Weighted matching with vertex weights: An application to scheduling training sessions in NASA space shuttle cockpit simulators

Necessary and sufficient conditions are provided for optimality of a matching in a weighted matching problem for which the weight of edge (i,j) is the sum of non-negative values, wi and wj. The impact of adding one or more dummy vertices i with wi=0 is investigated. Results are exploited in the design of a heuristic approach for weekly scheduling of NASA space shuttle training sessions in each of two cockpit simulators.