Variability in admissions and lengths of stay inherently leads to variability in bed occupancy. The aim of this paper is to analyse the impact of these sources of variability on the required amount of capacity and to determine admission quota for scheduled admissions to regulate the occupancy pattern. For the impact of variability on the required number of beds, we use a heavy-traffic limit theorem for the G/G/∞ queue yielding an intuitively appealing approximation in case the arrival process is not Poisson. Also, given a structural weekly admission pattern, we apply a time-dependent analysis to determine the mean offered load per day. This time-dependent analysis is combined with a Quadratic Programming model to determine the optimal number of elective admissions per day, such that an average desired daily occupancy is achieved. From the mathematical results, practical scenarios and guidelines are derived that can be used by hospital managers and support the method of quota scheduling. In practice, the results can be implemented by providing admission quota prescribing the target number of admissions for each patient group.

No abstract

In this study we consider the optimal scheduling of a certain number of appointments in a given number of time slots. Given a set of appointment slots, we assume that customers can arrive early or late according to a known distribution around the scheduled arrival time. Analytical methods exist for this problem when all customers are assumed to be punctual, but evaluating methods when this assumption is relieved do not yet exist. The reason why this is difficult, is that the order of service is no longer fixed when possible arrival times of two consecutive customers overlap. Therefore we use simulation to evaluate schedules, and optimisation via simulation techniques to optimize schedules. We develop and compare several strategies, among which random local search and nested partitions. Numerical experiments show that significant improvements can be achieved compared to standard scheduling practice. INTRODUCTIONAppointment scheduling is an area of health care operations management that has received considerable attention in the scientific literature. See, for example, Cayirli and Veral (2003) and Gupta and Denton (2008) for overviews of the literature. The objective is to determine appointment times for a given number of patients such that certain, often conflicting, objectives are each satisfied to a certain extent. These objectives usually include patient waiting times and doctor idle time and lateness, which is the time the doctor is still working after the end of the scheduled time. The canonical formulation is mathematically attractive and challenging, explaining the attention it received. It is also practically relevant, although its use in practice is still limited.Part of the reason for the lack of applications is that most of these studies use assumptions that are unrealistic from a practical point of view. One notable assumption is the punctuality of patients, where only in some cases no-shows are allowed but never late (or early) arrivals. Most papers that obtain numerical or structural results assume punctuality, with Jouini and Benjaafar (2012) as an exception. The reason is that, when patients can arrive late, overtaking can occur, which makes the problem technically more complicated. Another feature that is hard to deal with analytically is the inclusion of unplanned emergency arrivals, which usually have some form of priority over the scheduled arrivals. No analytical technique exists that can handle all possible features.It is the objective of this paper to present a technique that requires no unrealistic assumptions and that allows to find (nearly) optimal appointment schedules. In our opinion the only candidate method is optimization via simulation. In this paper we show the use of this method for appointment scheduling. In the next section we define the problem in detail. In Section 3 we explain the optimization methods we used, to be followed by our numerical results in Section 4. We finish the paper by our conclusions and directions for future work.

No abstract