Many primary care offices and other medical practices regularly experience long backlogs for appointments. These backlogs are exacerbated by a significant level of last-minute cancellations or "no-shows," which have the effect of wasting capacity. In this paper, we conceptualize such an appointment system as a single-server queueing system in which customers who are about to enter service have a state-dependent probability of not being served and may rejoin the queue. We derive stationary distributions of the queue size, assuming both deterministic as well as exponential service times, and compare the performance metrics to the results of a simulation of the appointment system. Our results demonstrate the usefulness of the queueing models in providing guidance on identifying patient panel sizes for medical practices that are trying to implement a policy of "advanced access."Subject classifications: health care; queues: applications.

Hospital diagnostic facilities, such as magnetic resonance imaging centers, typically provide service to several diverse patient groups: outpatients, who are scheduled in advance; inpatients, whose demands are generated randomly during the day; and emergency patients, who must be served as soon as possible. Our analysis focuses on two interrelated tasks: designing the outpatient appointment schedule, and establishing dynamic priority rules for admitting patients into service.We formulate the problem of managing patient demand for diagnostic service as a finite-horizon dynamic program and identify properties of the optimal policies. Using empirical data from a major urban hospital, we conduct numerical studies to develop insights into the sensitivity of the optimal policies to the various cost and probability parameters and to evaluate the performance of several heuristic rules for appointment acceptance and patient scheduling. AbstractHospital diagnostic facilities, such as magnetic resonance imaging centers, typically provide service to several diverse patient groups: outpatients, who are scheduled in advance; inpatients, whose demands are generated randomly during the day; and emergency patients, who must be served as soon as possible. Our analysis focuses on two inter-related tasks: designing the outpatient appointment schedule, and establishing dynamic priority rules for admitting patients into service.We formulate the problem of managing patient demand for diagnostic service as a finite horizon dynamic program and identify properties of the optimal policies.Using empirical data from a major urban hospital, we conduct numerical studies to develop insights on the sensitivity of the optimal policies to the various cost and probability parameters and to evaluate the performance of several heuristic rules for appointment acceptance and patient scheduling.

Most existing estimates of the shortage of primary care physicians are based on simple ratios, such as one physician for every 2,500 patients. These estimates do not consider the impact of such ratios on patients' ability to get timely access to care. They also do not quantify the impact of changing patient demographics on the demand side and alternative methods of delivering care on the supply side. We used simulation methods to provide estimates of the number of primary care physicians needed, based on a comprehensive analysis considering access, demographics, and changing practice patterns. We show that the implementation of some increasingly popular operational changes in the ways clinicians deliver care-including the use of teams or "pods," better information technology and sharing of data, and the use of nonphysicians-have the potential to offset completely the increase in demand for physician services while improving access to care, thereby averting a primary care physician shortage.

The Bass diffusion model is a well-known parametric approach to estimating new product demand trajectory over time. This paper generalizes the Bass model by allowing for a supply constraint. In the presence of a supply constraint, potential customers who are not able to obtain the new product join the waiting queue, generating backorders and potentially reversing their adoption decision, resulting in lost sales. Consequently, they do not generate the positive "word-of-mouth" that is typically assumed in the Bass model, leading to significant changes in the new product diffusion dynamics. We study how a firm should manage its supply processes in a new product diffusion environment with backorders and lost sales. We consider a make-to-stock production environment and use optimal control theory to establish that it is never optimal to delay demand fulfillment. This result is interesting because immediate fulfillment may accelerate the diffusion process and thereby result in a greater loss of customers in the future. Using this result, we derive closed-form expressions for the resulting demand and sales dynamics over the product life cycle. We then use these expressions to investigate how the firm should determine the size of its capacity and the time to market its new product. We show that delaying a product launch to build up an initial inventory may be optimal and can be used as a substitute for capacity. Also, the optimal time to market and capacity increase with the coefficients of innovation and imitation in the adoption population. We compare our optimal capacity and time to market policies with those resulting from exogeneous demand forecasts in order to quantify the value of endogenizing demand.Marketing-Operation Interface, Bass Diffusion Model, New Product Forecasting, Capacity Planning

We consider a rental firm with two types of customers. Contract customers pay fixed, prenegotiated rental fees and expect a high quality of service. Walk-in customers have no contractual relations with the firm and are "shopping for price." Given multiple contract and walk-in classes, the rental firm has to decide when to offer service to contract customers and what fees to charge walk-in customers for service. We formulate this rental management problem as a problem in stochastic control and characterize optimal policies for managing contract and walk-in customers. We also consider static, myopic controls that are simpler to implement, and we analytically establish conditions under which these policies perform optimally. Complementary numerical tests provide a sense of the range of systems for which myopic policies are effective.dynamic programming, services, rentals, revenue management