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We present a modelling approach and the results of two different algorithms applied to the instances of the first international nurse rostering competition. The first algorithm, variable depth search, is an ejection chain based method. It was applied to the sprint instances for which a maximum computation time of 10 seconds was allowed. The second algorithm, a branch and price method, was applied to the medium and long instances for which maximum computation times of 10 minutes and 10 hours respectively were allowed. As will be shown, however, the branch and price algorithm was generally able to solve these instances to proven optimality well within the time allowed.