The problem of allocating scarce medical resources to patients with different diseases and needs is encountered in many situations of clinical practice, such as in the emergency room or in crisis areas. Often, there is a significant discrepancy between the desired efficiency and the actual results achieved. Peter Sieb models a corresponding scenario using a dynamic optimization problem and examines it in terms of optimal allocation rules. Based on the usually uncertain health conditions and waiting times of patients, as well as organizational and logistical circumstances while adhering to resource constraints, Peter Sieb derives easily implementable guidelines that determine which treatment should be assigned to which patient.