### Highlights fromRectangular maximal assignment with lattice of dual price

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# Rectangular maximal assignment with lattice of dual price

13 Mar 2007 (Updated 13 Mar 2007)

Computes the maximal ractangular matching as well as the prices and surplus in both cases 1) rows bi

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Description

auction_match: Compute optimal (maximal) weighted assignment
% and the corresponding "lattice of dual prices" supporting the
% optimal assignment.
% auction_match(disMatrix) computes the optimal assignment for the
% given rectangular value matrix, for example the assignment
% of bidders (in rows) to objects (in columns) and vice versa.

% [assignment,r,p,u,v,value] = ASSIGNMENTOPTIMAL(DISTMATRIX) returns the assignment
% vector (in assignment) and the overall value (in value) and
% v: surplus of columns if columns were bidding for rows.
% u: the corresponding prices of rows.
% p: prices for columns if rows were bidding for columns
% r: the corresponding surplus of rows.
%

% Note that (p,-r) forms the lower corner and (v,-u) forms the
% upper corner in the lattice of optimal dual vector supporting
% the optimal assignment thus giving the complete lattice.
% Ref. the survey "From the Assignment Model to Combinatorial Auctions"
% by S. Bikhchandani and J. Ostroy

% This is update of the assignment code by Markus Buehren which used Munkres
% Algorithm for MINIMAL weighted matching. A description of Munkres algorithm
% (also called Hungarian algorithm) can easily be found on the web.

Acknowledgements

Functions For The Rectangular Assignment Problem inspired this file.

MATLAB release MATLAB 7 (R14)
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