Nowadays, a proper selection decision. Taking decision

Nowadays,
in order to survive in increasing competitions, companies try to find better
locations, system design, materials, and so on. Therefore, selection problems
are of the most challenging decision making areas the management of a company
encounters. There are many research subjects within the research field of
selection problems: portfolio selection, supplier selection, technology
selection, material selection and so on. It is due to this reason that so many
approaches have been suggested for selection problems and this problem has
found a significant number of applications in various fields.

Even
though a good amount of research work carried out on selection problems, there
is still a need for simple and systematic scientific methods or mathematical
tools to guide user organizations in taking a proper selection decision. Taking
decision in the presence of multiple conflicting criteria is known as multiple
criteria decision making (MCDM) process, and MCDM approaches like AHP and DEA
methods are the most common approaches, which have been used in selection
problems.

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DEA is a
non-parametric method for measuring efficiency of a set of decision making
units (DMUs) such as firms or public sector agencies.  Inherent philosophy of DEA approach is
allowing each DMU to have the most favorable weights as long as the efficiency
scores of all DMUs calculated from the same set of weights, do not exceed one.
This flexibility in selecting the weights deters the comparison among DMUs on a
common base. Furthermore, it has some drawbacks such as unrealistic
input/output weights, lack of discrimination among efficient DMUs and finding
the most efficient DMU.

AHP is a
widely used multiple criteria decision analysis methodology. It operates by
structuring a decision problem as a hierarchical model consisting of criteria
and alternatives. A very important step in an AHP application is the need to
estimate weights of decision entries (which can be criteria or alternatives).
The flexibility of AHP has allowed its use in group decision making. Group
decision making process is strongly evident in many organizations in today’s
highly competitive business environment where most decisions are usually made
after extensive studies and consultation, either internal or external (Dong and Cooper, 2015).

This
paper proposes an integration of DEA and group AHP methods for efficiency
evaluation. The procedure maintains the philosophy inherent in DEA, allowing
each DMU to produce its own vector of weights which maximizes the efficiency
score of that DMU as long as the efficiency scores of all DMUs calculated from
the same set of weights, do not exceed one. These vectors of weights are used
to construct a group of pairwise comparison matrices whether they are perfectly
consistent. In other words, each DMU is asked (as a decision maker) to compare
the relative importance of inputs/outputs, and a pairwise comparison matrix is
developed using the efficiency judgments (by solving one of the DEA models).
Then, we utilize group AHP method to produce the best common weights which are
consistent with DMUs judgments. Based on these common weights, we can calculate
the efficiency score of DMUs and using them for ranking and finding the most
efficient DMU which is a desirable goal in many applications of DEA. 

The rest
of this paper is organized as follows: In section 2 we discuss briefly about
DEA and group AHP. In section 3 we present the model Group DEAHP, which
combines DEA and AHP. In section 4 the applicability of the proposed integrated
model is illustrated using a real data set of a case study, which consists of
19 facility layout alternatives, and finally, conclusion is given in section
5. 

1. Literature review

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.

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: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:

 The
flexibility of AHP has allowed its use in group decision making. The AHP
literature describes two different ways of approaching group decision making
with a view to obtaining group priorities. These are: (i) Aggregation of individual judgments (AIJ) and (ii) Aggregation of individual priorities (AIP). In AIJ
procedure, a new judgment matrix for the group as a whole is constructed on the
basis of individual judgments using the weighted geometric mean method (WGMM),
and then the group’s priorities being drawn from this group judgment matrix. In
AIP, we obtain the individual priorities using the row geometric mean method
(RGMM), and the group’s priorities are established on the basis of individual
priorities using the weighted geometric mean method (Blagojevic et al., 2015).