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.

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.