Darold T. Barnum

Comparing the Efficiency of Public Transportation Subunits Using Data Envelopment Analysis

This paper discusses the need for a performance measure that compares the efficiencies of subunits within a transportation organization, reflects the diversity of inputs and outputs, and is objective and consistent. The study presents a method for developing such a performance indicator, and illustrates its use with an application to the park-and-ride lots of the Chicago Transit Authority. The proposed method applies Data Envelopment Analysis supplemented by Stochastic Frontier Analysis to estimate efficiency scores for each subunit. The research shows how the scores can provide objective and valid indicators of each subunit’s efficiency, while accounting for key goals and values of internal and external stakeholders. The scores can be practically applied by a transit agency to identify subunit inefficiencies, and, as demonstrated by several brief case studies, this information can be used as the basis for changes that will improve both subunit and system performance.

Improving the efficiency of metropolitan area transit by joint analysis of its multiple providers

Public transportation in a metropolitan area often is supplied by multiple types of transit. This paper develops and illustrates a DEA-based procedure for estimating: overall efficiency of an area’s public transportation; technical efficiencies of the individual transit types; effect of each type on overall efficiency; and efficiency of the allocation of resources among types and an algorithm for improving it. The paper concludes that the overall efficiency of an urban area’s public transportation can be validly estimated only if the technical efficiency of each major transport type and the efficiency in allocating resources among them are taken into consideration.

Measuring Hospital Efficiency with Data Envelopment Analysis: Nonsubstitutable vs. Substitutable Inputs and Outputs

There is a conflict between Data Envelopment Analysis (DEA) theory’s requirement that inputs (outputs) be substitutable, and the ubiquitous use of nonsubstitutable inputs and outputs in DEA applications to hospitals. This paper develops efficiency indicators valid for nonsubstitutable variables. Then, using a sample of 87 community hospitals, it compares the new measures’ efficiency estimates with those of conventional DEA measures. DEA substantially overestimated the hospitals’ efficiency on the average, and reported many inefficient hospitals to be efficient. Further, it greatly overestimated the efficiency of some hospitals but only slightly overestimated the efficiency of others, thus making any comparisons among hospitals questionable. These results suggest that conventional DEA models should not be used to estimate the efficiency of hospitals unless there is empirical evidence that the inputs (outputs) are substitutable. If inputs (outputs) are not substitutes, efficiency indicators valid for nonsubstitutability should be employed, or, before applying DEA, the nonsubstitutable variables should be combined using an appropriate weighting scheme or statistical methodology.

Bias and precision in the DEA two-stage method

In Data Envelopment Analysis (DEA), the two-stage method is a popular procedure for accounting for exogenous influences on efficiency. With the conventional two-stage method, a DEA is first conducted using only traditional (endogenous) inputs and outputs. Then, the first-stage DEA scores are regressed on the environmental/contextual (exogenous) inputs of interest. The regression outcomes are used to identify exogenous inputs that influence the first-stage DEA scores to a statistically significant degree, and to adjust DEA scores to account for these influences. Herein, it is demonstrated empirically that the conventional method exhibits substantial bias and low precision, with the degree of bias and precision affected by input variance and correlation. A reverse two-stage procedure that yields estimates without the bias and precision problems that compromise the validity of the conventional methods estimates is suggested.

Technical efficiency bias in data envelopment analysis caused by intra-output aggregation

We show that an organizations technical efficiency scores are biased downward by linear aggregation of the quantities of the same type of output that are produced by multiple subunits (intra-output aggregation). We expand the models of Färe et al. (2002, 2004) and Barnum and Gleason (2005) to account for intra-output aggregation bias, yielding an expanded model in which technical efficiency is unbiased by any type of input or output aggregation. We illustrate intra-output aggregation bias with data envelopment analysis results from Canadian paratransit operations.

Technical efficiency bias caused by intra-input aggregation in data envelopment analysis

The study shows that technical efficiency scores in Data Envelopment Analysis are biased by linear aggregation of the quantities of the same type of input that are used by all outputs (intra-input aggregation). Färe et al. s (2004) models are expanded to account for this additional bias, and the extent of its impact on reported technical efficiency scores is commented on.

Biases in technical efficiency scores caused by intra-input aggregation: mathematical analysis and a DEA application using simulated data

In Data Envelopment Analysis (DEA) applications involving multiple inputs and outputs, inputs are aggregated into the total amounts of each type of input. For example, if input types ‘labour’ and ‘capital’ are used to produce multiple outputs, the total amount of labour used to produce all outputs is treated as one aggregated input and the total amount of capital as another. Resources are not disaggregated into input variables measuring the amount of labour used to produce the first output, the amount of labour used to produce the second output, the amount of labour used to produce the third output and so on, for both labour and capital. It is shown that such intra-input aggregation causes downward bias in reported technical efficiency scores, with variations in bias unrelated to true technical efficiency. Therefore, with few exceptions, any technical efficiency comparisons among DMUs are invalid. The presence of intra-input aggregation bias is demonstrated mathematically, simulation is used to exhibit its severity, and the exceptions that permit intra-input aggregation without causing bias are identified. It is concluded that, for multiple-input, multiple-output DEA applications, inputs must be disaggregated into the amounts used to produce each output in order to validly report technical efficiency, unless one of the exceptions is present.

Improving the Efficiency of Distributive and Clinical Services in Hospital Pharmacy

Three problems impede the assessment of hospital pharmacy efficiency. First, although multiple efficiency indicators are utilized to measure a large variety of activities, it has not been possible to validly measure overall efficiency. Second, there have been no widely-used clinical activity indicators, so key outputs often have not been accounted for. Third, there has been no effective methodology for identifying when declines in efficiency are normal random variations and when they represent true decreases in performance. This paper presents a procedure that simultaneously addresses these three problems. It analyzes data from a group of U.S. hospital pharmacies that collect an inclusive set of clinical and distributional indicators. It employs Data Envelopment Analysis to develop comprehensive efficiency measures from the numerous outputs and inputs. It applies statistical Panel Data Analysis to estimate confidence intervals within which each pharmacy’s true efficiency resides, and to develop control charts for signaling when a pharmacy’s efficiency has declined by more than can be attributed to random variation. This integrated efficiency evaluation system is transferable to other hospital pharmacy systems, thereby offering decision makers a better way of measuring, controlling and improving hospital pharmacy efficiency.

Measuring efficiency in allocating inputs among outputs with DEA

Building on Data Envelopment Analysis technical efficiency models developed by Färe et al. (2004) and Barnum and Gleason (2005), a procedure is illustrated for estimating a firms efficiency in allocating inputs among the production technologies producing its outputs.

The credibility of drug tests: A multi-stage Bayesian analysis

The authors show that even when drug tests are extremely accurate by conventional measures, under some circumstances they will yield a high “false accusation rate” (that is, a high percentage of those testing positive for drugs will not have drugs in their systems). For example, if a drug-testing process that produces only one false positive per 2,000 drug-free specimens, and no false negatives, is administered to a population in which 0.1% of the people use the targeted drugs, one-third of those identified as drug users will be falsely accused. The authors propose a multi-stage Bayesian algorithm—an approach commonly used in management science but novel to industrial relations—that assures that a drug-testing process will have a low enough false accusation rate to provide credible evidence of drug use. They also identify other types of employee evaluations to which Bayesian modeling could be applied.