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.

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).