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Article Excerpt
Many hospitals face the problem of insufficient capacity to meet demand for inpatient beds, especially during demand surges. This results in quality degradation of patient care due to large delays from admission time to the hospital until arrival at a floor. In addition, there is loss of revenue because of the inability to provide service to potential patients. A solution to the problem is to proactively transfer patients between floors in anticipation of a demand surge. Optimal reallocation poses an extraordinarily complex problem that can be modeled as a finite-horizon Markov decision process. Based on the optimization model, a decision-support system has been developed and implemented at Windham Hospital in Willimantic, Connecticut. Projections from an initial trial period indicate very significant financial gains of about 1% of their total revenue, with no negative impact on any standard quality of care or staffing effectiveness indicators. In addition, the hospital showed a marked improvement in quality of care because of a resulting decrease of almost 50% in the average time that an admitted patient has to wait from admission until being transferred to a floor.
Subject classifications: hospitals; health care; dynamic programming; Markov decision processes; decision-support systems.
Area of review: OR Practice.
History: Received July 2005; revisions received May 2006, March 2007, August 2007; accepted December 2007. Published online in Articles in Advance January 5, 2009.
1. Introduction
Over the past 25 years, United States hospitals have been subjected to significant transformations of the operating landscape. The large-scale penetration of health maintenance organizations in the early 1980s, the Emergency Medical Treatment and Labor Act in 1986, and Medicare reform associated with the Balanced Budget Act of 1997, have limited the ability of hospitals to turn away patients that are unable to pay for services, and have placed limits on the amount hospitals are able to collect for the services they provide. These changes have forced hospitals to improve operating efficiency (Krein and Casey 1998). As a result, hospitals have aggressively reduced inefficiencies by cutting staff, managing length of stay, and finding innovative ways to reduce incidental costs.
One side effect of these cost-containment efforts has been a reduction in the number of inpatient beds for which hospitals maintain staff and to which patients can be admitted. The United States lost a total of 100,000 hospital beds, including 7,800 intensive care beds between 1990 and 1999 (Kellerman 2001). The loss of inpatient beds has left many hospitals with minimal surge capacity to handle spikes in demand. The result is that beds are often in short supply, and the problem is expected to get worse (Dodge 2001, Solberg et al. 2003, Wilson 2001).
Emergency department (ED) overcrowding is another undesirable result of insufficient floor capacity. In a March 2003 report (GAO 2003), the United States General Accounting Office found that the factor most commonly associated with crowding was the inability to move emergency patients to inpatient beds, once a decision had been made to admit them as hospital patients, rather than to treat and release them. The impact on ED management is clear. As the number of "boarding" patients who are waiting for beds on their assigned floors increases, the resources available to treat other ED patients are reduced, and eventually the department ceases to function effectively. Often hospitals will then attempt to divert ambulances to other facilities until some of the boarded patients are transferred out of the ED, yielding a very significant negative outcome for patients and the hospital. For patients, the effect of diversion is a longer ambulance ride, which prolongs the delay in receiving medical treatment. For the hospital, each ambulance that is diverted represents lost revenue. In addition, when the ED becomes overcrowded, patients with minor complaints tend to leave the hospital before being seen by a physician. In these cases, the hospital has missed the opportunity to provide a service for which payment would otherwise have been rendered.
An example of a hospital facing the problems delineated above is Windham Community Memorial Hospital (WCMH), located in Willimantic, Connecticut, and servicing a surrounding community of approximately 100,000 people. Of interest here was that in 2004, when this study was initiated, WCMH would often begin to experience capacity-related problems that resulted in patients being boarded in the ED for the short term, e.g., 4-6 hours, well before all inpatient beds were utilized. As a result, delays were incurred when a patient had to be transferred from a given floor to make room for a new patient that could only be assigned to that floor. These "last-minute" transfers are often done under duress during critical "crunch" periods and are generally undesirable from the standpoints of patient flow and quality of care.
The "bed manager" (decision maker) determines the initial assignments of patients to floors. Another task is to determine when, and if, it is necessary to transfer patients from one floor to another, even in noncrunch periods. While it is generally undesirable to transfer patients after admission, it was determined that there was a critical need at WCMH for an optimality-based decision-support system (DSS) for the bed manager that would allow for preemptive (prior to the occurrence of a demand surge) transfers of patients between floors, and for the assignment of patients to floors based partially on capacity considerations. For the former, in-house patients are transferred for the purpose of capacity reallocation (proactive transfer), as opposed to as a "last-minute" immediate response to make room for newly admitted patients (reactive transfer). For the latter, even when beds are available on the "ideal" (based strictly on floor specialization) floor, newly admitted patients may be assigned to feasible "alternate" floors.
We modeled the problem of finding an optimal capacity utilization strategy based on patient allocation as a multidimensional, discrete-time, finite-horizon Markov decision process. The model has been integrated into a DSS that has been implemented and, based on an initial trial period, is projected to result in very significant financial gains of about $600,000 per year, or 1% of total revenue. No negative impact resulted on any standard quality of care or staffing effectiveness indicators. In addition, there was a marked improvement in quality of care because of a resulting decrease of almost 50% in the average time that an admitted patient has to wait from admission until being transferred to a floor. Based on this success, WCMH decided to create an "operations manager" position, to be filled by an individual who will work with the system and will also identify other opportunities to improve patient flow and hospital efficiency.
1.1. Overview
Many hospitals maintain a myopic strategy of assigning admitted patients to their "ideal" floors, based on diagnosis, as long as there are available beds on those floors. Although this strategy works well in many cases, when capacity is limited it can result in patient flow bottlenecks that have a number of negative quality of care and financial implications.
In hospital settings, the general overall problem is quite complex. Departures must be considered as well as arrivals, and the number of floors and patient categories could be large. Although techniques have been developed for solving stochastic sequential decision problems, the basic problem presented here is challenging for a few reasons:
1. There generally are a large number of different patient categories and floors, depending on the size of the hospital and the range of diagnoses it can treat.
2. The number of possible actions/policies to consider is very large.
3. Random events such as patient arrivals and departures depend on patient category, type of floor, and the current state of the hospital, and are often nonhomogenous with respect to time of day, day of week, and season of the year.
4. The amount of time available to reach a decision is fairly short, i.e., typically less than five minutes.
In this paper, we develop and implement a solution methodology that addresses those issues. The remainder of this paper is organized as follows. First, we define the main problem under consideration in [section]2. In [section]3, we model the problem as a finite-horizon Markov decision process (MDP) and study the computational complexity of finding an optimal solution to the MDP and conclude that traditional approaches are not practical for this problem. In [section]3.7, we present an original approximation methodology that relies on event aggregation to find an approximate decision rule solution to the MDP. Section 4 deals with several issues related to the implementation of our approximation methodology in general, and we describe the "rolling-horizon" algorithm used to implement a DSS based on the MDP model. Section 5 describes our computational experience, and [section]6 presents the details of the implementation of the DSS at WCMH, including anecdotal experience, managerial insights, and an analysis of the impact on the hospital.
1.2. Literature Review
The related problems of hospital and ED crowding have been addressed from clinical and managerial viewpoints by health care researchers. Medical researchers have found that diverting ambulances significantly lessens the availability of ambulances for patients in need of medical treatment (Eckstein and Chan 2004). This diversion of ambulances has been found to be primarily due to holding admitted patients in the ED (Schull et al. 2003). The quality of care and financial impact of holding patients in the ED have been found to be significant for patients with chest pain (Bayley et al. 2005) and those in need of thrombolytic therapy (Schull et al. 2004).
Efforts to alleviate the ED crowding problem have...
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