / "stage 2 y(‘2’) d(‘2’) “;
loop(i, put p.tn(i,‘2’) ’ ');
put " s(‘2’) inv(‘2’) Bal_eq(‘2’) Sales_eq1(‘2’) Sales_eq2(‘2’)”;
put / "stage 3 y(‘3’) d(‘3’) “;
loop(i, put p.tn(i,‘3’) ’ ');
put " s(‘3’) inv(‘3’) Bal_eq(‘3’) Sales_eq1(‘3’) Sales_eq2(‘3’)”;
put / "stage 4 y(‘4’) d(‘4’) “;
loop(i, put p.tn(i,‘4’) ’ ');
put " s(‘4’) inv(‘4’) Bal_eq(‘4’) Sales_eq1(‘4’) Sales_eq2(‘4’)”;

However, please note that there is a bigger issue with your model. As I
can see it, you have 18 independent random variables, each with 1000
possible outcomes. This will result in 1000^18 scenarios which is just
too big to be handled.
Is this really what you had in mind or did you actually want to have
just 1000 scenarios? If this is the case, you should define your random
variables as joint random variables instead of independent random
variables. For more information please look for “jrandvar” in the
“Stochastic Programming (SP) with EMP” documentation, which you can find
in your installation folder or here:

http://www.gams.com/dd/docs/solvers/empsp/index.html

Best regards,
Lutz


On 1/30/2015 2:51 AM, Nazmi Åžener wrote:

Hi everybody,

I try to model multistage stochastic programming model. I get an error
which is
=C*** emp.info line 1402: Unknown uel: i
=C*** emp.info line 1402: Cannot find (random) variable or equation p in
model.
How can I solve this problem? I add model to attachment. I appreciate
your help and time.

Thanks in advance,

Nazmi


You received this message because you are subscribed to the Google
Groups “gamsworld” group.
To unsubscribe from this group and stop receiving emails from it, send
an email to gamsworld+...@googlegroups.com
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For more options, visit https://groups.google.com/d/optout.



Lutz Westermann LWest...@gams.com
GAMS Development Corporation GAMS Software GmbH
1217 Potomac St. NW, P.O. Box 40 59
Washington DC, 20007, USA 50216 Frechen, Germany
Fon/Fax: +1 202 342-0180/1 Fon/Fax: +49 221 949-9170/1
http://www.gams.com


To unsubscribe from this group and stop receiving emails from it, send an email to gamsworld+unsubscribe@googlegroups.com.
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Hi,

That is a file that you need to provide when solving a model of the type EMP. More info about the things you can write to it, when solving a stochastic problem, can be found in the documentation:

http://www.gams.com/help/index.jsp?topic=%2Fgams.doc%2Fuserguides%2Fuserguide%2F_u_g__e_m_p_s_p.html&anchor=EMPSP_SUMMARY_OF_KEYWORDS_AND_SOLVER_CONFIGURATIONS

There are also several examples in the GAMS EMP Library where such a file is created, e.g.

https://www.gams.com/emplib/libhtml/nbsimple.htm

Best regards,
Lutz



On 10/15/2015 1:01 PM, Babatunde Odetayo wrote:

Hello,
Please how can I access the emp.info
file?
Thank you.
Tunde

On Friday, January 30, 2015 at 1:40:36 AM UTC-7, Lutz Westermann wrote:

Nazmi,

This error is caused by the last three lines of your emp.info

file:

stage 2 y('2') d('2') p(i,'2') s('2') inv('2') Bal_eq('2')
Sales_eq1('2') Sales_eq2('2')
stage 3 y('3') d('3') p(i,'3') s('3') inv('3') Bal_eq('3')
Sales_eq1('3') Sales_eq2('3')
stage 4 y('4') d('4') p(i,'4') s('4') inv('4') Bal_eq('4')
Sales_eq1('4') Sales_eq2('4')

You cannot use p(i,'2') here. You need to write out all possibilities.
So you can replace your $onput ... $offput section by this one:

put / "stage 1 y('1') inv('1') Bal_eq('1')";
put / "stage 2 y('2') d('2') ";
loop(i, put p.tn (i,'2') ' ');
put   " s('2') inv('2') Bal_eq('2') Sales_eq1('2') Sales_eq2('2')";
put / "stage 3 y('3') d('3') ";
loop(i, put p.tn (i,'3') ' ');
put   " s('3') inv('3') Bal_eq('3') Sales_eq1('3') Sales_eq2('3')";
put / "stage 4 y('4') d('4') ";
loop(i, put p.tn (i,'4') ' ');
put   " s('4') inv('4') Bal_eq('4') Sales_eq1('4') Sales_eq2('4')";

However, please note that there is a bigger issue with your model. As I
can see it, you have 18 independent random variables, each with 1000
possible outcomes. This will result in 1000^18 scenarios which is just
too big to be handled.
Is this really what you had in mind or did you actually want to have
just 1000 scenarios? If this is the case, you should define your random
variables as joint random variables instead of independent random
variables. For more information please look for "jrandvar" in the
"Stochastic Programming (SP) with EMP" documentation, which you can
find
in your installation folder or here:

http://www.gams.com/dd/docs/solvers/empsp/index.html


Best regards,
Lutz


On 1/30/2015 2:51 AM, Nazmi Åžener wrote:
 > Hi everybody,
 >
 > I try to model multistage stochastic programming model. I get an
error
 > which is
 > =C*** emp.info  line 1402: Unknown uel: i
 > =C*** emp.info  line 1402: Cannot find (random)
variable or equation p in
 > model.
 > How can I solve this problem? I add model to attachment. I
appreciate
 > your help and time.
 >
 > Thanks in advance,
 >
 > Nazmi
 >
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--
Lutz Westermann LWest...@gams.com
GAMS Development Corporation          GAMS Software GmbH
1217 Potomac St. NW,                      P.O. Box 40 59
Washington DC, 20007, USA         50216 Frechen, Germany
Fon/Fax: +1 202 342-0180/1   Fon/Fax: +49 221 949-9170/1
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Lutz Westermann LWestermann@gams.com
GAMS Development Corporation GAMS Software GmbH
1217 Potomac St. NW, P.O. Box 40 59
Washington DC, 20007, USA 50216 Frechen, Germany
Fon/Fax: +1 202 342-0180/1 Fon/Fax: +49 221 949-9170/1
http://www.gams.com


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