Matching problems with generalized upper bound side constraints

In this article, we develop and compare procedures for the approximate solution of weighted nonbipartite matching problems with generalized upper bound side constraints. The approaches we consider are all based on Lagrangean relaxation and dual ascent. We also use a knapsack-based procedure for finding improved feasible solutions and a “k-best” solution enumeration procedure to guarantee optimality. Our computational experiments addressed two issues: the choice of the best combination of a matching code and postoptimality routine and the choice of a dual ascent rule. Our recommended combination of procedures consistently produced solutions with a very small deviation from optimality without having to resort to the enumeration procedure.