[Help-glpk] first model using GNU MathProg (a newbie question)

[Duilio Foschi]

I wrote my first model using GNU MathProg.

It is a set covering model and it should give me the best driver rostering
for a small bus line.

The bus line must "cover" M trips.

Using euristic methods, I have deviced N possible shifts. Each shift has a
cost, Ci (i=1..N).

Each shift covers some trips and does not covers others.

A binary matrix Aij has value 1 if shift i covers trip j, otherwise has
value 0.

I wrote:

set S;
/* shifts */

set T;
/* trips */

param C{s in S};
/* cost of shift s */

param A{s in S, t in T}, binary;  
/* 1 if shift s covers trip T, 0 otherwise */

var X(s in S}, binary;
/* 1 if shift s is choosen, 0 otherwise */

minimize cost: sum{s in S} C[s]*X[s];
/* total cost */

s.t. covers{t in T}: sum{s in S} A[s,t]*X[s]>=1;

data;

set S := one two three four five;

set T := A B C D E F G;

param C :=      one   100
                two   200
                three 300
                four  400
              five  400 ;

data;

set S := one two three four five;

set T := A B C D E F G;

param C :=      one   100
                two   200
                three 300
                four  400
              five  400 ;

param A :         A B C D E F G     :=
                      one   1 1 1 1 0 1 1
                      two   1 0 1 0 0 0 0
                      three 0 1 1 0 1 0 0
                      four  1 1 1 0 1 1 0
                      five  0 1 0 0 1 1 1  ;

end;

I was overjoyed to see that my model was happily compiled and run by GLPSOL
and the expected result (i.e. 400) given.

But how can I get what I want most, i.e. the X values that provided the
optimal result ?

In this sample code, it is easy to see that only shift "one" and "three"
were used, but in the real case, the shifts will be thousands...

Thank you

Duilio Foschi