Integrating DEA and Group AHP for Efficiency Evaluation and Identification of Most Efficient DMU

Document Type : Research Paper

Authors

1 Department of industrial engineering, Urmia university of technology, Urmia, Iran

2 Faculty of Industrial and Mechanical Engineering, Qazvin branch, Islamic Azad University, Qazvin, Iran

Abstract

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

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Alonso, S., Pérez, I. J., Cabrerizo, F. J. and Herrera-Viedma, E. (2013). A linguistic consensus model for Web 2.0 communities. Applied Soft Computing, Vol. 13, pp. 149-157.
Altuzarra, A., Moreno-Jimenez, J. M. and Salvador, M. (2010). Consensus Building in AHP-Group Decision Making: A Bayesian Approach, Operations Research, Vol. 58, pp. 1755-1773.
Amini, A., Alinezhad, A. and Salmanian, S. (2016). Development of Data Envelopment Analysis for the Performance Evaluation of Green Supply Chain with Undesirable Outputs, International Journal of Supply and Operations Management, Vol. 3(2), pp. 1267-1283.
Azadeh A., Ghaderi S. F. and Izadbakhsh, H. (2008). Integration of DEA and AHP with computer simulation for railway system improvement and optimization, Applied Mathematics and Computation, Vol. 195(2), pp. 755-785.
Azadi, M., Jafarian, M., Farzipoor Saen, R. and Mirhedayatian, S.M. (2015). A new fuzzy DEA model for evaluation of efficiency and effectiveness of suppliers in sustainable supply chain management context, Computers & Operations Research, Vol. 54, pp. 274–285.
Blagojevic, B., Srdjevic, B., Srdjevic, Z. and Zoranovic, T. (2015). Heuristic aggregation of individual judgments in AHP group decision making using simulated annealing algorithm, Information Sciences (Article in press).
Bolloju, N. (2001). Aggregation of analytic hierarchy process models based on similarities in decision makers’ preferences, European Journal of Operational Research, Vol. 128, pp. 499-508.
Brock, H. W. (1980). The Problem of" Utility Weights" in Group Preference Aggregation, Operations Research, Vol. 28, pp. 176-187.
Cabrerizo, F. J., Moreno, J. M., Perez, I. J. and Herrera-Viedma, E. (2010). Analyzing consensus approaches in fuzzy group decision making: advantages and drawbacks, Soft Computing, Vol. 14, pp. 451-463.
Charnes A., Cooper W.W. and Rhodes E. (1978). Measuring the efficiency of decision making units, European Journal of Operational Research, Vol. 2, pp. 429-444.
Chiclana, F., Herrera, F. and Herrera-Viedma, E. (2001). Integrating multiplicative preference relations in a multipurpose decision-making model based on fuzzy preference relations, Fuzzy Sets and Systems, Vol. 122, pp. 277-291.
Contreras I. (2011). A DEA-inspired procedure for the aggregation of preferences, Expert Systems with Applications, Vol. 38, pp. 564-570.
Dobos, I. and Vörösmarty, G. (2018). Inventory-related costs in green supplier selection problems with Data Envelopment Analysis (DEA), International Journal of Production Economics (Article in press).
Dong, Q. and Cooper, O. (2015). A peer-to-peer dynamic adaptive consensus reaching model for the group AHP decision making, European Journal of Operational Research (Article in press).
Dyer, R. F. and Forman, E. H. (1992). Group decision support with the Analytic Hierarchy Process, Decision Support Systems, Vol. 8, pp. 99-124.
Ertay T., Ruan D. and Tuzkaya U. R. (2006). Integrating data envelopment analysis and analytic hierarchy for the facility layout design in manufacturing systems, Information Sciences, Vol. 176, pp. 237–262.
Forman, E. and Peniwati, K. (1998). Aggregating individual judgments and priorities with the analytic hierarchy process, European Journal of Operational Research, Vol. 108, pp. 165-169.
Greco, S., Kadziński, M., Mousseau, V. and Słowiński, R. (2012). Robust ordinal regression for multiple criteria group decision: UTAGMS-GROUP and UTADISGMS-GROUP, Decision Support Systems, Vol. 52, pp. 549-561.
HakimiAsl, M., Sadegh Amalnicka, M., Zorriassatineb, F. and HakimiAsl, A. (2016). Green Supplier Evaluation by Using an Integrated Fuzzy AHP- VIKOR Approach, International Journal of Supply and Operations Management, Vol. 3(2), pp. 1284-1300.
Herrera, F., Herrera-Viedma, E. and Verdegay, J. L. (1995). A sequential selection process in group decision making with a linguistic assessment approach, Information Sciences, Vol. 85, pp. 223-239.
