A Potts feedback neural network approach for finding good solutions to resource allocation problems with a nonfixed topology is presented. As a target application, the airline crew scheduling problem is chosen. The topological complication is handled by means of a propagator defined in terms of Potts neurons. The approach is tested on artificial random problems tuned to resemble real-world conditions. Very good results are obtained for a variety of problem sizes. The computer time demand for the approach only grows like (number of flights)3. A realistic problem typically is solved within minutes, partly due to a prior reduction of the problem size, based on an analysis of the local arrival and departure structure at the single airports.