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Interfaces
Book Review
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Benjamin
Lev
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Interfaces,
Nov.-Dec. 2005, Vol. 35 Issue 6, 532-533
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Cook, Wade D., Joe
Zhu. 2005. Modeling Performance
Measurement:
Applications and Implementation Issues in
DEA.
Springer, New York.
407 pp. $99.00.
In Modeling
Performance Measurement, the authors
describe
their research into data envelopment analysis (DEA)
since the mid ’90s. They extend the original DEA
models to include the use of ordinal data and to
facilitate budgeting. The
authors strike a balance
between
extending DEA theory and emphasizing its
application to decision making. The book should
interest researchers and practitioners.
In each
chapter, the authors present a reformulation of the
DEA model to suit a particular type of
performance-measurement problem. For example, Chapter 4
is on benchmarking. After providing context for
benchmarking the authors establish the need for
benchmarking, models that can evaluate performance on
several measures via one relative efficiency measure
and integrated benchmarking. They present
two DEA models along with theorems and proofs to
establish their correctness and applicability to the
problem at hand. They then describe a managerial example
to aid practitioners in application. They repeat
this pattern in most of the chapters.
Cook and
Zhu discuss the difficulties encountered in
applying quantitative methods to business problems.
In
Chapter 5, for example, they write about determining
whether a variable is an input or output measure
and a two-stage approach that first determines the
status of each variable, input or output, and then
uses those inputs and outputs in a DEA analysis
leading to performance measures for each of the
decision-making units (DMUs). In this case, they
discuss logistic regression, multiple discriminant analysis,
goal programming, and integer goal programming as
methods for accomplishing the first stage,
while embedding expert knowledge into the model.
In
another context, the authors consider the evaluation of
capital construction projects, which entails ranking
and selecting fundable projects subject to a constrained
budget and considering installation cost, operating
cost, environmental impact, contribution to capacity,
impact on ongoing initiatives, and senior management
support. The cost considerations are certainly quantitative,
while the others are likely or certainly qualitative.
In Chapter 7, the authors describe a method
of optimally combining these quantitative and
qualitative measures. It may not be reasonable to evaluate
some projects, however, on all decision criteria. To solve
this problem, the authors developed a model for
evaluating an alternative on a proper subset of the
full set of criteria using their approach; they examine
the performance of an alternative relative to the ideal
performance for that alternative, which they call
benevolent evaluation.
Multicriteria
decision making is a consistent theme throughout
the book, whether in combining multiple measures
in benchmarking, evaluating capital construction models,
or ranking players in tournaments. In their
discussion of the treatment of ordinal criteria and their
inclusion in DEA models, the authors present
the theory for determining optimal rating scores
for decision models that include cardinal and ordinal
criteria and the results.
They
consider resource allocation in a DEA context using
qualitative criteria and also allowing for partial
funding of alternatives. Especially interesting is the
method of determining a set of multipliers to aggregate
several managers’ opinions of the impact of increasing
or decreasing the budgets for all projects using a
preemptive linear-programming model. This approach
allows aggregation of managers’ opinions into an overall
consensus set of ratings, which are then used
as inputs for the resource (re)allocation integer
programs. Cook and Zhu present a numerical example.
Another
form of performance-measurement modeling is
project prioritization with resource constraints. Individual
projects make contributions in several areas,
such as capacity, profit, and new capabilities. They also
require resources from several areas, such as budget
and available labor. One could use a binary knapsack
representation to solve this type of problem, which
would require some objective evaluation multiplier for each
project. The difficulty with these problems is that
such an objective multiplier may not exist or may be
subject to dispute among the interested parties.
Cook and Zhu propose to solve this difficulty by
allowing those proposing each project to evaluate it using
a binary choice, DEA-based approach. They describe
two examples of this extension to DEA; a research-and-development
project prioritization and a site-selection
problem for a chain of retail stores.
Aggregating
preference ranking has been a problem of
interest for over 200 years (Borda 1781). The existing preference-aggregation
models can be considered deficient
because they don’t provide a fair composite evaluation
of the first-place, second-place, thirdplace standings,
and so on. Cook and Zhu present a model
that derives a set of fair multipliers. Part of their
definition of fair is that the set of multipliers for each
candidate may differ from those for any other candidate.
Using this definition, they can calculate the most
favorable standing for each candidate.
In the
last chapter, the authors discuss hierarchies of
decision-making units. The authors describe a model
for determining the efficiency of group decision-making
units and individual decisionmaking units
along with numerical results from a study of
power plants in Canada.
They point out the need for
further research in this area..
The
software included with the book, DEAFrontier (www.deafrontier.com),
is a Microsoft Excel add-in that uses
the built-in solver. It includes the models discussed
in the book.
I recommend Modeling Performance
Measurement to researchers
and practitioners.
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