It would be more clear if you tell, what you want to do instead of what you do not want to do.
If you start with a usual cost matrix (whatever cost function you have) and you have to assign N to N this reduces to the well-known Munkre’s algorithm (see for example: http://gallery.rcpp.org/articles/minimal-assignment/). If you have to assign M to N, it is an extended version of the Munkre’s algorithm which has been covered by Bourgeois and Lassalle (1971). All this is graph theory. Best Simon On 14 Nov 2013, at 19:24, Jean-Francois Chevalier <jean-francois.cheval...@bisnode.com> wrote: > Hello, > I'm trying to solve a multiple assignment problem. > I found a package Adagio and its function mknapsack which > > maximize vstar = p(1)*(x(1,1) + ... + x(m,1)) + ... ... + p(n)*(x(1,n) + ... > + x(m,n)) > > subject to w(1)*x(i,1) + ... + w(n)*x(i,n) <= k(i) for i=1,...,m > > x(1,j) + ... + x(m,j) <= 1 for j=1,...,n x(i,j) = 0 or 1 for i=1,...,m , > j=1,...,n , > It's close to what I'm trying to do except that > 1)k(i) = k for any I (not an issue) > 2)p is dependent of the item AND the knapsack > 3)each item must be assigned > > maximize vstar = p(1,1)*x(1,1) + ... + p(m,1)*x(m,1) + ... ... + > p(1,n)*x(1,n) + ... + p(m,n)*x(m,n) > > with p(j,i) profit of assigning item i to knapsack j > > subject to w(1)*x(i,1) + ... + w(n)*x(i,n) <= k for i=1,...,m > > x(1,j) + ... + x(m,j) = 1 for j=1,...,n x(i,j) = 0 or 1 for i=1,...,m , > j=1,...,n , > It would be really helpful if you could indicate me any package, function > that would solve my problem? > Thanks in advance, > Best regards, > > Jean-François > > > > **** DISCLAIMER ****\ "This e-mail and any attachments t...{{dropped:13}} > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
