An interactive MOLP method for solving output-oriented DEA problems with undesirable factors

Ali Ebrahimnejad; Madjid Tavana; Seyed Mehdi Mansourzadeh

doi:10.3934/jimo.2015.11.1089

Article Contents

2015, Volume 11, Issue 4: 1089-1110. Doi: 10.3934/jimo.2015.11.1089

This issue Previous Article Comparative analysis of supply chain financing strategies between different financing modes Next Article Second order sufficient conditions for a class of bilevel programs with lower level second-order cone programming problem

An interactive MOLP method for solving output-oriented DEA problems with undesirable factors

1.
Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr 47651-61964
2.
Business Systems and Analytics Department, Lindback Distinguished Chair of Information Systems and Decision Sciences, La Salle University, Philadelphia, PA 19141, United States, Business Information Systems Department, Faculty of Business Administration and Economics, University of Paderborn, D-33098 Paderborn
3.
Department of Mathematics, University of Mazandaran, Babolsar 47416-95447

Received: April 2014

Revised: July 2014

Published: October 2015

Abstract / Introduction Related Papers Cited by

Abstract

Data Envelopment Analysis (DEA) and Multiple Objective Linear Programming (MOLP) are widely used for performance assessment in organizations. Although DEA and MOLP are similar in structure, DEA is used to assess and analyze past performance and MOLP is used to predict future performance. Several equivalence models between output-oriented DEA models and MOLP models have been proposed in the literature. However these models are not applicable to performance evaluation problems with undesirable outputs. We propose an interactive method for solving output-oriented DEA models with undesirable outputs. We show that the output-oriented BCC model of Seiford and Zhu [47] can be equivalently stated as the maximization of the minimum of several objectives over the production possibility set, which in turn is a scalarization of a multi-objective linear program. We then employ the well-known Zionts-Wallenius procedure to solve the multi-objective optimization problem. We present an example to demonstrate the applicability of the proposed method and exhibit the efficacy of the procedures and algorithms.

Keywords:

Mathematics Subject Classification: Primary: 90C05, 68M20; Secondary: 90C29.

Citation:

Related Papers

Cited by

References

[1]	R. Allen, A. Athanassopoulis, R. G. Dyson and E. Thanassoulis, Weights restrictions and value judgements in data envelopment analysis: Evolution, development and future directions, Annals of Operations Research, 73 (1997), 13-34.
[2]	A. Amirteimoori and S. Kordrostami, An alternative clustering approach: a DEA-based procedure, Optimization: A Journal of Mathematical Programming and Operations Research, 62 (2013), 227-240.doi: 10.1080/02331934.2011.585466.
[3]	J. Aparicio, J. L. Ruiz and I. Sirvent, Closest targets and minimum distance to the Pareto-efficient frontier in DEA, Journal of Productivity Analysis, 28 (2007), 209-218.doi: 10.1007/s11123-007-0039-5.
[4]	M. Asmild, J. C. Paradi, D. N. Reese and F. Tam, Measuring overall efficiency and effectiveness using DEA, European Journal of Operational Research, 178 (2007), 305-321.doi: 10.1016/j.ejor.2006.01.014.
[5]	R. D. Banker, A. Charnes and W. W. Cooper, Some models for estimating technical and scale inefficiencies in data envelopment analysis, Management Science, 30 (1984), 1078-1092.doi: 10.1287/mnsc.30.9.1078.
[6]	C. P. Barros, S. Managi and R. Matousek, The technical efficiency of Japanese banks: Non radial directional performance measurement with undesirable output, Omega, 40 (2012), 1-8.doi: 10.1016/j.omega.2011.02.005.
[7]	G. Bi, J. Ding, Y. Luo and L. Liang, Resource allocation and target setting for parallel production system based on DEA, Applied Mathematical Modelling, 35 (2011), 4270-4280.doi: 10.1016/j.apm.2011.02.048.
[8]	R. Benayoun, J. Montgolfier, J. Tergny and O. Laritchev, Linear programming with multiple objective functions: Step method (STEM), Mathematical Programming, 1 (1971), 366-375.doi: 10.1007/BF01584098.
[9]	A. Charnes, W. W. Cooper and E. Rhodes, Measuring the efficiency of decision making units, European Journal of Operational Research, 2 (1978), 429-444.doi: 10.1016/0377-2217(78)90138-8.
[10]	A. Charnes, W. W. Cooper, Z. M. Huang and D. B. Sun, Polyhedral cone-ratio DEA models with an illustrative application to large commercial banks, Journal of Econometrics, 46 (1990), 73-91.doi: 10.1016/0304-4076(90)90048-X.
[11]	R. G. Dyson and E. Thannassoulis, Reducing weight flexibility in data envelopment analysis, Journal of Operational Research Society, 39 (1988), 563-576.doi: 10.2307/2582861.
[12]	A. Ebrahimnejad, A new link between output-oriented BCC model with fuzzy data in the present of undesirable outputs and MOLP, Fuzzy Information and Engineering, 3 (2011), 113-125.doi: 10.1007/s12543-011-0070-0.
[13]	A. Ebrahimnejad, R. Shahverdi, F. Rezai Balf and M. Hatefi, Finding target units in FDH model by least-distance measure model, Measurement, 49 (2013), 619-635.
[14]	A. Ebrahimnejad, M. Tavana, F. Hosseinzadeh Lotfi, R. Shahverdi and M. Yousefpour, A three-stage data envelopment analysis model with application to banking industry, Measurement, 49 (2014), 308-319.doi: 10.1016/j.measurement.2013.11.043.
[15]	A. Ebrahimnejad and M. Tavana, An interactive MOLP method for identifying target units in Output-Oriented DEA models: The NATO enlargement problem, Measurement, 52 (2014), 124-134.doi: 10.1016/j.measurement.2014.03.016.
[16]	M. Ehrgott, Multicriteria Optimization, $2^{nd}$ edition, Springer, Berlin, 2005.
[17]	R. Fare and S. Grosskopf, Modelling undesirable factors in efficiency evaluation: Comment, European Journal of Operational Research, 157 (2004), 242-245.doi: 10.1016/S0377-2217(03)00191-7.
[18]	R. Fare, S. Grosskopf, C. A. K. Lovell and C. Pasurka, Multilateral productivity comparisons when some outputs are undesirable: A nonparametric approach, The Review of Economics and Statistics, 71 (1989), 90-98.doi: 10.2307/1928055.
[19]	R. Fare, S. Grosskopf and C. Pasurka, Accounting for air pollution emissions in measures of state manufacturing productivity growth, Journal of Regional Science, 41 (2001), 381-409.doi: 10.1111/0022-4146.00223.
[20]	A. M. Geoffrion, J. S. Dyer and A. Feinberg, An interactive approach for multi-criterion optimization with an application to the operation of an academic department, Part I, Management Science, 19 (1972), 357-368.
[21]	B. Golany, An interactive MOLP procedure for the extension of DEA to effectiveness analysis, Journal of the Operational Research Society, 39 (1988), 725-734.doi: 10.2307/2583767.
[22]	M. A. Hinojosa and A. M. Mármol, Axial solutions for multiple objective linear problems. An application to target setting in DEA models with preferences, Omega, 39 (2011), 159-167.doi: 10.1016/j.omega.2010.06.001.
