Benneyan, James C.
Cullinane, Thomas P., Sherman, David
Date of Award
Northeastern University, 2008
Department or Academic Unit
College of Engineering. Department of Mechanical and Industrial Engineering.
Industrial engineering, Data envelopment analysis, Proportional data, Weight restrictions
This dissertation addresses two problems when handling proportional data and weight constraints frequently arise in Data Envelopment Analysis (DEA), motivated by several healthcare studies. DEA is a mathematical method for measuring the relative efficiencies of multiple decision making units (DMUs) at transforming multiple inputs (e.g., number of medical staff, number of beds, per patient costs) into multiple outputs (e.g., mortality, clinical outcomes, patient satisfaction), also computing target values and optimal weights for each input and output, where here the DMUs could be hospitals, departments, healthcare systems, physicians, public policies, and so on. The primary contributions of this research are methods for (1) handling proportional and bounded data, (2) rationally constraining the input-output weights, and (3) measuring efficiency robustness over ranges of possible weight constraints. The first problem is motivated by the fact that in some DEA applications the usual assumption is violated that all data must only be nonnegative, namely for proportional data bound between 0 and 1 (e.g., mortality, adverse event, defect, or market penetration rates). Solving conventional constant-returns-to-scale (CRS) DEA models in such cases can produce output targets exceeding their upper bounds (e.g., 130 percent survival). Values bound on a fixed interval (e.g., satisfaction scores between 1 and 5) present a similar problem. Given the common use of CRS models, this research proposes and investigates an odds-ratio transformation that forces all targets between their bounds. The second problem is motivated by periodic ""irrational"" weights, such as placing less (or no) weight on mortality than on patient satisfaction. Since the two most common approaches in the literature (rank ordering or setting lower bounds for individual weights) have scale, solution feasibility, and arbitrariness limitations, we propose and compare a method that constrains each weight by a percent of the total (POT) of all weights. To remove the subjectivity of these percentages and as a measure of efficiency robustness, iterative search, numeric, and Monte Carlo algorithms (the last implemented in an Excel-based program) are developed that determine POT regions within which each DMU is on the frontier and compute an overall ""hyper efficiency"" score. All methods are demonstrated on several analyses of VA medical facilities, the U.S. News and World Report (USNWR) ""best"" departments, and national healthcare systems using data from the World Health Organization (WHO). Interestingly, results for U.S. hospitals and national healthcare systems both are poorly correlated with the more arbitrary weighted USNWR and WHO rankings.
Sunnetci, Aysun, "Handling proportional data and weight constraints in data envelopment analysis (DEA)" (2008). Industrial Engineering Dissertations. Paper 1. http://hdl.handle.net/2047/d10017276
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