Linda V. Green

Managing Patient Service in a Diagnostic Medical Facility

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.

Reducing Delays for Medical Appointments: A Queueing Approach

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.”

ANNIVERSARY ARTICLE: Improving Emergency Responsiveness with Management Science

While the goal of OR/MS is to aid decision makers, implementation of published models occurs less frequently than one might hope. However, one area that has been significantly impacted by management science is emergency response systems. Dozens of papers on emergency service management appeared in the OR/MS literature in the 1970s alone, many of which were published inManagement Science. Three of these papers won major prizes. More importantly, many of these papers led to the implementation of substantially new policies and practices, particularly in policing and firefighting. Much of this work originated in New York City, though many other cities subsequently adopted the resulting models and strategies. In this paper, we look at the context, content, and nature of the research and the factors that led to these early implementation successes. We then track the extent to which these original models are still affecting decision making in emergency response systems. We also examine the pace of development of new OR/MS models and applications in the area. Finally, we look at issues in emergency responsiveness that have emerged recently as a result of the national focus on terrorism and discuss the potential for future OR/MS modeling and application.

How Many Hospital Beds

For many years, average bed occupancy level has been the primary measure that has guided hospital bed capacity decisions at both policy and managerial levels. Even now, the common wisdom that there is an excess of beds nationally has been based on a federal target of 85% occupancy that was developed about 25 years ago. This paper examines data from New York state and uses queueing analysis to estimate bed unavailability in intensive care units (ICUs) and obstetrics units. Using various patient delay standards, units that appear to have insufficient capacity are identified. The results indicate that as many as 40% of all obstetrics units and 90% of ICUs have insufficient capacity to provide an appropriate bed when needed. This contrasts sharply with what would be deduced using standard average occupancy targets. Furthermore, given the models assumptions, these estimates are likely to be conservative. These findings illustrate that if service quality is deemed important, hospitals need to plan capacity based on standards that reflect the ability to place patients in appropriate beds in a timely fashion rather than on target occupancy levels. Doing so will require the collection and analysis of operational data—such as demands for and use of beds, and patient delays—which generally are not available.

Capacity Planning and Management in Hospitals

Faced with diminishing government subsidies, competition, and the increasing influence of managed care, hospitals are under enormous pressure to cut costs. In response to these pressures, many hospitals have made drastic changes including downsizing beds, cutting staff, and merging with other hospitals. These critical capacity decisions generally have been made without the help of OR model-based analyses, routinely used in other service industries, to determine their impact. Not surprisingly, this has often resulted in diminished patient access without any significant reductions in costs. Moreover, payers and patients are increasingly demanding improved clinical outcomes and service quality. These factors, combined with their complex dynamics, make hospitals an important and rich area for the development and use of OR/MS tools and frameworks to help identify capacity needs and ways to use existing capacity more efficiently and effectively. In this chapter we describe the general background and issues involved in hospital capacity planning, provide examples of how OR models can be used to provide important insights into operational strategies and practices, and identify opportunities and challenges for future research.

Some effects of nonstationarity on multiserver Markovian queueing systems

We examine the effects of nonstationarity on the performance of multiserver queueing systems with exponential service times and sinusoidal Poisson input streams. Our primary objective is to determine when and how a stationary model may be used as an approximation for a nonstationary system. We focus on a particular question: How nonstationary can an arrival process be before a simple stationary approximation fails? Our analysis reveals that stationary models can seriously underestimate delays when the actual system is only modestly nonstationary. Other findings include confirmation and elaboration of S. M. Rosss conjecture that expected delays increase with nonstationarity, and the identification of easily computed and tight lower and upper bounds for expected delay and the probability of delay. These empirical results are based on a series of computer experiments in which the differential equations governing system behavior are solved numerically.

Queueing Analysis in Health Care

Many organizations, such as banks, airlines, telecommunications companies, and police departments, routinely use queueing models to help determine capacity levels needed to respond to experienced demands in a timely fashion. Though queueing analysis has been used in hospitals and other health care settings, its use in this sector is not widespread. Yet given the pervasiveness of delays in health care and the fact that many health care facilities are trying to meet increasing demands with tightly constrained resources, queueing models can be very useful in developing more effective policies for bed allocation and staffing, and in identifying other opportunities for improving service. Queueing analysis is also a key tool in estimating capacity requirements for possible future scenarios, including demand surges due to new diseases or acts of terrorism. This chapter describes basic queueing models as well as some simple modifications and extensions that are particularly useful in the health care setting, and gives examples of their use. The critical issue of data requirements is also discussed, as well as model choice, model-building, and the interpretation and use of results.

A Queueing System in Which Customers Require a Random Number of Servers

We consider a multiserver queueing system in which customers request service from a random number of identical servers. In contrast to batch arrival queues, customers cannot begin service until all required servers are available. Servers assigned to the same customer may free separately. For this model, we derive the steady-state distribution for waiting time, the distribution of busy servers, and other important measures. Sufficient conditions for the existence of a steady-state distribution are also obtained.

Identifying Good Nursing Levels: A Queuing Approach

Nursing care is arguably the single biggest factor in both the cost of hospital care and patient satisfaction. Inadequate inpatient nursing levels have also been cited as a significant factor in medical errors and emergency room overcrowding. Yet, there is widespread dissatisfaction with the current methods of determining nurse staffing levels, including the most common one of using minimum nurse-to-patient ratios. In this paper, we represent the nursing system as a variable finite-source queuing model. We develop a reliable, tractable, easily parameterized two-dimensional model to approximate the actual interdependent dynamics of bed occupancy levels and demands for nursing. We use this model to show how unit size, nursing intensity, occupancy levels, and unit length-of-stay affect the impact of nursing levels on performance and thus how inflexible nurse-to-patient ratios can lead to either understaffing or overstaffing. The model is also useful for estimating the impact of nurse staffing levels on emergency department overcrowding.

A Queueing System with General-Use and Limited-Use Servers

We consider a queueing system with two types of servers and two types of customers. General-use servers can provide service to either customer type while limited-use servers can be used only for one of the two. Though the apparent Markovian state space of this system is five-dimensional, we show that an aggregation results in an exact two-dimensional representation that is also Markovian. Matrix geometric theory is used to obtain approximations for the mean delay times and other measures of interest for each customer type. We illustrate the methodology by applying it to analyze a token discount policy used by the Triborough Bridge and Tunnel Authority.