Reduction in problem size for ranking alternatives in group decision- making (Q1088864)

We examine the problem of finding a group ranking of alternatives, based on the rankings of several raters, that minimizes the number of reversals with respect to the raters' rankings. We characterize the possible structure of an optimal solution. This leads to a graph-theoretical method that pre-orders the alternatives, thereby sub-dividing the problem into problems of smaller sizes. The smaller size problems can then be solved using either branch and bound techniques or existing heuristics. Applications to complete and incomplete rankings are presented.