Using Enhanced Russell Model to Solve Inverse Data Envelopment Analysis Problems

This paper studies the inverse data envelopment analysis using the nonradial enhanced Russell model. Necessary and sufficient conditions for inputs/outputs determination are introduced based on Pareto solutions of multiple-objective linear programming. In addition, an approach is investigated to identify extra input/lack output in each of input/output components (maximum/minimum reduction/increase amounts in each a of input/output components). In addition, the following question is addressed: if among a group of DMUs, it is required to increase inputs and outputs to a particular unit and assume that the DMU maintains its current efficiency level with respect to other DMUs, how much should the inputs and outputs of the DMU increase? This question is discussed as inverse data envelopment analysis problems, and a technique is suggested to answer this question. Necessary and sufficient conditions are established by employing Pareto solutions of multiple-objective linear programming as well.

[1]  Jesús T. Pastor,et al.  An enhanced DEA Russell graph efficiency measure , 1999, Eur. J. Oper. Res..

[2]  Jian-Bo Yang,et al.  Integrating DEA-oriented performance assessment and target setting using interactive MOLP methods , 2009, Eur. J. Oper. Res..

[3]  Lawrence M. Seiford,et al.  Recent developments in dea : the mathematical programming approach to frontier analysis , 1990 .

[4]  Xiang-Sun Zhang,et al.  A project evaluation system in the state economic information system of China , 1999 .

[5]  Jianzhong Zhang,et al.  An inverse DEA model for inputs/outputs estimate , 2000, Eur. J. Oper. Res..

[6]  Ali Asghar Foroughi,et al.  A generalized DEA model for inputs/outputs estimation , 2006, Math. Comput. Model..

[7]  Adel Hatami-Marbini,et al.  A taxonomy and review of the fuzzy data envelopment analysis literature: Two decades in the making , 2011, Eur. J. Oper. Res..

[8]  Shabnam Razavyan,et al.  The outputs estimation of a DMU according to improvement of its efficiency , 2004, Appl. Math. Comput..

[9]  A. Hadi-Vencheh,et al.  A DEA model for resource allocation , 2008 .

[10]  Emmanuel Thanassoulis,et al.  Simulating Weights Restrictions in Data Envelopment Analysis by Means of Unobserved Dmus , 1998 .

[11]  Lawrence M. Seiford,et al.  Data envelopment analysis (DEA) - Thirty years on , 2009, Eur. J. Oper. Res..

[12]  Hung-Tso Lin,et al.  An efficiency-driven approach for setting revenue target , 2010, Decis. Support Syst..

[13]  Boaz Golany,et al.  An Interactive MOLP Procedure for the Extension of DEA to Effectiveness Analysis , 1988 .

[14]  Jian-Bo Yang,et al.  Using interactive multiobjective methods to solve DEA problems with value judgements , 2009, Comput. Oper. Res..

[15]  W. Cooper,et al.  Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software , 1999 .

[16]  Ali Ebrahimnejad,et al.  Target setting in the general combined-oriented CCR model using an interactive MOLP method , 2010, J. Comput. Appl. Math..

[17]  A. Charnes,et al.  Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis , 1984 .

[18]  A. U.S.,et al.  Measuring the efficiency of decision making units , 2003 .

[19]  Hong Yan,et al.  DEA models for resource reallocation and production input/output estimation , 2002, Eur. J. Oper. Res..

[20]  R. Färe,et al.  Nonparametric Cost Approach to Scale Efficiency , 1985 .

[21]  Stanley Zionts,et al.  An interactive approach to improve estimates of value efficiency in data envelopment analysis , 2003, Eur. J. Oper. Res..

[22]  Shu-Cherng Fang,et al.  Inverse data envelopment analysis model to preserve relative efficiency values: The case of variable returns to scale , 2011, Comput. Ind. Eng..

[23]  Shabnam Razavyan,et al.  Input estimation and identification of extra inputs in inverse DEA models , 2004, Appl. Math. Comput..

[24]  Ali Ebrahimnejad,et al.  Relationship between MOLP and DEA based on output-orientated CCR dual model , 2010, Expert Syst. Appl..