DATA ENVELOPMENT ANALYSIS CROSS EFFICIENCY EVALUATION APPROACH TO THE TECHNOLOGY SELECTION

Year 2015, Volume: 3 Issue: 1, 1 - 14, 08.05.2015

H.hasan Örkcü , Mediha Örkcü

Abstract

This paper proposes two data envelopment analysis (DEA) cross efficiency models for selecting the most efficient alternatives in manufacturing technology. The cross efficiency evaluation (CEE) method which is developed as a contribution to the classical Data Envelopment Analysis (DEA) is a method successively used in the ranking problems. In its original, the CEE method includes the efficiency evaluations made use for the reusage of optimal weights in the other DMUs obtained for a DMU by the classical DEA. Since the optimal weights in the classical DEA solutions have usually multiple solutions, this reduces the usefulness of CEE method. This study suggests new methods for the second stage of CEE method to remove the question of multiple optimal weights. A numerical example illustrates the model, and an application in technology selection with multi-inputs/multi-outputs shows the usefulness of the proposed approaches. 

Keywords

Data envelopment analysis, technology selection, cross efficiency, multiple optimal weights.

References

• Knott K, Getto RD, “A model for evaluating alternative robot systems under uncertainty”, Int J Prod Res, 20(2):155–165, (1982).
• Huang PY, Ghandforoush P, “Robotics procedures given for evaluating selecting robots”, Ind Eng 16(4):44– 48, (1984).
• Rai, R., Kameshwaran, S., Tiwari, M.K., “Machine- tool selection and operation allocation in FMS: Solving a fuzzy goal-programming model using a genetic algorithm”, International Journal of Production Research, 40 (3):641–665, (2002).
• Chan, F.T.S, Swarnkar, R., Tiwari, M.K., “Fuzzy goal-programming model with an artificial immune system (AIS) Approach for a machine tool selection and operation allocation problem in a flexible manufacturing system”, International Journal of Production Research, 43(19): 4147–4163, (2005).
• Jaganathan S., Erinjeri, J.J., Ker J., “Fuzzy analytic hierarchy process based group decision support system to select and evaluate new manufacturing technologies”, International
• Technology, 32(11–12): 1253–1262, (2007). Advanced
• Manufacturing [6] Graves SC, Whitney DE, “A mathematical programming procedure for equipment selection and system
• Proceedings of the 18th IEEE conference on decision and control, Fort Lauderdale, 531–536, (1979).
• Booth DE, Khouja M, Hu M, “A robust multivariate statistic procedure for evaluation and selection of industrial robots”, Int J Oper Prod Manag, 12(2):15–24, (1993).
• Imany MM, Schlesinger RJ, “Decision models for robot selection: a comparison of ordinary least squares and linear goal programming methods”, Decis Sci 20(1):40–53, (1989).
• Khouja M, Booth DE, “A decision model for the robot selection problem using robust regression”, Decis Sci 22(3):656– 662, (1991).
• Agrawal VP, Kohli V, Gupta S, “Computer aided robot selection: the multiple attribute decision making approach”, Int J Prod Res 29(8):1629–1644, (1991).
• Baker RC, Talluri S, “A closer look at the use of data envelopment analysis for technology selection”, Comput Ind Eng 32(1):101–108, (1997).
• Bhangale PP, Agrawal VP, Saha SK, “Attribute based specification, comparison and selection of a robot”, Mech Mach Theory, 39(12):1345–1366, (2004).
• Bhattacharya A, Sarkar B, Mukherjee SK, “Integrating AHP with QFD for robot selection under requirement perspective”, Int J Prod Res 43(17):3671– 3685, (2005).
• Chatterjee P, Athawale VM, Chakraborty S., “Selection of industrial robots using compromise ranking and outranking methods”, Robotics Comput Integr Manuf , 26(5):483–489, (2010).
• Goh CH, “Analytic hierarchy process for robot selection”, J Manuf Syst 16(5):381–386, (1997).
• Goh CH, Tung YC, Cheng CH, “A revised weighted sum decision model for robot selection”, Comput Ind Eng, 30(2):193–199, (1996).
• Kentli A, Kar AK, “A satisfaction function and distance measure based multi-criteria robot selection procedure”, Int J Prod Res, 49:5821–5832, (2011).
• Rao RV, Patel BK, Parnichkun M, “Industrial robot selection using a novel decision making method considering objective and subjective preferences”, Robot Auton Syst 59(6):367–375, (2011).
• Chu TC, Lin YC., “A fuzzy topsis method for robot selection”, Int J Adv Manuf Technol 21(4): 284–290, (2003).
• Kahraman C, Cevik S, Ates NY, Gulbay M., “Fuzzy multicriteria evaluation of industrial robotic systems”, Comput Ind Eng, 52(4):414–433, (2007).
• [21 Kapoor V, Tak SS. “Fuzzy application to the analytic hierarchy process for robot selection”, Fuzzy Optim Decis Making, 4(3):209–234, (2005).
• Khouja M, Booth DE, “Fuzzy clustering procedure for evaluation and selection of industrial robots”, J Manuf Syst 14(4):244–251, (1995).
• Koulouriotis DE, Emiris DM, “An intelligent decision support system for industrial robot selection”, Trends and perspectives in modern computational science. Lecture series on computer and computational sciences, Brill, Leiden, 7, 649–655, (2006).
• Liang GS, Wang MJJ , “A fuzzy multi-criteria decision making approach for robot selection”, Robot Comput Integr Manuf, 10(4):267–274, (1993).
• Zhao L, Tsujimura Y, Gen M., “Genetic algorithm for robot selection and work station assignment problem”, Comput Ind Eng, 31(3-4):599–602, (1996).
• Karsak EE, “Choquet integral-based decision making approach for robot selection”, Knowledge-based intelligent information and engineering systems. Lecture notes in artificial intelligence, Springer, Berlin, 3682, 635–641, (2005).
• Parkan C,Wu ML,
• performance measurement models with applications to robot selection”, Comput Ind Eng, 36(3):503–523, (1999). “Decision-making
• and Khouja M, Rabinowitz G, Mehrez A, “Optimal robot operation and selection using quality and output trade- off.”, Int J Adv Manuf Technol ,10(5):342–355, (1995)
• Kumar R, Garg RK, “Optimal selection of robots by using distance based approach method” , Robot Comput Integr Manuf, 26(5):500–506, (2010).
• Offodile OF, Acar W, “Comprehensive situation mapping for robot evaluation and selection”, Int J Oper Prod Manag, 13(1):71–80, (1993). [31] Rao
• identification and comparison of industrial robots using digraph and matrix methods”, Robot Comput Integr Manuf, 22(4):373–383, (2005). KK,
• “Selection, [32] Koulouriotis D, Ketipi M, “A fuzzy digraph method for robot evaluation and selection”, Expert Syst Appl, 38(9):11901–11910, (2011).
• Athawale VM, Chakraborty S, “A comparative study on the ranking performance of some multi-criteria decision-making methods for industrial robot selection”, Int J Ind Eng Comput, 2(4):819–830, (2011).
• Koulouriotis DE, Ketipi MK, Robot selection methods in industrial applications: review, classification and comparative analysis, Multiple criteria decision aiding, advances in operations research. Nova, New York, (2010).
• Khouja, M., “The use of data envelopment analysis for technology selection”, Computers and Industrial Engineering, 28(1):123–132, (1995).
• Karsak, E.E., “A two-phase robot selection procedure”, Production Planning & Control, 9 (7), 675– 684, (1998).
• Karsak, E.E., “ A DEA-based robot selection procedure
• Proceedings of the IEEE international conference on fuzzy criteria
• values”, systems, man, and cybernetics, Tokyo, Japan, 1073– 1078, (1999).
• Talluri, S. and Yoon, K.P., “A cone-ratio DEA approach for AMT justification. International Journal of Production Economics, 66 (2), 119–129, (2000).
• Charnes A, Cooper W.W., Rhodes E.,. Measuring the efficiency of decision making units, European Journal of Operational Research, 2, 429-444, (1978).
• Meza, L.A., Lins, M.P.E.,. “Review of Methods for Increasing
• Analysis”, Annals of Operations Research, 116, 225– 242, (2002). in Data
• Envelopment [41] Adler, N., Friedman L. Sinuany-Stern Z.,. “Review of ranking methods in the data envelopment analysis context”, European Journal of Operational Research, 140, 249–265, (2002).
