Re: [Help-glpk] subspace problem

[address@hidden]

Hi Andrew,

Thank you very much for your detailed reply. I'd like to clarify a point 
regarding the "max" bit, please scroll down.

Andrew Makhorin wrote:
> > I want to understand the use of "max" in MathProg and how to specify
> > "coordinates" in MathProg. I have written a small example to try this out. 
> >     
>
>   
> > # author: Benson I.P. Hoi
> > # date: Tuesday 05 Feb 2008
> > # motivations: 
> > # 1. to test max works in MathProg and to check the syntax
> > # 2. to test whether the Pre-assignment set PRA works. 
> >     
>
>   
> > /* SETS */
> >     
>
>   
> > set TUTORS; # a list of tutors
> > set TUTEES; # a list of tutees
> > set ROOMS; # a list of rooms
> >     
>
>   
> > set PRA := {tutor in TUTORS, tutee in TUTEES, r in ROOMS}; # a list of
> > pre-assignments of (tutor, tutee, r), is this syntax correct?
> >     
>
>   
> > ### sample assignment
> >     
>
>   
> > /* VARIABLES */
> > var x {tutor in TUTORS, tutee in TUTEES, r in ROOMS}, binary >= 0; #
> > binary variables, 1 if the combination is assigned, 0 otherwise
> >     
>
> The condition '>= 0' is not needed, because 'binary' assumes that.
>
>   
> > /* OBJECTIVE FUNCTION */
> > maximize z: sum{tutor in TUTORS, tutee in TUTEES, r in ROOMS}   x[tutor, 
> > tutee,r]  ; # arbritary
> >     
>
>   
> > /* CONSTRAINTS */
> > ### all tutees have at most one tutor
> > s.t. uniqueTutor{tutee in TUTEES}: sum{tutor in TUTORS} (max{r in ROOMS} x[tutor, 
> > tutee, r])<=1;
> >     
>
>   
> > # what I want to say is to ignore whatever room has been assigned,
> > subspace as x[tutor, tutee] is what I want.. how I express that? Does "max"
> > do the trick? GLPK is complaining about syntax. Is there any other to
> > express this?
> >     
>
> You cannot use variables as operands of max, because this leads to
> non-linear constraints. Your constraint can be written as follows:
>
> s.t. uniqueTutor{tutee in TUTEES, r in ROOMS}:
>      sum{tutor in TUTORS} x[tutor, tutee, r] <= 1;
>   
I would like my constraint to capture the idea that a tutee can have at 
most one tutor, (regardless of the number of rooms which have been 
assigned), is there any possible way I have express the idea of x{tutee, 
tutor}, i.e. a subpace of x{tutee, tutor, room}, is there a linear way 
to do this?
(The constraint that you have specified does not capture this idea)
>   
> > ### pre-assignments to be taken into account
> > s.t. preassignment{(tutor, tutee,r) in PRA} x[tutor, tutee, r] =1;
> >     
>
>   
> > data;
> > set TUTORS := ar3 su2 mrc;
> > set TUTEES := iph04 sr104;
> > set ROOMS := ra rb rc;
> > set PRA := (ar3, iph04, ra) (su2, iph04, rb) (mrc, sr104, rc); 
> > # GLPK is complaining that PRA does not need data,why? 
> > # iph04 has 2 tutors, I want the MathProg to detect and report this.
> >     
>
> This is because you already specified an expression to compute PRA
> in the model section:
>
> set PRA := {tutor in TUTORS, tutee in TUTEES, r in ROOMS};
>
> which means that PRA is the cross product TUTORS x TUTEES x ROOMS.
> The correct declaration of PRA is the following:
>
> set PRA, dimen 3;
>
> or
>
> set PRA, in {tutor in TUTORS, tutee in TUTEES, r in ROOMS};
>
> if you want to check that all triplets specified in the data section
> are in TUTORS x TUTEES x ROOMS.
>
>   
> > end;
> >     
>  
>
>
>
>