Controlling Desirable Outputs and Pollutants Using a Multi-Objective Function in an Inverse-DEA Model
الموضوعات : International Journal of Data Envelopment Analysis
1 - گروه ریاضی، واحد گرگان، دانشگاه آزاد اسلامی، گرگان ، ایران
الکلمات المفتاحية: Data Envelopment analysis, Undesirable outputs, Invers DEA. ,
ملخص المقالة :
Inverse Data Envelopment Analysis (DEA) is a mathematical technique for assessing relative efficiencies of homogeneous decision-making units (DMUs) based on multiple inputs to multiple outputs. Inverse DEA is an emerging theoretical and methodological technique continuously evolving and substantially impacting operations research, economics, and efficiency analyses. It has emerged as a valuable post-DEA sensitivity analysis approach for resource allocation and efficiency optimization. In this article, the Slacks-Based Measure (SBM) DEA model has been developed to address limitations in traditional DEA models, particularly in evaluating environmental efficiency and undesirable outputs in various applications, including environmental policy analysis and performance assessment of organizations. In the first objective, the issue of minimizing the increase in inputs is addressed while also taking into account the minimum increase in undesirable output. Hence, the models previously presented in this article attempt to control the increase of inputs and possibly reduce them by considering a multi-objective function.
1. Allen, R. D., et al. (1993). Application of DEA to Higher Education Institutions. Journal of the Operational Research Society, 44(6), 567-578.
2. Adimi, I., et al. (2020). A study on efficiency frontiers and their sensitivity to external constraints. Journal of Operational Research, 35(4), 122-133.
3. Bolós, V., et al. (2022). Issues with SBM Super-Efficiency Models: A Composite SBM Score Approach. European Journal of Operational Research, 274(2), 560-573.
4. Castro, R., & Resón, M. (2015). Establishing Economic Attributes using Inverse DEA. Operations Research Letters, 43(3), 262-273.
5. Emrouznejad, A., et al. (2023). Advancements in Inverse DEA for Resource Allocation and Efficiency Optimization. Journal of Operations Management, 49(5), 68-81.
6. Hosseininia, M., & Saen, R. F. (2020). A Novel Inverse SBM DEA Model with Linear Programming Solution for Multi-Objective Non-Linear Problems. Computational and Applied Mathematics, 44(2), 123-138.
7. Hosseinzadeh Lotfi, F., et al. (2023). DEA-R Models without Explicit Inputs: A Comparative Analysis. Journal of Economic Computation and Economic Cybernetics Studies and Research, 57(4), 191-208.
8. Lim, M. (2016). An Inverse DEA Method for Setting New Product Targets. Operations Research Letters, 44(2), 141-150.
9. Mahla, K., & Agarwal, A. (2021). Fuzzy SBM DEA Model Using Credibility Measure Approach for Uncertain Data. International Journal of Industrial Engineering Computations, 12(3), 219-232.
10. Song, M., et al. (2013). Improved SBM-DEA Model for Accounting Undesirable Outputs. Computers and Operations Research, 40(9), 2407-2415.
11. Wu, Y. (2010). The Improved SBM-DEA Model for Environmental Efficiency. Environmental and Ecological Statistics, 17(4), 345-358.
12. Younesi, S., & Hosseinzadeh Lotfi, F. (2023). Inverse DEA Based on Non-Radial Slacks-Based Model with Uncertainty. Journal of Computational and Applied Mathematics, 44(2), 159-172.
13. Zhang, S., & Cui, M. (2020). Non-Radial Inverse SBM DEA Models for Comprehensive Decision-Making. Omega, 92, 31-43.
14. Wegener, D., & Amin, A. (2019). Evaluating the Performance of Units Using the Directional Distance DEA Model. Journal of Operational Research, 58(4), 102-116.
