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.

Several queueing processes may be modelled as random walks on a multi-dimensional grid. In this paper the equilibrium distribution for the case of a two-dimensional grid is considered. In previous research it has been shown that for some two-dimensional random walks the equilibrium distribution has the form of an infinite series of products of powers which can be constructed with a compensation procedure. The object of the present paper is to investigate under which conditions such an elegant solution exists and may be found with a compensation approach. The conditions can be easily formulated in terms of the random behaviour in the inner area and the drift on the boundaries.

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Admissions planning decides on the number of patients admitted for a specialty each day, but also on the mix of patients admitted. Within a specialty different categories of patients can be distinguished on behalf of their requirement of resources. The type of resources required for an admission may involve beds, operating theatre capacity, nursing capacity and intensive care beds. The mix of patients is, therefore, an important decision variable for the hospital to manage the workload of the inflow of patients. In this paper we will consider the following planning problem: how can a hospital generate an admission profile for a specialty, given a target patient throughput and utilization of resources, while satisfying given restrictions? For this planning problem, we will develop an integer linear programming model, that has been tested in a pilot setting in a hospital. The paper includes an analysis of the planning problem, a description of the model developed, an application of a specialty orthopaedics, and a discussion of the results obtained.

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