Patient mix optimisation and stochastic resource requirements: a case study in cardiothoracic surgery planning

Cardiothoracic surgery planning involves different resources such as operating theatre time, beds, IC beds and nursing staff. In the daily practice of the Thorax Centre case study setting, the planning focuses on optimal use of operating theatre time, though the performance of the Thorax Centre as a whole is often more limited by other resources. For operating theatres a master surgical schedule is used to allocate operating theatre resources at tactical level for a longer period. Operational schedules at weekly level are derived from this master schedule. Within cardiothoracic surgery different categories of patients can be distinguished based on their requirement of resources. The mix of patients operated is, therefore, an important decision variable for the Thorax Centre to manage the use of these resources. In this paper we will consider the planning problem at the tactical level to generate a master surgical schedule that realises a given target of patient throughput and optimises an objective function for the utilisation of resources. The problem can be mathematically approached by mixed integer linear programming, which we already demonstrated in a previous paper. The specific topic of the current paper is to investigate the influence of using a stochastic instead of a deterministic length of stay. We will discuss the new mathematical model developed for this planning problem. The results obtained by the model indicate that we can generate master surgical schedules with a better performance on target utilization levels of resources by considering the stochastic length of stay.