Analytics Scheduling patients at the outpatient clinic

In this research we develop a model that prescribes the (near) optimal appointment date for a patient at the moment this patient makes his request at the outpatient clinic. In order to differentiate between different types of patients, such as new patients, control patients and several grades of priorities, we distinguish two categories of patients. One category is characterised by a maximum recommended waiting time. Since the actual scheduled appointment time is reflected in costs, the sooner these patients are scheduled the lower the costs and when the maximum recommended waiting time is exceeded extra costs are incurred. The other category is characterised by a specific appointment time. The closer the scheduled appointment time is to the specific appointment time the lower the costs. The objective is to minimise the long-run expected average cost. We model the scheduling process as a Markov Decision Process (MDP) and we solve this MDP to optimality using value iteration. However, due to the curse of dimensionality, it is computationally infeasible to solve our MDP to optimality for the scheduling process over more than three working days and a reasonable available capacity on a day. To overcome the problem of the curse of dimensionality we apply the Bellman Error Minimisation (BEM) method as an Approximate Dynamic Programming technique in order to derive an estimate of the optimal value function of our MDP of which the near optimal policy (appointment date) can be derived. To determine the set of representative states, which is an element of the BEM method, we use the Hartigan and Wong k-means algorithm. We test several approximation functions and find an approximation function that outperforms all other functions in the scheduling process over three, five, ten and twenty working days. In general it holds that the higher the arrival rate of patients at the outpatient clinic, the better our BEM method performs. But if the arrival rate reaches a certain value the load of the system becomes that high that it does not matter what policy is applied, since many patients have to be rejected.