Choosing columns so that sum(rows) are equal 1

GAMS
1

Hello,

i got a table b(i,j) which looks like that:
j1 j2 j3 j4 j5 j6 j7 j8 j9
i1 1 0 0 1 0 0 0 1 1
i2 0 1 1 0 0 0 1 0 0
i3 0 1 0 0 1 0 0 0 1
i4 1 0 0 0 0 1 0 0 1
i5 0 0 0 0 0 0 1 1 1
i6 0 0 1 1 0 1 0 0 0

and i got a function F for costs that need to be minimized …
Now i want a restriction that says the sum of each row is exactly 1 and the model shall tell me which j’s are to be used.

I wrote a script in which everything works except for this restriction. The restriction is called NB… in the script. I am pretty sure I need an alias in some way but i cannot get it run without errors … would be very thankful for any help!


Here’s the script:

$title Bonusaufgabe

Sets
i Altersgruppen /i1i6/
j Medientypen /j1j9/;
alias(i,t)
;

Parameter
r(j) Kosten fuer j /j1 20000, j2 45000, j3 60000, j4 45000, j5 30000, j6 55000, j7 52000, j8 60000, j9 105000/
a(i) Beschränkung jeder Altersgruppe i /i1 1, i2 1, i3 1, i4 1, i5 1, i6 1/
;

table b(i,j)
$include Altersgruppen.txt
;

Variables
ZF Zielfunktionswert
;

positive variables
x(j) gewählte Menge von Medientypen j
;

Equations
ZFkt1 Zielfunktion
NB Nebenbedingung
;

ZFkt1…
ZF =e= sum((j,i), r(j) * x(j));

NB…
sum(t$(ord(t)<=ord(i)), b(j,t)) =e= a(t);

model Bonusaufgabe /ZFkt1,NB/;
solve Bonusaufgabe minimizing ZF using LP;
display ZF.l;

2

you need to use mixed integer programming instead of linear programming

3

you need to use mixed integer programming instead of linear programming

Thank you for the hint, of course, but that doesn’t solve my problem with the restriction. I still got some errors. I think it’s a Syntax problem.

What do I need to change in the NB… to get it run? For now i have

NB..
         sum(t$(ord(t)<=ord(i)), a(t) * x(j)) =e= 1;

and the error says

— Starting compilation
— Bonusaufgabe.gms(18) 3 Mb
— .Altersgruppen.txt(7) 3 Mb
— Bonusaufgabe.gms(41) 3 Mb 2 Errors
*** Error 154 in \psf\Home\Downloads\Bonusaufgabe.gms
Set for ‘ord’ is not controlled
*** Error 149 in \psf\Home\Downloads\Bonusaufgabe.gms
Uncontrolled set entered as constant
— Bonusaufgabe.gms(44) 3 Mb 3 Errors
*** Error 257 in \psf\Home\Downloads\Bonusaufgabe.gms
Solve statement not checked because of previous errors
— Bonusaufgabe.gms(45) 3 Mb 4 Errors
*** Error 141 in \psf\Home\Downloads\Bonusaufgabe.gms
Symbol declared but no values have been assigned. Check for missing
data definition, assignment, data loading or implicit assignment
via a solve statement.
A wild shot: You may have spurious commas in the explanatory
text of a declaration. Check symbol reference list.
— Bonusaufgabe.gms(45) 3 Mb 4 Errors
*** Status: Compilation error(s)
— Job Bonusaufgabe.gms Stop 06/15/17 15:19:59 elapsed 0:00:00.044
Exit code = 2

4

You should define your constraint per user group (“Altersgruppe”):


Equations
ZFkt1 Zielfunktion
*NB Nebenbedingung
NB(i)
;

ZFkt1…
ZF =e= sum((j,i), r(j) * x(j));

*NB…
*sum(t$(ord(t)<=ord(i)), b(j,t)) =e= a(t);

NB(i)…
sum(j,b(i,j)*x(j))=e=1;

5

That works! Brilliant! Thank you so much :slight_smile: