We variable.Selection problems which contain many criteria are

We believe that the main advantage of Integrating DEA
and group AHP is that it is independent of the used prioritization method while
other tested group aggregation procedures are not. By Integrating DEA and group
AHP minimum values of the group Euclidean distance are computed and the highest
degree of consensus is achieved without changing any of the individual
judgments of decision makers participating in the group. Based on the results
presented in this paper, we think that the proposed approach within the AHP
group decision making framework could be extended to situations when decision
makers do not have equal weights, unlike in the examples we used in this paper,
and also for cases when other cardinal error measures (e.g. Manhattan distance)
are used.

.As explained in Section 1, the selection problem is a
very important problem in many organizations. There are some disadvantages in
some approaches which are used to solve this problem. For example, AHP which is
based on the corresponding pairwise comparison judgment matrices made by
relevant decision makers contains much subjective opinion. On the other hand,
DEA, which is based on the objective quantitative data of the selected
input/output factors, has no subjective views of the decision makers.

We Will Write a Custom Essay Specifically
For You For Only $13.90/page!


order now

This paper introduced a three-step approach, which
combines both the DEA and group AHP to solve this problem, which can find a
balance between the subjectivity and the objectivity. After the opinion of DEA
is gathered to formulate the pairwise comparison judgment matrices, the
normalized weighs are calculated and to be used to synthesize the final
evaluations.

The proposed model is based on the integration of DEA
and group AHP models which causes it takes the best
of both models and it will be computationally efficient. It gives a full
ranking of DMUs and it is suitable for situations in which return to scale is
constant or variable.Selection
problems which contain many criteria are important and complex problems and
different approaches have been proposed to fulfill this job. The Analytic
Hierarchy Process (AHP) can be very useful in reaching a likely result which
can satisfy the subjective opinion of a decision maker. On the other hand, the
Data Envelopment Analysis (DEA) has been a popular method for measuring
relative efficiency of decision making units (DMUs) and ranking them
objectively with the quantitative data. In this paper, a Three-step procedure
based on both DEA and AHP is formulated and applied to a case study. The
procedure maintains the philosophy inherent in DEA by allowing each DMU to
generate its own vector of weights. These vectors of weights are used to
construct a group of pairwise comparison matrices which are perfectly
consistent. Then, we utilize group AHP method to produce the best common
weights which are compatible with the DMUs judgments. Using the proposed
approach can give precise evaluation, combining the subjective opinion with the
objective data of the relevant factors. 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. 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.

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.