Optimal Capacity Management in a Chronic Illness Treatment Facility

To paraphrase Pierskalla & Brailer [7], capacity planning relates to the optimal selection of resource levels that need to be determined at the time of construction of a new facility. In health care, quantities such as the number of operating rooms, bed spaces or X-ray machines are examples of interest. This is an introductory exploration into capacity management for facilities that treat chronic illnesses. For the sake of concreteness, we will focus our attention on the End-Stage Renal Disease (ESRD). ESRD is a fatal kidney disease that affects close to half a million patients in the US and many more worldwide [8], [9]. ESRD patients rely on dialysis therapy for continuance of survival, and upon registration with a dialysis clinic a new patient begins receiving therapy thrice a week until a kidney transplant is performed. We shall define one unit of capacity as the level of resource required to provide maintenance treatment to one patient. For those afflicted with ESRD, it may take several years to identify a suitable kidney donor [6]. In the meantime, patients are frequently hospitalized for complications from the dialysis treatment itself, giving rise to temporary freed capacity at the clinic. This hospitalization effect is characteristic of facilities for chronic illnesses in general, and is analogous to the concept of statistical multiplexing in telecommunications engineering. Kelly [15] provides a detailed account, but the basic idea is as follows: the number of online users an Internet service provider can serve is constrained by both its bandwidth and the requirements of each user. To guarantee perfect quality, a bandwidth equal in size to the peak rate used by each person must be set aside. However by mixing a lot of users’ traffic together, peak usage of one user cancels the trough of another and the probability of exceeding the total bandwidth decays rapidly. Thus by tolerating a small drop in quality, more users can now remain online. In the context of our situation, bandwidth refers to capacity at the clinic and the registered patients are either using the facility at peak rate or not at all (while in the hospital). Within this framework, it is natural to ask how patient characteristics influence the capacity gain resulting from patient hospitalizations. The details of our investigation will be organized as follows. The first half of this presentation will be of particular interest to practitioners. We describe the queuing network used to model patient flow through the clinic and hospital. As in any capacity management problem, the fundamental obstacle to perfect forecasting of demand arises from three sources of uncertainty: