Incorporating value judgments in data envelopment analysis

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Abstract

Data Envelopment Analysis (DEA) is a linear programming technique for measuring the
relative efficiencies of a set of Decision Making Units (DMUs). Each DMU uses the same
set of inputs in differing amounts to produce the same set of outputs in differing quantities.
Weights are freely allocated in order to allow these multiple incommensurate inputs and
outputs to be reduced to a single measure of input and a single measure of output. A
relative efficiency score of a DMU under Constant Returns to Scale is given by maximising
the sum of its weighted outputs to the sum of its weighted inputs, such that this ratio can
not exceed I for any DMU; with the weights derived from the model being taken to
represent the value attributed to the inputs and outputs of the assessment.
It is well known in DEA that this free allocation of weights can lead to several problems in
the analysis. Firstly inputs and outputs can be virtually ignored in the assessment; secondly
any relative relationships between the inputs or outputs can be ignored, and thirdly any
relationships between the inputs and outputs can be violated. To avoid/overcome these
problems, the Decision Maker's (DM) value judgments are incorporated into the
assessment. At present there is one main avenue for the inclusion of values, that of weights
restrictions, whereby the size of the weights are explicitly restricted. Thus to include the
relative value of the inputs or outputs, the relative value of the weights for these related
inputs or outputs are restricted. The popularity of this approach is mainly due to its
simplicity and ease of use.
The aim of this thesis is, therefore, firstly, to demonstrate that, although the weights
restrictions approach is appropriate for many DMs, for a variety of reasons some DMs,
may prefer an alternative form for the expression of their values, e.g. so that they can
include local values in the assessment. With this in mind, the second aim of this thesis is to
present a possible alternative approach for the DMs to incorporate their values in a DEA
assessment and, thirdly, it aims to utilise this alternative approach to improve envelopment.
This alternative approach was derived by considering the basic concept of DEA, which is
that it relies solely on observed data to form the Production Possibility Set (PPS), and then
uses the frontier of this PPS to derive a relative efficiency score for each DMU. It could be
perceived, therefore, that the reason for DMUs receiving inappropriate relative efficiency
scores is due to the lack of suitable DEA-efficient comparator DMIUs. Thus, the proposed
approach attempts to estimate suitable input output levels for these missing DEA-efficient
comparator DMUs, i.e. Unobserved DMUs. These Unobserved DMUs are based on the
manipulation of observed input output levels of specific DEA-efficient DMUs.
The aim of the use of these Unobserved DMUs is to improve envelopment, and the specific
DEA-efficient DMTJs that are selected as a basis for the Unobserved DMILTs are those that
delineate the DEA-efficient frontier from the DEA-inefficient frontier. So, the proposed
approach attempts to extend the observed PPS, while assuming that the values of the
observed DEA-efficient DMIJs are in line with the perceived views of the DM.
The approach was successfully applied to a set of UK bank branches. To illustrate that no
approach is all-purpose, and that each has its strengths and weaknesses and, therefore, its
own areas of application, a brief comparison is made between the approach of weights
restrictions and the approach proposed in this thesis.
This thesis is divided into three sections: A - Overview of the research area;
B - An alternative perspective for incorporating values in DEA; C - The use of UDMUs
to express the DM's values to improve envelopment

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