Optimal Capacity Overbooking for the Regular Treatment of Chronic Conditions

Operations Research 57:4:852-865 (2009)

36 Pages Posted: 27 Nov 2020

See all articles by Donald Lee

Donald Lee

Emory University - Goizueta Business School; Emory University - Dept of Biostatistics & Bioinformatics

Stefanos A. Zenios

Stanford Graduate School of Business

Date Written: 2009

Abstract

Patients suffering from a chronic condition often require periodic treatment. For example, patients with End-Stage Renal Disease (ESRD) require dialysis three times a week. These patients are also frequently hospitalized for complications from their treatment, resulting in idle capacity at the clinic. These temporary patient absences make overbooking at the clinic attractive. This paper develops a semi-closed migration network to capture patient flow into the clinic and between the clinic and hospital. We consider a simple class of stationary control policies for patient admissions and provide algorithms for selecting one that maximizes long-run average earnings. Local diffusion approximations were constructed to provide square-root loading formulas for the optimal capacity level and patient overbooking level: as the total patient arrival rate increases, the deviation between the optimal and fluid-limit capacity and overbooking levels scale up with the square root of the total arrival rate. We find that high hospitalization rates and long inpatient stays allow for more overbooking. Numerical examples based on the typical dialysis clinic in the US suggest an increase in earnings of 11%-14% over policies derived from traditional M/M/N models that do not account for hospitalizations and do not allow overbooking, while keeping the probability of capacity shortage arbitrarily small.

Keywords: health care: chronic diseases, capacity planning: newsvendor, queues, statistical multiplexing

JEL Classification: C44, I10

Suggested Citation

Lee, Donald and Lee, Donald and Zenios, Stefanos A., Optimal Capacity Overbooking for the Regular Treatment of Chronic Conditions (2009). Operations Research 57:4:852-865 (2009), Available at SSRN: https://ssrn.com/abstract=3708466

Donald Lee (Contact Author)

Emory University - Goizueta Business School ( email )

1300 Clifton Road
Atlanta, GA 30322-2722
United States

Emory University - Dept of Biostatistics & Bioinformatics ( email )

Atlanta, GA 30322
United States

Stefanos A. Zenios

Stanford Graduate School of Business ( email )

655 Knight Way
Stanford, CA 94305-5015
United States

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