The operation of drilling rigs is highly expensive. It is therefore important to be able to identify and analyse factors affecting rig operations. We investigate the use of two Genetic Algorithms, K2GA and ChainGA, to induce a Bayesian Network model for the real world problem of Rig Operations Management. We sample from a unique dataset derived from the commercial market intelligence databases assembled by ODS-Petrodata Ltd. We observe a trade-off between K2GA, which finds significantly better scoring networks on our dataset, and ChainGA, which uses only one quarter of the computation time. We analyse the best structures produced from an industry standpoint and conclude by outlining a few potential applications of the models to support rig operations.