[23]	F. Hosseinzadeh Lotfi, G. R. Jahanshaloo, A. Ebrahimnejad, M. Soltanifar and S. M. Manosourzadeh, Target setting in the general combined-oriented CCR model using an interactive MOLP method, Journal of Computational and Applied Mathematics, 234 (2010), 1-9.doi: 10.1016/j.cam.2009.11.045.
[24]	F. Hosseinzadeh Lotfi, G. R. Jahanshaloo, M. Soltanifar, A. Ebrahimnejad and S. M. Manosourzadeh, Relationship between MOLP and DEA based on output-orientated CCR dual model, Expert Systems with Applications, 37 (2010), 4331-4336.doi: 10.1016/j.eswa.2009.11.066.
[25]	H. H. Hu, Q. Qi and C. H. Yang, Evaluation of China's regional hospital efficiency: DEA approach with undesirable output, Journal of the Operational Research Society, 63 (2011), 715-725.doi: 10.1057/jors.2011.77.
[26]	Z. S. Hua, Y. W. Bian and L. Liang, Eco-efficiency analysis of paper mills along the Huai River: An extended DEA approach, Omega, 35 (2007), 578-587.doi: 10.1016/j.omega.2005.11.001.
[27]	X. Huang, D. Hu and Z. Zhou, Measuring efficiency in Chinese commercial banks using a DEA model with undesirable output, International Journal of Information and Decision Sciences, 5 (2013), 140-153.doi: 10.1504/IJIDS.2013.053801.
[28]	S. Jain, K. P. Triantis and S. Liu, Manufacturing performance measurement and target setting: A data envelopment analysis approach, European Journal of Operational Research, 214 (2011), 616-626.doi: 10.1016/j.ejor.2011.05.028.
[29]	A. Jess, H. Th. Jongen, L. Neralic and O. Stein, A semi-infinite programming model in data envelopment analysis, European Journal of Operational Research, 49 (2001), 369-385.doi: 10.1080/02331930108844538.
[30]	P. J. Korhonen and M. Luptacik, Eco-efficiency analysis of power plants: an extension of data envelopment analysis, European Journal of Operational Research, 154 (2004), 437-446.doi: 10.1016/S0377-2217(03)00180-2.
[31]	P. Korhonen, S. Stenfors and M. Syrjänen, Multiple objective approach as an alternative to radial projection in DEA, Journal of Productivity Analysis, 20 (2003), 305-321.
[32]	S. Kumar Mandal and S. Madheswaran, Environmental efficiency of the Indian cement industry: An interstate analysis, Energy Policy, 38 (2010), 1108-1118.
[33]	H. F. Lewis and T. R. Sexton, Data envelopment analysis with reverse inputs and outputs, Journal of Productivity Analysis, 21 (2004), 113-132.doi: 10.1023/B:PROD.0000016868.69586.b4.
[34]	Y. Liu and U. R. Sumaila, Estimating pollution abatement costs of salmon aquaculture: A joint production approach, Land Economics, 86 (2010), 569-584.
[35]	C. A. K. Lovell, J. T. Pastor and J. A. Turner, Measuring macroeconomic performance in the OECD: A comparison of European and non-European countries, European Journal of Operational Research, 87 (1995), 507-518.
[36]	S. Lozano and E. Gutierrez, Efficiency analysis and target setting of Spanish airports, Netw. Spat. Econ., 11 (2011), 139-157.doi: 10.1007/s11067-008-9096-1.
[37]	W. M. Lu and S. F. Lo, A closer look at the economic-environmental disparities for regional development in China, European Journal of Operational Research, 183 (2007), 882-894.doi: 10.1016/j.ejor.2006.10.027.
[38]	M. Mahdiloo, A. Noorizadeh and R. Farzipoor Saen, Developing a new data envelopment analysis model for customer value analysis, Journal of Industrial and Management Optimization, 7 (2011), 531-558.doi: 10.3934/jimo.2011.7.531.
[39]	N. Malekmohammadi, F. Hosseinzadeh Lotfi and A. B. Jaafar, Target setting in data envelopment analysis using MOLP, Applied Mathematical Modelling, 35 (2011), 328-338.doi: 10.1016/j.apm.2010.06.007.
[40]	H. Nakayama and Y. Sawaragi, Satisficing trade-off method for multiobjective programming. An interactive decision analysis, in Lecture notes in economics and mathematical systems (eds. M. Grauer and A.P. Wierzbicki), Laxenburg: Springer, 229 (1984), 113-122.doi: 10.1007/978-3-662-00184-4_13.
[41]	F. Pedraja-Chaparro, J. Salinas-Jimenez and P. Smith, On the role of weight restrictions in data envelopment analysis, Journal of Productivity Analysis, 8 (1997), 215-230.
[42]	V. V. Podinovski, Suitability and redundancy of non-homogeneous weight restrictions for measuring the relative efficiency in DEA, European Journal of Operational Research, 154 (2004), 380-395.doi: 10.1016/S0377-2217(03)00176-0.
[43]	S. Reinhard, C. A. K. Lovell and G. Thijssen, Environmental efficiency with multiple environmentally detrimental variables; estimated with SFA and DEA, European Journal of Operational Research, 121 (2000), 287-303.doi: 10.1016/S0377-2217(99)00218-0.
[44]	S. Reinhard and G. Thijssen, Nitrogen efficiency of Dutch dairy farms: A shadow cost system approach, European Review of Agricultural Economics, 27 (2000), 167-186.doi: 10.1093/erae/27.2.167.
