The thesis makes an analysis of methods available for scheduling nursing staff on a week by week basis. As illustration it considers the situation pertaining at the Simpson Memorial Maternity Pavilion between 1973 and 1978, where student midwives have to be allocated in order to satisfy staffing requirements on each ward, while simultaneously ensuring that each nurse receives the necessary experience on different wards in the course of her year's training. Section I analyses the constraints governing nurse scheduling at the S.M.M.P. under two separate systems used between 1973 and 1978, and provides an exhaustive survey of alternative course structures and solution formulation methods. Section 2 details the existing solution in 1973 and describes two models of that situation which were formulated in order to permit computer simulation of the problem. In Section 3 the scheduling problem at the S.M.M.P. is put into the context of generalised allocation methods. The suitedness of existing mathematical techniques to this problem is considered, and that of sub-gradient optimisation is tested extensively, with modifications to published techniques being detailed where an improvement has been made in the applicability to the present problem. The method is found to be weak when applied to problems of this scale, so a new method is developed which uses a heuristic algorithm to allocate nurses to a set of acceptable schedules. This approach is more powerful and may have applications in other fields. Section 4 describes changes in the training constraints which make it possible to adopt a cyclically repetitive standard schedule at the S.M.M.P. Drawbacks in the present allocation pattern are pointed out, and a new scheduling system developed which eliminates these. In the Conclusions comparison is made between the above methods of allocation with regard to their suitability to the real situation as typified by that at the S.M.M.P.