Minor modifications of the basic problem structure
are easily handled with the standard solution
procedures. A problem in which the objective function is to be maximized can be easily converted
into a minimization problem by either (a)
multiplying all of the cijs by 1, or (b) replacing
each cij by cmax cij, where cmax is the maximum
of the cijs, thus converting the problem to one of
minimizing ‘‘regret’’. A problem that is not balanced
(i.e., one for which the numbers of tasks
and agents differ) can be easily converted into a
balanced problem by adding a sufficient number
of ‘‘dummy’’ tasks or agents (whichever is in
shorter supply) with costs of 0. One may also use
non-zero costs for assignments using dummy tasks
or agents to reflect differences based on which
agents or tasks are not assigned.