Operating theatre represents one of the most critical and expensive hospital resources since a high percentage of the hospital admissions is due to surgical interventions. The main objectives are to guarantee the optimal utilization of medical resources, the delivery of surgery at the right time, the maximisation of profitability (i.e., patient flow) without incurring additional costs or excessive patient waiting time. The operating theatre management is a process very complex: the use of mathematical and simulation models, and quantitative techniques plays, thus a crucial role. The main aim of this paper is to provide a structured literature review on how Operational Research can be applied to the surgical planning and scheduling processes. A particular attention is on the published papers that present the most interesting mathematical (optimization and simulation) models and solution approaches developed to address the problems arising in operating theatres. Directions for future researches are also highlighted.

The efficient radiotherapy patient scheduling, within oncology departments, plays a crucial role in order to ensure the delivery of the right treatment at the right time. In this context, generating a high quality solution is a challenging task, since different goals (i.e., all the activities are scheduled as soon as possible, the patient waiting time is minimized, the device utilization is maximized) could be achieved and a large set of constraints (i.e., every device can be used by only one patient at time, the treatments have to be performed in an exact time order) should be taken into account. We propose novel optimization models dealing with the efficient outpatient scheduling within a radiotherapy department defined in such a way to represent different real-life situations. The effectiveness of the proposed models is evaluated on randomly generated problems and on a real case situation. The results are very encouraging since the developed optimization models allow to overcome the performance of human experts (i.e., the number of patients that begin the radiotherapy treatment is maximized).

Week Hospital is an innovative inpatient health care organization and management, by which hospital stay services are planned in advance and delivered on week-time basis to elective patients. In this context, a strategic decision is the optimal clinical management of patients, and, in particular, devising efficient and effective admission and scheduling procedures, by tackling different requirements such as beds' availability, diagnostic resources, and treatment capabilities. The main aim is to maximize the patient flow, by ensuring the delivery of all clinical services during the week. In this paper, the optimal management of Week Hospital patients is considered. We have developed and validated an innovative integer programming model, based on clinical resources allocation and beds utilization. In particular, the model aims at scheduling Week Hospital patients' admission/discharge, possibly reducing the length of stay on the basis of an available timetable of clinical services. The performance of the model has been evaluated, in terms of efficiency and robustness, by considering real data coming from a Week Hospital Rheumatology Division. The experimental results have been satisfactory and demonstrate the effectiveness of the proposed approach.

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