Productivity Growth and Efficiency Measurements in Fuzzy Environments with an Application to Health Care

Productivity Growth and Efficiency Measurements in Fuzzy Environments with an Application to Health Care

Adel Hatami-Marbini (Université catholique de Louvain, Belgium), Madjid Tavana (La Salle University, USA) and Ali Emrouznejad (Aston Business School, UK)
Copyright: © 2012 |Pages: 35
DOI: 10.4018/ijfsa.2012040101
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Abstract

Health care organizations must continuously improve their productivity to sustain long-term growth and profitability. Sustainable productivity performance is mostly assumed to be a natural outcome of successful health care management. Data envelopment analysis (DEA) is a popular mathematical programming method for comparing the inputs and outputs of a set of homogenous decision making units (DMUs) by evaluating their relative efficiency. The Malmquist productivity index (MPI) is widely used for productivity analysis by relying on constructing a best practice frontier and calculating the relative performance of a DMU for different time periods. The conventional DEA requires accurate and crisp data to calculate the MPI. However, the real-world data are often imprecise and vague. In this study, the authors propose a novel productivity measurement approach in fuzzy environments with MPI. An application of the proposed approach in health care is presented to demonstrate the simplicity and efficacy of the procedures and algorithms in a hospital efficiency study conducted for a State Office of Inspector General in the United States.
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Introduction

Data envelopment analysis (DEA) introduced by Charnes et al. (1978) is a widely used mathematical programming approach for comparing the inputs and outputs of a set of homogenous decision making units (DMUs) by evaluating their relative efficiency. The DEA generalizes the usual efficiency measurement from a single-input single-output ratio to a multiple-input multiple-output ratio by using a ratio of the weighted sum of outputs to the weighted sum of inputs. While DEA does not provide a precise mechanism for achieving efficiency, it does help in quantifying the magnitude of change required to make the inefficient DMUs efficient and hence contribute to productivity growth.

In addition to comparing the relative performance of a set of DMUs at a specific period, the conventional DEA can also be used to calculate the productivity change of a DMU over time using the Malmquist productivity index, hereafter referred to as MPI. The MPI was first introduced by Malmquist (1953). Cave et al. (1982a, 1982b) proposed a MPI, which calculated the relative performance of a DMU for different time periods using a parametric method. Färe et al. (1989) and Färe, Ggrosskopf, and Lovell (1994) proposed a non-parametric Malmquist index for productivity analysis that relied on constructing a best practice frontier and computing the distance of individual observations from the frontier. Productivity is measured by the MPI and defined as the ratio between efficiency, as calculated by the DEA, for the same DMU in two different time periods. Several modifications for calculating MPI have been proposed in the literature. Jacobs et al. (2006, Ch. 6) provided a comprehensive review of the MPI in health care.

MPI is a very useful method for calculating the productivity change in the DMUs and many applications have been reported in the literature (Chang et al., 2009; Chen, 2003; Chen & Ali, 2004; Emrouznejad & Thanassoulis, 2010; Fiordelisi & Molyneux, 2010; Hashimoto et al., 2009; Kao, 2010; Liu & Wang, 2008; Odeck, 2000, 2006, 2009; Oliveira et al., 2009; Swanson Kazley & Ozcan, 2009; Tsekouras et al., 2004; Zhou et al., 2010). In health care, the growing trends of rising costs have forced the government agencies and health care providers to be more concerned with their profitability and productivity. MPI has been widely used in health care to evaluate productivity change in hospitals, nursing homes, dialysis providers, and pharmacies, among others (Chang et al., 2011; Färe et al., 1995; Ouellette & Vierstraete, 2004; Ozgen, 2006; Retzlaff-Roberts et al., 2004; Kirigia et al., 2004; O’Neill et al., 2008; Kirigia et al., 2008). Hollingsworth (2008) provides a comprehensive review of the DEA literature in health care.

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