Inputs and Outputs Estimation in Inverse DEA

Iranian Journal of Optimization

مقاله 12، دوره 9، شماره 2، اسفند 2017، صفحه 119-129   

نوع مقاله: Research Paper

نویسنده

Saeid Ghobadi^*

Islamic azad university-khomeinishahr-Isfahan

چکیده

The present study addresses the following question: if among a group of decision making units, the decision maker is required to increase inputs and outputs to a particular unit in which the DMU, with respect to other DMUs, maintains or improves its current efficiency
level, how much should the inputs and outputs of the DMU increase? This question is considered as a problem of inverse data envelopment analysis, and a method is introduced to
answer this question. Using (weak) pareto solutions of multiple-objective linear programming, necessary and sufficient conditions for inputs and outputs estimation are established.
An application of inverse DEA using real data (for choosing a suitable strategy for spreading educational departments in a university) is presented. In addition, two new optimal notions are introduced for multiple-objective programming problems: semi-pareto and semi-weak pareto optimal notions. The aforementioned solutions are used to answer the above question.

کلیدواژه‌ها

Data Envelopment Analysis (DEA)؛ Efficiency؛ Inverse DEA؛ Multiple-Objective Linear Programming (MOLP)؛ (Weak) Pareto Solution؛ Semi-(Weak)Pareto Solution

مراجع

Banker, R. D., Charnes, A., and Cooper, W. W. (1984). Some models for estimating technical and scale efficiencies in data envelopment analysis, Management Science 30, 1078-1092.

Charnes, A.,  Cooper, W. W., and  Rhodes, E. (1978). Measuring the efficiency of decision making units, European Journal of Operational Research 2,  429-444.

Cook, W. D. and  Seiford, L. M. (2009). Data envelopment analysis (DEA)-Thirtyyears on. European Journal of Operational Research 192, 1-17.

Cooper, W. W.,  Seiford, L. M., and  Tone, K. (1999).} DataEnvelopment Analysis: A Comprehensive Text With Models,Applications, References and DEA-Solver Software. Kluwer AcademicPublisher.

Ehrgott, M. (2005).}  Multi criteria Optimization,  Springer.

Fare, R. and  Grosskopf, S. (1985).} A nonparametric costapproach to scale efficiency. Scandinavian Journal of Economics 87, 594-604.

Gattoufi, S.,  Amin, G. R., and  Emrouznejad, E. (2012). A new inverse DEA methodfor merging banks. IMA Journal of Management Mathematics  1-15.

Ghobadi, S. and  Jahangiri, S. (2015). Inverse DEA: review,extension and application. International Journal of Information Technology and Decision Making,14, 805-824.

Golany, B. (1988).} An interactive MOLP procedure for the extension ofDEA to effectiveness analysis. Journal of the Operational ResearchSociety 39,  725-734.

Hadi-Vencheh, A. and  Foroughi, A. A. (2006). A generalized DEA model for inputs/outputsestimation, Mathematical and Computer Modelling, 43, 447-457.

Hadi-Vencheh, A.,  Foroughi, A. A., and Soleimani-damaneh, M. (2008). {A DEA model for resourceallocation}, Economic Modelling, 25 (5) 983-993.

Hatami-Marbini, A., Emrouznejad, A., and  Tavana, M. (2011). A taxonomy and review of the fuzzydata envelopment analysis literature: Two decades in the making,European Journal of Operational Research 214, 457-472.

Hosseinzadeh Lotfi, F., Jahanshaloo, G. R., Ebrahimnejad, A., Soltanifar, M.  and Manosourzadeh, S. M. ( 2010b).  Relationship between MOLP and DEA basedon output orientated CCR dual model. Expert  Systems withApplications 37, 4331-4336.

HosseinzadehLotfi, F., Jahanshaloo, G. R., Ebrahimnejad, A., Soltanifar, M.  andManosourzadeh, S. M. ( 2010a).  Target setting in the generalcombined-oriented CCR model using an interactive MOLP method.Journal of Computational and Applied Mathematics 234, 1-9.

Isermann, H. (1977). The enumeration of the set of all efficientsolutions for a linear multiple objective program. OperationalResearch Quarterly 28, 711-725.

