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GCI Working Paper Series - 2008
Estimating DEA Confidence Intervals for
Canadian Urban Paratransit Agencies
Using Panel Data Analysis
Darold T. Barnum, John M. Gleason, & Brendon Hemily
January 2008
GCP-08-01
This paper illustrates three concepts new to the Data Envelopment Analysis (DEA)
literature, and applies them to data from Canadian urban paratransit agencies. First,
it predicts valid confidence intervals and trends for each agency’s true efficiency.
Second, it uses Panel Data Analysis methodology, a set of statistical procedures that
are more likely to produce valid estimates than those commonly used in DEA studies.
Third, it uses a new method of identifying and adjusting for environmental effects that
has more power than conventional procedures.
DEA Efficiency Analysis Involving
Multiple Production Processes with an Application to Urban Mass Transit
Darold T. Barnum & John M. Gleason
February 2008
GCP-08-02
This paper addresses Data Envelopment Analysis (DEA) efficiency analysis in organizations with multiple production
processes. It shows how to measure the impact on an organization’s overall efficiency of (a) inefficient and
superefficient subunits, and (b) the efficiency with which input resources are allocated to the subunits. It
introduces a simple model for efficiently allocating inputs among subunits, and applies the entire analytical
process to a large urban mass transit agency.
Estimating Data Envelopment Analysis
Frontiers for Nonsubstitutable Inputs and
Outputs: The Case of Urban Mass Transit
Darold T. Barnum & John M. Gleason
February 2008
GCP-08-03
Conventional data envelopment analysis (DEA) models assume that inputs are substitutable for each other, and that
outputs are substitutable for each other. However, recent DEA articles frequently include outputs that cannot be
substituted for each other and inputs that cannot be substituted for each other. In this paper, we demonstrate
that conventional DEA models report invalid efficiency scores when outputs and/or inputs are nonsubstitutable.
We use artificial data to illustrate the differences between the efficient frontiers of substitutable and
nonsubstitutable variables. Assuming that the inputs and outputs are nonsubstitutable, we compare the DEA scores
from a conventional DEA model with those from a new model, the Fixed Proportion Additive (FPA) model, which we
developed to deal with nonsubstitutable variables. Then, we apply the conventional and FPA models to real-world
data involving urban mass transit systems, where the outputs are nonsubstitutable, and where the inputs are
nonsubstitutable. Finally, we make recommendations for model use when inputs or outputs are nonsubstitutable,
one involving the development of new models and the others involving adaptations that can be made if one wishes to
use conventional models.
Comparing the Performance of
Urban Transit Bus Routes after Adjusting
for the Environment, Using Data Envelopment Analysis
Darold T. Barnum, Sonali Tandon, & Sue McNeil
April 2008
GCP-08-05
Urban transit managers strive to attain multiple goals with tightly constrained resources. Ratio
analysis has evolved into a powerful tool for dealing with these goals and constraints. Ratio
analysis provides analytical methods for comparing the performance of multiple agencies, as well
as the performance of subunits within a particular agency, in order to identify opportunities for
improvement. One ratio analysis procedure that has become increasingly popular is Data Envelopment
Analysis (DEA). DEA yields a single, comprehensive measure of performance, the ratio of the aggregated,
weighted outputs to aggregated, weighted inputs. This paper makes two contributions to the practice of
urban transit performance evaluation using DEA. First, instead of using DEA to compare the performance
of multiple transit systems, it uses DEA to compare the performance of multiple bus routes of one urban
transit system. Second, it introduces a new procedure for adjusting the raw DEA scores that modifies
these scores to account for the environmental influences that are beyond the control of the transit agency.
A Quality Control Framework
for Bus Schedule Reliability
Jie Lin, Ming L. Wang, & Darold T. Barnum
May 2008
GCP-08-06
This paper develops and demonstrates a quality control framework for bus schedule
reliability. Automatic Vehicle Location (AVL) devices provide necessary data; Data
Envelopment Analysis (DEA) yields a valid summary measure from partial reliability
indicators; and Panel Data Analysis provides statistical confidence boundaries for each
route-direction’s DEA scores. If a route-direction’s most recent DEA score is below its
lower boundary, it is identified as in need of immediate attention. The framework is
applied to 29 weeks of AVL data from 24 Chicago Transit Authority bus routes (and
therefore 48 route-directions), thereby demonstrating that it can provide quick and
accurate quality control.
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