• Bal, H., Örkcü, H.H., “A Goal Programming Approach to Weight Dispersion Problem in Data Envelopment Analysis and Simulation Study”, Gazi University Journal of Science, 20 (4), 117-125, (2007).
• Örkcü, H.H., Bal, H., “Goal Programming Approaches for Data Envelopment Cross Efficiency Evaluation”, Applied Mathematics and Computation, 218 (2), 346-356, (2011).
• Sexton, T.R., Silkman, R.H., Hogan, A.J.,. Data envelopment Analysis: critique and Extension. In: Silkman R.H. (Ed.), Measuring efficiency: An assesment of Data Envelopment Analysis, vol 32. Jossey-Bass, San Fransisco, 73-105, (1986).
• Anderson, T.R., Hollingsworth, K.B., Inman, L.B., “The fixed weighting nature of a cross evaluation model, Journal of Productivity Analysis, 18(1), 249–255, (2002).
• Doyle, J.R., Green, R., “Efficiency and cross- efficiency in data envelopment analysis: derivatives, meanings and uses”, Journal of Operational Research Society, 45(5), 567-578 (1994).
• Liang, L., Wu, J., Cook, W.D., Zhu, J., “Alternative secondary goals in DEA cross efficiency evaluation”, International Journal of Production Economics, 113, 1025-1030, (2008).
• Li, X. B., Reeves, G.R., “A multiple criteria approach to data envelopment analysis”, European Journal of Operational Research, 115: 507-517, (1999). [49] Ertay, T., & Ruan, D., “Data envelopment analysis based decision model for optimal operator allocation in CMS”, European Journal of Operational Research, 164, 800–810, (2005).
• Ertay, T., Ruan, D., & Tuzkaya, U. R., “Integrating data envelopment analysis and analytic hierarchy for the facility layout design in manufacturing systems”, Information Sciences, 176, 237–262, (2006).
• Amin, G. R., Toloo, M., & Sohrabi, B., “An improved MCDM DEA model for technology selection”, International Journal of Production Research, 44, 2681–2686, (2006).
• Amin, G. R., Toloo, M. “Finding the most efficient DMUs in DEA: An improved integrated model”, Computers and Industrial Engineering, 52(2), 71–77, (2007).
• Amin, G. R., “A note on ‘‘an improved MCDM DEA model for technology selection’’, International Journal of Production Research, 46, 7073–7075, (2008). [54] Amin, G. R., “Comments on finding the most efficient DMUs in DEA: An improved integrated model”,. Computers and Industrial Engineering, 56, 1701–1702, (2009).
• Amin, G. R., & Emrouznejad A. “Finding relevant search engines results: A minimax linear programming approach”, Journal of the Operational Research Society, 61, 1144–1150, (2010).
• Amin, G. R., Gattoufia, S., & Rezaee Serajib, E., “A maximum discrimination DEA method for ranking association rules in data mining”, International Journal of Computer Mathematics, 88(11), 2233–2245, (2011).
• Foroughi, A. A. “A new mixed integer linear model for selecting the best decision making units in data envelopment analysis”, Computers and Industrial Engineering, 60(4), 550–554 (2011).
• Wang, Y.-M., & Jiang, P. “Alternative mixed integer linear programming models for identifying the most efficient decision making unit in data envelopment analysis”, Computers and Industrial Engineering, 62, 546–553, (2012).
• Toloo, M., “The most efficient unit without explicit inputs: An extended MILPDEA model. Measurement”, 46, 3628–3634, (2013).
• Toloo, M., “An epsilon-free approach for finding the most efficient unit in DEA”, Applied Mathematical Modelling, 38, 3182–3192, (2014).
• Toloo, M., “Alternative minimax model for finding the most efficient unit in data envelopment analysis”, Computers & Industrial Engineering, 81,186–194, (2015).
• Örkcü, H.H., Bal, H., “A New Approach to Cross Efficiency
• Performance Evaluation of Turkey Cities”, Gazi University Journal of Science, 25 (1), 107-117, (2012).
• Bal, H., Örkcü, H.H., Çelebioğlu, S., “A New Method Based on the Dispersion of Weights in Data Envelopment Analysis”, Computers and Industrial Engineering, 54 (3), 502-512, (2008).