Using goal programming method to solve DEA problems with value judgments
DOI:
https://doi.org/10.2298/YJOR121221015IKeywords:
data envelopment analysis (DEA), multiple objective linear programming (MOLP), goal programmingAbstract
Data envelopment analysis (DEA) is a linear programming approach for measuring relative efficiency of peer decision making units that have multiple inputs and outputs. DEA was developed without consideration of the decision maker’s preference structures. DEA and multiple objective linear programming are tools that can be used in management control and planning. This paper shows how a data envelopment analysis problem can be solved by transforming it into MOLP formulation. We use the goal programming method to reflect the decision making preferences in the process of assessing efficiency, such that the value judgments of the decision maker are considered. Therefore, the proposed method can find a solution that satisfies the decision maker’s goal levels. A case study is provided to illustrate how data envelopment oriented efficiency analysis can be conducted by using goal programming method.References
Athanassopoulis, A., “Goal programming and data envelopment analysis (GoDEA) for target based multi-level planning: allocating central grants to the Greek local authorities”, European Journal of Operational Research, 87 (1995) 35-50.
Athanassopoulis, A., “Decision support for target-based resource allocation of public services in multiunit and multilevel systems”, Management Science, 39 (10) (1998) 1261-4.
Charnes A, Cooper W, “Polyhedral cone-ratio DEA models with an illustrative application to large commercial banking”, Journal of Econometrics, 46 (1990) 73-9.
Charnes A, Cooper W, Lewin A, Seiford L., Data envelopment analysis: theory, methodology and applications, Dordrecht: Kluwer Academic Publishers, 1994.
Charnes A, Cooper W.W., “Rhodes E., Measuring the efficiency of decision making units”, Euro.J. Operat. Res., 2 (1978) 429-444.
Dyson R, Thanassoulis E., “Reducing weight flexibility in data envelopment analysis”, Journal of Operational Research Society, 39 (6) (1998) 563-76.
Gal, T., Hanne, T., and Stewart, T. (ed.), Advances in multiple criteria decision making, Kluwer Academic Publishers, 1999.
Golany B., “An interactive MOLP procedure for the extension of DEA to effectiveness analysis”, Journal of the Operational Research Society, 39(8) (1988) 725-34.
Golany B, Roll Y., “Measuring efficiency of power plants in Israel by data envelopment analysis”, IEEE Transactions on Engineering Management, 41 (3) (1994) 291-301.
Halme, M., Joro, T., Korhonen, P., Salo, S., and Wallenius, J., “A value efficiency approach to incorporating preference information in data envelopment analysis”, Management Science, 45 (1) (1999) 103-115.
Hosseinzadeh Lotfi F., Jahanshahloo G.R., “Soltanifar M., Ebrahimnejad A., Mansourzadeh S.M., Relationship between MOLP and DEA based on output-orientated CCR dual model”, Expert Systems with Applications, 37 (2010) 4331-4336.
Joro, R., Korhonen, P., and Wallenius, J., “Structural comparison of data envelopment analysis and multiple objective linear programming”, Management Science, 44 (7) (1998) 962-970.
Joro, R., Korhonen, P., and Zionts, S., “An interactive approach to improve estimates of value efficiency in data envelopment analysis”, European Journal of Operations Research, 149 (2003) 688-699.
Koopmans, T. C., Analysis of production as an efficient combination of activities, Analysis of Production and Allocation, John Wiley, Inc., 1951, 33-97.
Korhonen, P., Somismaa, M., and Siljamaki, A., “On the use of value efficiency analysis and some further developments”, Journal of Productivity Analysis, 17 (2002) 49-65.
Post, T., and Spronk, J., “Performance benchmarking using interactive data envelopment analysis”, European Journal of Operational Research, 115 (1999) 472-487.
Sawaragi, Y., Nakayama, H., and Tanino, T., Theory of multiobjective optimization, Academic Press Inc. 1985.
Thanassoulis E, Dyson R., “Estimating preferred target input-output levels using data envelopment analysis”, European Journal of Operations Research, 56 (1992) 80-97.
Thanassoulis E, Allen R., “Simulating weights restrictions in data envelopment analysis by means of unobserved DMUs”, Management Science, 44 (4) (1998) 586-94.
Thompson R, Langemeier L, Lee C, Thrall R., “The role of multiplier bounds in efficiency analysis with application to Kansas farming”, Journal of Econometrics, 46 (1990) 93-108.
Wierzbicki, A. P., Makowski, M., and Wessels, J., (ed.), Model-based decision support methodology with environmental applications”, Kluwer Academic Publishers, 2000.
Wong H, Beasley J., “Restricting weight flexibility in data envelopment analysis”, Journal of Operational Research Society, 41 (9) (1990) 829-35.
Wong B.Y.H., Luque M., Yang J., “Using interactive multiobjective methods to solve DEA problems with value judgments”, Computers and Operations Research, 36 (2009) 623-636.
Wong BY, Yang JB, Greatbanks R., Using DEA and the ER approach for performance measurement of UK retail banks, MCDM 2004. Whistler, Canada, 2004.
Yang, J. B., Wong, B. Y. H., Xu, D. L., and Stewart, T. J., “Integrating DEA-oriented performance assessment and target setting using interactive MOLP methods”, European Journal of Operations Research, 195 (2009) 205-222.
Zhu J., “Data envelopment analysis with preference structure”, Journal of Operational Research Society, 47 (1) (1996) 136-50.
Downloads
Published
Issue
Section
License
Copyright (c) 2014 YUJOR
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
