topic Re: "Infeasible or Unbounded" Solution. What am i doing wrong? in Mathematical Optimization, Discrete-Event Simulation, and OR

"Infeasible or Unbounded" Solution. What am i doing wrong?

usamasm10 — Tue, 09 Oct 2018 15:06:33 GMT

proc optmodel;

var xc1w1, xc1w2, xt1w1, xt1w2, xfw1, xfw2, xc2w1, xc2w2, xt2w1, xt2w2 >=0 integer;

var yc2 binary;
var yt2 binary;

maximize z=82*xc1w1+83*xc1w2+45*xt1w1+49*xt1w2+30*xfw1+35*xfw2+84*xc2w1+81*xc2w2+42*xt2w1+54*xt2w2+41000*yc2+21700*yt2;

con Demand1: xc1w1+xc2w1+xt1w1+xt2w1+xfw1=6000;
con Demand2: xc1w2+xc2w2+xt1w2+xt2w2+xfw2=5200;

con china1: xc1w1+xc1w2<=1500;
con china2: xc2w1+xc2w2<=2000;
con turkey1: xt1w1+xt1w2<=1800;
con turkey2: xt2w1+xt2w2<=2200;
con france: xfw1+xfw2<=6000;

con linkc2: xc2w1+xc2w2-2000*yc2<=0;
con linkt2: xt2w1+xt2w2-2200*yc2<=0;

con Fixc2: xc2w1+xc2w2<=1000000*yc2;
con Fixt2: xt2w1+xt2w2<=1000000*yt2;

con repurpose: yc2+yt2<=1;

solve;

print xc1w1 xc1w2 xt1w1 xt1w2 xfw1 xfw2 xc2w1 xc2w2 xt2w1 xt2w2 z;

quit;

Re: "Infeasible or Unbounded" Solution. What am i doing wrong?

ballardw — Tue, 09 Oct 2018 15:35:12 GMT

It mean that given the constraints you have provided there is no solution.

I would be strongly tempted to graph the constraint areas China2 LInkC2 and Fixc2 to see if one or more of those is actually redundant,

Re: "Infeasible or Unbounded" Solution. What am i doing wrong?

RobPratt — Tue, 09 Oct 2018 15:47:51 GMT

I suspect that you meant for all the x* variables to be >= 0 and integer, but your first VAR statement imposes those restrictions on only the last one. The log provides a hint:

NOTE: The problem has 12 variables (9 free, 0 fixed).
NOTE: The problem has 2 binary and 1 integer variables.

You can see the detail by using the EXPAND statement:

SAS Output

Var xc1w1                                                                                      
Var xc1w2                                                                                      
Var xt1w1                                                                                      
Var xt1w2                                                                                      
Var xfw1                                                                                       
Var xfw2                                                                                       
Var xc2w1                                                                                      
Var xc2w2                                                                                      
Var xt2w1                                                                                      
Var xt2w2 INTEGER >= 0                                                                         
Var yc2 BINARY                                                                                 
Var yt2 BINARY                                                                                 
Maximize z=82*xc1w1 + 83*xc1w2 + 45*xt1w1 + 49*xt1w2 + 30*xfw1 + 35*xfw2 + 84*xc2w1 + 81*xc2w2 
+ 42*xt2w1 + 54*xt2w2 + 41000*yc2 + 21700*yt2                                                  
Constraint Demand1: xc1w1 + xc2w1 + xt1w1 + xt2w1 + xfw1 = 6000                                
Constraint Demand2: xc1w2 + xc2w2 + xt1w2 + xt2w2 + xfw2 = 5200                                
Constraint china1: xc1w1 + xc1w2 <= 1500                                                       
Constraint china2: xc2w1 + xc2w2 <= 2000                                                       
Constraint turkey1: xt1w1 + xt1w2 <= 1800                                                      
Constraint turkey2: xt2w1 + xt2w2 <= 2200                                                      
Constraint france: xfw1 + xfw2 <= 6000                                                         
Constraint linkc2: xc2w1 + xc2w2 - 2000*yc2 <= 0                                               
Constraint linkt2: xt2w1 + xt2w2 - 2200*yc2 <= 0                                               
Constraint Fixc2: xc2w1 + xc2w2 - 1000000*yc2 <= 0                                             
Constraint Fixt2: xt2w1 + xt2w2 - 1000000*yt2 <= 0                                             
Constraint repurpose: yc2 + yt2 <= 1

The simplest fix is the following:

var xc1w1 >=0 integer, xc1w2 >=0 integer, xt1w1 >=0 integer, xt1w2 >=0 integer, xfw1 >=0 integer, xfw2 >=0 integer, xc2w1 >=0 integer, xc2w2 >=0 integer, xt2w1 >=0 integer, xt2w2 >=0 integer;

But your code would be more readable and less error-prone if you instead use index sets. For example, you could declare x as follows:

set ISET = /c1 t1 f c2 t2/;
set JSET = /w1 w2/;
var x {ISET, JSET} >=0 integer;

Also, arbitrarily large values like 1000000 tend to cause unnecessary numerical difficulty. In this case, you can just omit the Fix* constraints because they are implied by the link* constraints.

Re: "Infeasible or Unbounded" Solution. What am i doing wrong?

usamasm10 — Tue, 09 Oct 2018 15:48:20 GMT

It is a requirement to keep demand functions to be equalities.
As for the Fixc2 and Fixt2, only one of them can have a value

Re: "Infeasible or Unbounded" Solution. What am i doing wrong?

usamasm10 — Tue, 09 Oct 2018 17:49:02 GMT

I did not notice in that in the notes. That helped.

Thanks a lot 🙂