1. INTRODUCTION
Data Envelopment Analysis (DEA) developed by Charnes, Cooper and
Rhodes (1978) (CCR) assumes that data on the inputs and outputs are known
exactly. However, this assumption may not be true. For example, some
outputs and inputs may be only known as in forms of bounded or interval
data, ordinal data, and ratio bounded data. Cook, Kress and Seiford (1993),
(1996) were the first who developed a modified DEA sturcture where the
inputs and outputs are represented as rank positions in an ordinal, rather than
numerical sense (see chapter 2).
If we incorporate such imprecise data information directly into the
standard linear CCR model, the resulting DEA model is a non-linear and
non-convex program. Such a DEA model is called imprecise DEA (IDEA)
in Cooper, Park and Yu (1999) who discuss how to deal with bounded data
and weak ordinal data and provide a unified IDEA model when weight
restrictions are also present
1
. In a similar work, Kim, Park and Park (1999)
discuss how to deal with bounded data, (strong and weak) ordinal data, and
ratio bounded data.
As shown in Cook and Zhu (2006), the IDEA approach of Kim, Park and
Park (1999) and Cooper, Park and Yu’s (1999) approach is actually a direct
result of Cook, Kress and Seiford (1993; 1996) with respect to the use of
variable alternations.
Zhu (2003a; 2004) on the other hand shows that the non-linear IDEA can
be solved in the standard linear CCR model via identifying a set of exact
data from the imprecise input and output data. This approach allows us to
use all existing DEA techniques to analyze the performance of DMUs and
additional evaluation information (e.g., performance benchmarks, paths for
efficiency improvement, and returns to scale (RTS) classification) can be
obtained.
Chen, Seiford and Zhu (2000) and Chen (2006) calls the existing IDEA
approaches multiplier IDEA (MIDEA) because these approaches are based
upon the DEA multiplier models. These authors also show that IDEA
models can be built on the envelopment DEA models. That is, the interval
data and ordinal data can be introduced directly into the envelopment DEA
model. We can the resulting DEA approach as envelopment IDEA (EIDEA).
It is shown that EIDEA yields the worst scores whereas the MIDEA yields
the best efficiency scores. Using the techniques developed in Zhu (2003a;
2004), the EIDEA can also be converted into linear DEA models.
1
Zhu (2003a) shows that such weight restrictions are redudant when ordinal and ratio
bounded data are present. This can substantially reduce the computation burden.
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Chapter 3