Intraday dynamic rescheduling under patient no-shows.

Patient no-shows are a major source of uncertainty for outpatient clinics. A common approach to hedge against the effect of no-shows is to overbook. The trade-off between patient's waiting costs and provider idling/overtime costs determines the optimal level of overbooking. Existing work on appointment scheduling assumes that appointment times cannot be updated once they have been assigned. However, advances in communication technology and the adoption of online (as opposed to in-person) appointments make it possible for appointments to be flexible. In this paper, we describe an intraday dynamic rescheduling model that adjusts upcoming appointments based on observed no-shows. We formulate the problem as a Markov Decision Process in order to compute the optimal pre-day schedule and the optimal policy to update the schedule for every scenario of no-shows. We also propose an alternative formulation based on the idea of 'atomic' actions that allows us to apply a shortest path algorithm to solve for the optimal policy more efficiently. Based on a numerical study using parameter estimates from existing literature, we find that intraday dynamic rescheduling can reduce expected cost by 15% compared to static scheduling.

Mathematical modeling to reduce waste of compounded sterile products in hospital pharmacies.

In recent years, many US hospitals embarked on "lean" projects to reduce waste. One advantage of the lean operational improvement methodology is that it relies on process observation by those engaged in the work and requires relatively little data. However, the thoughtful analysis of the data captured by operational systems allows the modeling of many potential process options. Such models permit the evaluation of likely waste reductions and financial savings before actual process changes are made. Thus the most promising options can be identified prospectively, change efforts targeted accordingly, and realistic targets set. This article provides one example of such a datadriven process redesign project focusing on waste reduction in an in-hospital pharmacy. A mathematical model of the medication prepared and delivered by the pharmacy is used to estimate the savings from several potential redesign options (rescheduling the start of production, scheduling multiple batches, or reordering production within a batch) as well as the impact of information system enhancements. The key finding is that mathematical modeling can indeed be a useful tool. In one hospital setting, it estimated that waste could be realistically reduced by around 50% by using several process changes and that the greatest benefit would be gained by rescheduling the start of production (for a single batch) away from the period when most order cancellations are made.