We believe that the main advantage of Integrating DEAand group AHP is that it is independent of the used prioritization method whileother tested group aggregation procedures are not. By Integrating DEA and groupAHP minimum values of the group Euclidean distance are computed and the highestdegree of consensus is achieved without changing any of the individualjudgments of decision makers participating in the group.
Based on the resultspresented in this paper, we think that the proposed approach within the AHPgroup decision making framework could be extended to situations when decisionmakers 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 avery important problem in many organizations. There are some disadvantages insome approaches which are used to solve this problem. For example, AHP which isbased on the corresponding pairwise comparison judgment matrices made byrelevant decision makers contains much subjective opinion. On the other hand,DEA, which is based on the objective quantitative data of the selectedinput/output factors, has no subjective views of the decision makers.
This paper introduced a three-step approach, whichcombines both the DEA and group AHP to solve this problem, which can find abalance between the subjectivity and the objectivity. After the opinion of DEAis gathered to formulate the pairwise comparison judgment matrices, thenormalized weighs are calculated and to be used to synthesize the finalevaluations. The proposed model is based on the integration of DEAand group AHP models which causes it takes the bestof both models and it will be computationally efficient. It gives a fullranking of DMUs and it is suitable for situations in which return to scale isconstant or variable.Selectionproblems which contain many criteria are important and complex problems anddifferent approaches have been proposed to fulfill this job. The AnalyticHierarchy Process (AHP) can be very useful in reaching a likely result whichcan satisfy the subjective opinion of a decision maker. On the other hand, theData Envelopment Analysis (DEA) has been a popular method for measuringrelative efficiency of decision making units (DMUs) and ranking themobjectively with the quantitative data. In this paper, a Three-step procedurebased on both DEA and AHP is formulated and applied to a case study.
Theprocedure maintains the philosophy inherent in DEA by allowing each DMU togenerate its own vector of weights. These vectors of weights are used toconstruct a group of pairwise comparison matrices which are perfectlyconsistent. Then, we utilize group AHP method to produce the best commonweights which are compatible with the DMUs judgments. Using the proposedapproach can give precise evaluation, combining the subjective opinion with theobjective data of the relevant factors. The applicability of the proposedintegrated model is illustrated using a real data set of a case study, whichconsists of 19 facility layout alternatives. Nowadays,in order to survive in increasing competitions, companies try to find betterlocations, system design, materials, and so on.
Therefore, selection problemsare of the most challenging decision making areas the management of a companyencounters. There are many research subjects within the research field ofselection problems: portfolio selection, supplier selection, technologyselection, material selection and so on. It is due to this reason that so manyapproaches have been suggested for selection problems and this problem hasfound a significant number of applications in various fields.
Eventhough a good amount of research work carried out on selection problems, thereis still a need for simple and systematic scientific methods or mathematicaltools to guide user organizations in taking a proper selection decision. Takingdecision in the presence of multiple conflicting criteria is known as multiplecriteria decision making (MCDM) process, and MCDM approaches like AHP and DEAmethods are the most common approaches, which have been used in selectionproblems.DEA is anon-parametric method for measuring efficiency of a set of decision makingunits (DMUs) such as firms or public sector agencies. Inherent philosophy of DEA approach isallowing each DMU to have the most favorable weights as long as the efficiencyscores 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 acommon base. Furthermore, it has some drawbacks such as unrealisticinput/output weights, lack of discrimination among efficient DMUs and findingthe most efficient DMU.AHP is awidely used multiple criteria decision analysis methodology. It operates bystructuring a decision problem as a hierarchical model consisting of criteriaand alternatives.
A very important step in an AHP application is the need toestimate weights of decision entries (which can be criteria or alternatives).The flexibility of AHP has allowed its use in group decision making. Groupdecision making process is strongly evident in many organizations in today’shighly competitive business environment where most decisions are usually madeafter extensive studies and consultation, either internal or external (Dong and Cooper, 2015).Thispaper proposes an integration of DEA and group AHP methods for efficiencyevaluation. The procedure maintains the philosophy inherent in DEA, allowingeach DMU to produce its own vector of weights which maximizes the efficiencyscore of that DMU as long as the efficiency scores of all DMUs calculated fromthe same set of weights, do not exceed one. These vectors of weights are usedto construct a group of pairwise comparison matrices whether they are perfectlyconsistent. In other words, each DMU is asked (as a decision maker) to comparethe relative importance of inputs/outputs, and a pairwise comparison matrix isdeveloped using the efficiency judgments (by solving one of the DEA models).
Then, we utilize group AHP method to produce the best common weights which areconsistent with DMUs judgments. Based on these common weights, we can calculatethe efficiency score of DMUs and using them for ranking and finding the mostefficient DMU which is a desirable goal in many applications of DEA. The restof this paper is organized as follows: In section 2 we discuss briefly aboutDEA and group AHP. In section 3 we present the model Group DEAHP, whichcombines DEA and AHP. In section 4 the applicability of the proposed integratedmodel is illustrated using a real data set of a case study, which consists of19 facility layout alternatives, and finally, conclusion is given in section5.