Monte Carlo and discrete ordinate calculations have been performed to determine the doses at several locations in a positron emission tomography (PET) facility in China, where the radiation source is a cyclotron that is used for the production of the isotopes necessary for PET scans. The energy-dependent neutron source term is obtained by calculations using the ALICE code, and is interpolated for input to Monte Carlo and discrete ordinate calculations. The building that houses the cyclotron has a labyrinth of walls to minimise dose to operators and to other occupants of the building. Unbiased Monte Carlo calculations did not converge after more than one week of CPU time, whereas direction biasing alone resulted in convergence in several days. A study of several biasing techniques indicated that about a factor of 3 in computational efficiency is obtained using evaluated biasing methods. The use of adjoint fluxes for biasing Monte Carlo calculations can improve computational efficiencies by one or two orders of magnitude for some problems.