Jahanshahloo, G. R.,  Hadi-Vencheh, A.,   Foroughi, A. A., and KazemiMatin, R. (2004a). Inputs/outputs estimation in DEA when some factors areundesirable. Applied Mathematics and Computation 156, 19-32.

Jahanshahloo, G. R.,  Hosseinzadeh Lotfi, F.,  Rostamy- Malkhalifeh, M., and  ghobadi, S. (2014).Using Enhanced Russell Model to Solve Inverse DataEnvelopment Analysis Problems. Hindawi Publishing Corporation, The Scientific World Journal, doi:10.1155/571896.

Jahanshahloo, G. R.,  Hosseinzadeh Lotfi, F.,  Shoja, N.,Tohidi, G., and  Razavyan, S. (2004b). Input estimation and identification of extrain  inverse DEA models. Applied Mathematics and Computation 156,  427-437.

Jahanshahloo, G. R.,  HosseinzadehLotfi, F.,  Shoja, N.,Tohidi, G., and  Razavyan, S. (2005). Sensitivity of efficiency classificationsin the inverse DEA models. Applied Mathematics and Computation 169,  905-916.

Jahanshahloo, G. R.,  Soleimani-damaneh, M., and ghobadi, S. (2015). Inverse DEA under inter-temporal dependence using multiple-objective programming. European Journal of Operational Research , 240, 447-456.

Joro, R.,  Korhonen, P., and  Zionts, S. (2003).} An interactive approach toimprove estimates of value efficiency in data envelopmentanalysis. European Journal of Operations Research 149, 688-699.

Lertworasirikul, S.,  Charnsethikul, P., and  Fang, S. C. (2011). Inverse data envelopment analysis model topreserve relative efficiency values: The case of variable returnsto scale. Computers and Industrial Engineering 61, 1017-1023.

 Lin, H. T. (2010). An effficiency-driven approach for setting revenuetarget, Decision Support Systems 49, 311-317.

Lins, M. P. E.,  Angulo-Meza, L.,  and   da Silva, A. C. M. (2004).A multi-objective approach to determine alternative targets in data envelopment analysis. Journal of the Operational Research Society, 55, 1090-1101.

Luque, M.  and Yang, J. B. (2009).} Using interactivemultiobjective methods to solve DEA problems with value judgements. Computers and Operations Research 36,623-636.

Quariguasi Frota Neto, J. and Angulo-Meza, L., (2007).Alternative targets for data envelopment analysis through multi-objective linear programming: Rio de Janeiro Odontological Public Health System Case Study. Journal of the Operational  Research Society, 58, 865-873.

Seiford, L. M. and Thrall, R. M. (1990).} Recent developments in DEA, the mathematical programmingapproach to frontier analysis. Journal of Econometrics 46,7-38.

Steuer, R. E. (1986). Multiple Criteria Optimization:Theory, Computation, and Application. Wiley, New York.

Thanassoulis, E. and   Allen, R. (1998). Simulating weights restrictions indata envelopment analysis by means of unobserved DMUs. ManagementScience 44, 586-594.

Wei, Q. L. and   Yu, G. (1997).} Analysis the properties of K-cone in generalized data envelopmentanalysis model, Journal of Economic 80, 63-84.

 Wei, Q. L.,  Zhang, J., and  Zhang, X. (2000). An inverse DEAmodel for input/output estimate, European Journal of OperationalResearch 121 (1)  151-163.

 Yan, H.,  Wei, Q., and  Hao, G. (2002).  DEA models for resourcereallocation and production input/output estimation. EuropeanJournal of Operational Research 136, 19-31.

 Yang, J. B.,  Wong, B. Y. H., Xu, D. L., and   Stewart, T. J.  (2009). IntegratingDEA-oriented performance assessment and target setting usinginteractive MOLP methods. European Journal of OperationsResearch 195, 205-222.

Yu, G.,   Wei, Q. L., and Brockett, P. (1996). A generalized data envelopmentanalysis model:A unification and extension of existing methods  for efficiencyanalysis of decision making units, Annals of Operational Research 66, 47-89.

 Zhang, X. S. and Cui, J. C., (1999). A project evaluation system in thestate economic information system of china an operations research practice in public sectors. International Transactions in Operational Research, 6, 441-452.