This paper develops a framework and proposes heuristic dynamic policies for scheduling patient appointments, taking into account the fact that patients may cancel or not show up for their appointments. In a simulation study that considers a model clinic, which is created using data obtained from an actual clinic, we find that the heuristics proposed outperform all the other benchmark policies, particularly when the patient load is high compared with the regular capacity. Supporting earlier findings in the literature, we find that the open access policy, a recently proposed popular scheduling paradigm that calls for "meeting today's demand today," can be a reasonable choice when the patient load is relatively low.service operations, health-care management, stochastic methods

Motivated by the rising popularity of electronic appointment booking systems, we develop appointment scheduling models that take into account the patient preferences regarding when they would like to be seen. The service provider dynamically decides which appointment days to make available for the patients. Patients arriving with appointment requests may choose one of the days offered to them or leave without an appointment. Patients with scheduled appointments may cancel or not show up for the service. The service provider collects a “revenue” from each patient who shows up and incurs a “service cost” that depends on the number of scheduled appointments. The objective is to maximize the expected net “profit” per day. We begin by developing a static model that does not consider the current state of the scheduled appointments. We give a characterization of the optimal policy under the static model and bound its optimality gap. Building on the static model, we develop a dynamic model that considers the current state of the scheduled appointments, and we propose a heuristic solution procedure. In our computational experiments, we test the performance of our models under the patient preferences estimated through a discrete choice experiment that we conduct in a large community health center. Our computational experiments reveal that the policies we propose perform well under a variety of conditions.

Motivated by the patient triage problem in emergency response, we consider a single-server clearing system in which jobs may abandon the system if they are not taken into service within their "lifetime." In this system, jobs are characterized by their lifetime and service time distributions.Our objective is to dynamically determine the optimal or near-optimal order of service for jobs so as to minimize the total number of abandonments. We first show that if the jobs can be ordered in such a way that the job with the shortest lifetime (in the sense of hazard rate ordering) also has the shortest service time (in the sense of likelihood ratio ordering), then the optimal policy gives the highest priority to this "time-critical" job independently of the system state. For the case where the jobs with shorter lifetimes have longer service times, we observed that the optimal policy generally has a complex structure that may depend on the type and number of jobs available. For this case, we provide partial characterizations of the optimal policy and obtain sufficient conditions under which a state-independent policy is optimal. Furthermore, we develop two state-dependent heuristic policies, and by means of a numerical study, show that these heuristics perform well, especially when jobs abandon the system at a relatively faster rate when compared to service rates.Based on our analytical and numerical results, we develop several insights on patient triage in the immediate aftermath of a mass casualty event. For example, we conclude that in a worstcase scenario, where medical resources are overwhelmed with a large number of casualties who need immediate attention, it is crucial to implement state-dependent policies such as the heuristic policies proposed in this paper.

M any service systems that work with appointments, particularly those in healthcare, suffer from high no-show rates.While there are many reasons why patients become no-shows, empirical studies found that the probability of a patient being a no-show typically increases with the patient's appointment delay, i.e., the time between the call for the appointment and the appointment date. This paper investigates how demand and capacity control decisions should be made while taking this relationship into account. We use stylized single server queueing models to model the appointments scheduled for a provider, and consider two different problems. In the first problem, the service capacity is fixed and the decision variable is the panel size; in the second problem, both the panel size and the service capacity (i.e., overbooking level) are decision variables. The objective in both cases is to maximize some net reward function, which reduces to system throughput for the first problem. We give partial or complete characterizations for the optimal decisions, and use these characterizations to provide insights into how optimal decisions depend on patient's no-show behavior in regards to their appointment delay. These insights especially provide guidance to service providers who are already engaged in or considering interventions such as sending reminders in order to decrease no-show probabilities. We find that in addition to the magnitudes of patient show-up probabilities, patients' sensitivity to incremental delays is an important determinant of how demand and capacity decisions should be adjusted in response to anticipated changes in patients' no-show behavior.

This note discusses the relationships among three assumptions that appear frequently in the pricing/revenue management literature. These assumptions are mostly needed for analytical tractability, and they have the common property of ensuring a well-behaved "revenue function." The three assumptions are decreasing marginal revenue with respect to demand, decreasing marginal revenue with respect to price, and increasing price elasticity of demand. We provide proofs and examples to show that none of these conditions implies any other. However, they can be ordered from strongest to weakest over restricted regions, and the ordering depends upon the region.