Herrera, F., Herrera-Viedma, E. and verdegay, J. L. (1996). A model of consensus in group decision making under linguistic assessments, Fuzzy Sets and Systems, Vol. 78, pp. 73-87.
Ho, W. and Ma, X. (2017). The state-of-the-art integrations and applications of the analytic hierarchy process, European Journal of Operational Research (Article in press).
Ho, W. (2008). Integrated analytic hierarchy process and its applications – A literature review, European. Journal of. Operational. Research. Vol. 186, pp. 211–228.
Huang, Y.-S., Chang, W.-C., Li, W.-H. and Lin, Z.-L. (2013). Aggregation of utility-based individual preferences for group decision-making, European Journal of Operational Research, Vol. 229, pp. 462-469.
Keeney, R. L. and Kirkwood, C. W. (1975). Group Decision Making Using Cardinal Social Welfare Functions, Management Science, Vol. 22, pp. 430-437.
Li, X., Liu, Y., Wang, Y. and Gao, Z. (2016). Evaluating transit operator efficiency: An enhanced DEA model with constrained fuzzy-AHP cones, Journal of traffic and transportation engineering, Vol. 3(3), pp. 215-225.
Shang J. and Sueyoshi T. (1995). A Unified Framework for the Selection of a Flexible Manufacturing System, European Journal of Operational Research, Vol. 85(2), pp. 297-315.
Sinuany-Stern Z., Mehrez A. and Hadad Y. (2000). An AHP/DEA methodology for ranking decision making units, International Transactions in Operational Research, Vol. 7, pp. 109-124.
Ramanathan, R. & Ganesh, L.S. (1994). Group preference aggregation methods employed in AHP: An evaluation and an intrinsic process for deriving members’ weight ages, Eur. J. Oper. Res., Vol. 79, pp. 249–265.
Saaty T.L. (1980). The Analytic Hierarchy Process, McGraw-Hill: New York.
Saaty, T. L. (1994). Fundamentals of decision making and Priority Theory with The Analytic Hierarchy Process, RWS Publications, Pittsburgh.
Saaty, T. L. (1977). A scaling method for priorities in hierarchical structures, Journal of Mathematical Psychology, Vol. 15, pp. 234-281.
Tanino, T. (1984). Fuzzy preference orderings in group decision making, Fuzzy Sets and Systems, Vol. 12, pp. 117-131.
Tseng F., Chiu Y. and Chen J. (2009). Measuring business performance in the high-tech manufacturing industry: A case study of Taiwan’s large-sized TFT-LCD panel companies, Omega, Vol. 37(3), pp. 686-697.
Van Den Honert, R. C. and Lootsma, F. A. (1997). Group preference aggregation in the multiplicative AHP The model of the group decision process and Pareto optimality, European Journal of Operational Research, Vol. 96, pp. 363-370.
Van den Honert, R. C. (2001). Decisional power in group decision making: A note on the allocation of group members' weights in the multiplicative AHP and SMART. Group Decision and Negotiation 10, 275-286. Information Sciences, Vol. 181, pp. 150-162.
Wang , C. N., Nguyen, X. T. and Nguyen, X. H. (2015). Strategic Alliance Decision-making for the Auto Industry base on an Integrate DEA and GM (1,1) Approach, International Journal of Supply and Operations Management, Vol. 2, No. 3, pp. 856-870.
Wang Y., Liu J. and Elhag T. (2008). An integrated AHP–DEA methodology for bridge risk assessment, Computers and Industrial Engineering, Vol. 54(3), pp. 513-525.
Wu, Z. and Xu, J. (2012). Consensus reaching models of linguistic preference relations based on distance functions. Soft Computing, Vol. 16, pp. 577-589.
Xu, Z. (2009). An automatic approach to reaching consensus in multiple attribute group decision making, Computers & Industrial Engineering, Vol. 56, pp. 1369-1374.
Xu, Z. and Cai, X. (2011). Group consensus algorithms based on preference relations. Information Sciences, Vol. 181, pp. 150-162.
Xu, Y., Li, K. W. and Wang, H. (2013). Distance-based consensus models for fuzzy and multiplicative preference relations, Information Sciences, Vol. 253, pp. 56-73.
Yang T. and Kuo C.A. (2003). A hierarchical AHP/DEA methodology for the facilities layout design problem, European Journal of Operational Research, Vol. 147, pp. 128–136.
Yousefi A. and Hadi-Vencheh A. (2010). An integrated group decision making model and its evaluation by DEA for DEA for automobile industry, Expert Systems with Applications, Vol. 37(12), pp. 8543-8556.