The (2008) proposed integration of DEA and AHP

The
complexity of the decisions that management face makes it difficult to depend
on a single decision maker’s knowledge and capabilities to obtain a meaningful
and reliable solution. Therefore, group decision making has received
significant attention in both the research and in practice. Group decision
making (GDM) is a procedure that combines the individuals’ judgments into a
common opinion on behalf of a whole group. To express the judgments of
individuals, several formats are usually used in GDM, such as fuzzy preference
relations (Tanino, 1984; Cabrerizo et al., 2010; Xu et al., 2013) linguistic preference
relations (Herrera et al., 1995;
Herrera et al., 1996; Wu and Xu, 2012; Alonso et al., 2013) utility
functions (Brock, 1980;  Keeney and Kirkwood,
1975; Greco et al., 2012; Huang et al., 2013) and the Analytic Hierarchy Process (AHP) (Dyer and Forman, 1992; Van
Den Honert and Lootsma, 1997; Chiclana et al., 2001; Altuzarra et al., 2010).

Our
method integrates two well-known models, DEA and group AHP. Both DEA and AHP
are commonly used in practice and many researchers highlight the relationship
between DEA and AHP techniques.

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First of
all, Shang and Sueyoshi (1995) used a combination of DEA and AHP approaches for
selection of a flexible manufacturing system. Sinuany-Stern et al. (2000derived
the AHP pairwise comparison matrices mathematically from the input/output data,
by running pairwise DEA runs.  Yang and
Kuo (2003) proposed an AHP process and DEA approach to solve a plant layout
design problem. Ertay et al. (2006) addressed the evaluation of the facility
layout design by developing a robust layout framework based on the DEA/AHP
methodology. Azadeh et al. (2008) proposed integration of DEA and AHP with
computer simulation for railway system improvement and optimization. Wang et
al. (2008) proposed an integrated AHP–DEA methodology. Tseng et al. (2009) measured
business performance in the high-tech manufacturing industry, by using DEA,
AHP, and a fuzzy MCDM approach. Recently, Yousefi and Hadi-Vencheh (2010)
proposed a decision making model in automobile industry by integration of AHP,
TOPSIS and DEA. In Contreras (2011), the author proposed a new model consists
of two stages. First, a DEA-inspired model for the aggregation of preferences
is applied, wherein the objective is not the maximization of the aggregated
value but rather the ordinal position induced by these values. Second, in order
to obtain a group solution, the procedure derives a compromise solution by
determining a social vector of weights for evaluating the complete set of
alternatives.

Although
all these efforts developed their methods for selecting or evaluating DMUs,
some requirements cannot be satisfied. At first, the simple implementation of
the method is of prime importance. Moreover, most methods are qualitative and
the usual way that they make their evaluations is to list all the criteria in a
form and ask the decision makers to give their evaluations for each criterion.
In this paper, a quantitative method with a simple implementation is presented
to solve this problem. At first, the following two subsections describe DEA and
AHP methods briefly, after which, in section 3, a new hybrid model is
described.

2.1. DEA preliminaries

DEA was
first proposed by Charnes et al (1978) and during the past two decades, it has
emerged as an important tool in the field of efficiency measurement. DEA is a
nonparametric approach that does not require any assumption about the functional
form of production function. DEA is a quantitative method, which can avoid the
subjective factors of decision makers.

Assume
that there are n DMUs, (DMUj: j = 1, …, n) which consume m inputs (xij: i = 1,
…, m) to produce s outputs (yrj: r = 1, …, s). A standard formulation of DEA
creates a separate linear program for each DMU. It is instructive to apply the
output oriented version of the multiplier BCC model as follows:

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