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.