[45]	R. Riccardi, G. Oggioni and R. Toninelli, Efficiency analysis of world cement industry in presence of undesirable output: Application of data envelopment analysis and directional distance function, Energy Policy, 44 (2012), 140-152.doi: 10.1016/j.enpol.2012.01.030.
[46]	S. Saati, A. Hatami-Marbini, P. J. Agrell and M. Tavana, A common set of weight approach using an ideal decision making unit in data envelopment analysis, Journal of Industrial and Management Optimization, 8 (2012), 623-637.doi: 10.3934/jimo.2012.8.623.
[47]	M. Seiford and J. Zhu, Modeling undesirable factors in efficiency evaluation, European Journal of Operational Research, 142 (2002), 16-20.doi: 10.1016/S0377-2217(01)00293-4.
[48]	S. Shaik, G. A. Helmers and M. R. Langemeier, Direct and indirect shadow price and cost estimates of nitrogen pollution abatement, Journal of Agricultural and Resource Economics, 27 (2002), 420-432.
[49]	T. Sueyoshi and M. Goto, Data envelopment analysis for environmental assessment: Comparison between public and private ownership in petroleum industry, European Journal of Operational Research, 216 (2012), 668-678.doi: 10.1016/j.ejor.2011.07.046.
[50]	E. Thanassoulis, A. Boussofiane and R. G. Dyson, Exploring output quality targets in the provision of perinatal care in England using data envelopment analysis, European Journal of Operational Research, 80 (1995), 588-607.doi: 10.1016/0377-2217(94)00139-4.
[51]	R. G. Thompson, P. S. Dharmapala and R. M. Thrall, Linked-cone DEA profit ratios and technical efficiency with application to Illinois coal mines, International Journal of Production Economics, 39 (1995), 99-115.doi: 10.1016/0925-5273(94)00064-H.
[52]	R. G. Thompson, L. N. Langemeier, C. T. Lee and R. M. Thrall, The role of multiplier bounds in efficiency analysis with application to Kansas farming, Journal of Econometrics, 46 (1990), 93-108.doi: 10.1016/0304-4076(90)90049-Y.
[53]	R. G. Thompson, F. D. Singleton Jr, R. M. Thrall and B. A. Smith, Comparative site evaluations for locating a high-energy physics lab in Texas, Interfaces, 16 (1986), 35-49.doi: 10.1287/inte.16.6.35.
[54]	K. Tone, On returns to scale under weight restrictions in data envelopment analysis, Journal of Productivity Analysis, 16 (2001), 31-47.
[55]	A. P. Wierzbick, The use of reference objectives in multiobjective optimization, in Multiple criteria decision making theory and application. Lecture notes in economics and mathematics systems (eds. G. Fandel and T. Gal), Heidelberg: Springer, (1980), 468-486.
[56]	Y. H. B. Wong and J. E. Beasley, Restricting weight flexibility in data envelopment analysis, Journal of the Operational Research Society, 41 (1990), 829-835.doi: 10.2307/2583498.
[57]	H. Yang and M. Pollitt, Incorporating both undesirable outputs and uncontrollable variables into DEA: The performance of Chinese coal-fired power plants, European Journal of Operational Research, 197 (2009), 1095-1105.doi: 10.1016/j.ejor.2007.12.052.
[58]	J. B. Yang, B. Y. H. Wong, D. L. Xu and T. J. Stewart, Integrating DEA-oriented performance assessment and target setting using interactive MOLP methods, European Journal of Operational Research, 195 (2009), 205-222.doi: 10.1016/j.ejor.2008.01.013.
[59]	J. B. Yang, B. Y. H. Wong, D. L. Xu, X. B. Liu and R. E. Steuer, Integrated bank performance assessment and management planning using hybrid minimax reference point DEA approach, European Journal of Operational Research, 207 (2010), 1506-1518.doi: 10.1016/j.ejor.2010.07.001.
[60]	J. B. Yang and D. L. Xu, Interactive minimax optimisation for integrated performance analysis and resource planning, Computers and Operations Research, 46 (2014), 78-90.doi: 10.1016/j.cor.2014.01.002.
[61]	J. B. Yang, D. L. Xu and S. Yang, Integrated efficiency and trade-off analyses using a DEA-oriented interactive minimax reference point approach, Computers and Operations Research, 39 (2012), 1062-1073.doi: 10.1016/j.cor.2011.07.001.
[62]	S. You and H. Yan, A new approach in modelling undesirable output in DEA model, Journal of the Operational Research Society, 62 (2011), 2146-2156.doi: 10.1057/jors.2011.1.
[63]	M. M. Yu, Measuring physical efficiency of domestic airports in Taiwan with undesirable outputs and environmental factors, Journal of Air Transport Management, 10 (2004), 295-303.doi: 10.1016/j.jairtraman.2004.04.001.
[64]	S. Zionts and J. Wallenius, An interactive programming method for solving the multiple criteria problem, Management Science, 22 (1976), 652-663.doi: 10.1287/mnsc.22.6.652.
[65]	P. Zhou, P. W. Ang and K. L. Poh, Measuring environmental performance under different environmental DEA technologies, Energy Economics, 30 (2008), 1-14.doi: 10.1016/j.eneco.2006.05.001.