Abstract
This paper presents an approximation method for obtaining a feasible solution of a very large-scale assignment problem with priority order. The proposed method is applicable to assignment problems whose cost coefficients cannot clearly be determined. In the method, a feasible solution is rapidly found without considering priority order, and then resources are arranged to take priority order into consideration. This causes nonzero value of the sum of infeasibilities. Hence, the following three steps are iteratively carried out to decrease the sum monotonically;
(i) a set of integer variables to be changed is chosen by means of search trees,
(ii) the trees are modified after the integer variables are changed, and
(iii) the assignment is altered so that the number of deleted arcs is as small as possible.
If the sum results in zero, resources are rearranged to satisfy higher priority order. The above procedure is repeatedly performed until the sum doesn't become zero furthermore. The method has proved to be efficient as a result of applying it to very large-scale assignment problems, especially which have exceedingly large infeasibility amounts.
