Performance Analysis and Calculation of Marginal Rates in the Presence of Undesirable Input-output Factors and Non-Discretionary Indexes

Document Type : Research Paper

Authors

1 Ph.D. Candidate, Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran.

2 Prof., Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran.

3 Prof., Department of Applied Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran.

4 Assistant Prof., Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran.

Abstract

Objective: In many production processes, the efficiency of decision-making units should be investigated in the presence of undesirable inputs and outputs and non-discretionary factors. It is also important for managers to examine the impact of changes on one index on another. Therefore, the purpose of this paper is to develop an approach to estimate the efficiency of systems with undesirable inputs and outputs and non-discretionary measures and also to analyze changes.
Methods: First, a novel approach based on data envelopment analysis was presented in order to analyze efficiency in the presence of undesirable input-output indices and non-discretionary factors. In fact, the new weak disposability axiom was used and the efficiency of the systems was investigated in the presence of undesirable input-output index and non-discretionary factors. Then the impact of changes of one non-discretionary index on another index was measured by maintaining efficiency, and the marginal rates of these changes were calculated.
Results: In order to explain the proposed method in practice, an applied example provided based on 31 branches of Islamic Azad University (department of education) was presented and the results were discussed and analyzed. By using the suggested method, the efficiency scores and the impact of modifications were obtained.
Conclusion: Performance scores related to branches indicated that most of them behaved well. Also, it was observed that always increasing (decreasing) one index, while maintaining efficiency, does not end in an increase (decrease) in another index but it may remain unchanged or decreased (increased). Due to the inclusion of undesirable input and output measures and non-discretionary factors, the results of the proposed method were more acceptable than the classical DEA models.

Keywords

References

Amirteimoori, A., Maghbouli, M. & Kordrostami, S. (2016). Multi- dimensional Nondiscretionary Factors in Data Envelopment Analysis: A Slack-Based Measure. Computational Economics, 48(2), 211-223.
Banker, R.D., Morey, R.C. (1986). Efficiency Analysis for Exogenously Fixed Inputs and Outputs. Operations Research, 34(4), 513-521.
Banker, RD. & Morey, RC. (1986). The Use of Categorical Variables in Data Envelopment Analysis. Manage Sci. 1613-1627.
Banker, RD., Charnes, A. & Cooper, W.W. (1984). Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis. Manage Sci. 30(9), 1078-1092.
Camanho, A.S., Portela, M.C. & Vaz, C.B. (2009). Efficiency analysis accounting for internal and external non-discretionary factors. Computers & Operations Research, 36(5), 1591-1601.
Charnes, A., Cooper, W.W. & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2(6), 429-444.
Cooper, W.W., Park, D.K.S. & Ciurana, P.J.T.P. (2000). Marginal Rates and Elasticities of Substitution with Additive Models in DEA. J Product Anal., 13(2), 105-123.
Ebrahimi Kordlar, A., Jafarzadeh, A., Aliahmadi, M.H. (2018). Proposing a Model of Efficiency Evaluation Based on the Adjusted Range Measurement Model and Weight Restrictions (Case Study: Branches of Iran Insurance Company). Industrial Management Journal, 10(2), 161- 182. (in Persian)
Färe, R. & Grosskopf, S. (2004). Modeling undesirable factors in efficiency evaluation. European Journal of Operational Research, 157(1), 242-245.
Farrell, M.J. (1957). The Measurement of Productive Efficiency. Journal of the Royal Statistical Society: Series A (General), 120(3), 253.
Hadi Vencheh, A., Kazemi Matin R., & Tavassoli Kajani, M. (2005) Undesirable factors in efficiency measurement. Applied Mathematics and Computation,163(2), 547-552.
Hailu, A. & Veeman, TS.(2001). Non-parametric Productivity Analysis with Undesirable Outputs: An Application to the Canadian Pulp and Paper Industry. Am J Agric Econ. 83(3), 605-616.
Jahani Sayyad Noveiri, M., & Kordrostami, S. (2020). Trade-offs analysis of sustainability dimensions using integer-valued DEA. Croatian Operational Research Review, 11(2), 275-289.
Jahanshahloo, G.R., Lotfi, F.H., Shoja, N., Tohidi, G., & Razavyan, S. (2005). Undesirable inputs and outputs in DEA models. Applied Mathematics and Computation, 169(2), 917-925.
Kazemi Matin, R., & Azizi, R. (2012). Modeling Non-Discretionary Factors In Efficiency Measurement Of The Iranian Regional Electricity Companies. Iranian Electric Industry Journal of Quality And Productivity (IEIJQP), 1(1), 57-63. (in Persian)
Khoshandam, L., Amirteimoori, A. & Matin, R.K. (2014). Marginal rates of substitution in the presence of non-discretionary factors: A data envelopment analysis approach. Measurement, 58, 409-415.
Khoshandam, L., Kazemi Matin, R., & Amirteimoori, A. (2015). Marginal rates of substitution in data envelopment analysis with undesirable outputs: A directional approach. Measurement, 68, 49-57.
Kuosmanen, T. (2005). Weak Disposability in Nonparametric Production Analysis with Undesirable Outputs. American Journal of Agricultural Economics, 87(4), 1077-1082.
Lovell, C.A., Knox, L. (1994). Linear programming approaches to the measurement and analysis of productive efficiency. Top 2(2), 175-248.
Mahboubi, M., Kordrostami, S., Amirteimoori, A., & Ghane-Kanafi, A. (2021). Estimating Marginal Rates of Substitution in Two-Stage Processes with Undesirable Factors. Iranian Journal of Management Studies,14(2), 419-436.
Mahboubi, M., Kordrostami, S., Amirteimoori, A., & Ghane-Kanafi, A. (2021). Undesirable factors and marginal rates of substitution in Data Envelopment Analysis. Mathematical Sciences, 16, 1-13.
Mohaghar, A., Safari, H., Amirteimoori, A. R., Soufi, M. A. (2016). New Data Envelopment Analysis Model for Efficiency Measurement of Decision Making Units with Parallel Network Structure. Journal of Operational Research in Its Applications, 13 (3), 9-26. (in Persian)
Muñiz, M., Paradi, J., Ruggiero, J., & Yang, Z.(2006). Evaluating alternative DEA models used to control for non-discretionary inputs. Computers & Operations Research, 33(5), 1173-1183.
Radsar, M., Kazemi, A., Mehregan, M. & Razavi Hajiagha, S.H. (2021). Designing an algorithm based on network data envelopment analysis with desirable and undesirable indicators for the evaluation of the Iranian power industry. Industrial Management Journal, 13(1), 1-26. (in Persian)
Ramzaniyan, M.R., Yakideh, K. & Mohammadi Bazghaleh, N. (2020). Providing an Appropriate Model for Improving Multi-Criteria Inventory Classification Using SBM Model (Case Study: Pars Khazar Industrial Company). Industrial Management Journal, 12(3), 485-501. (in Persian)
Rosen, D., Schaffnit, C., & Paradi, J.C. (1998). Marginal Rates and Two-dimensional Level Curves in DEA. Journal of Productivity Analysis, 9(3), 205-232.
Ruggiero, J.(1996). On the measurement of technical efficiency in the public sector. European Journal of Operational Research, 90(3), 553-565.
 Ruggiero, J. (1998) Non-discretionary inputs in data envelopment analysis. European Journal of Operational Research, 111(3), 461-469.
Ruggiero, J. (2004). Performance evaluation when non-discretionary factors correlate with technical efficiency. European Journal of Operational Research, 159(1), 250-257.
Seiford, L.M., & Zhu, J. (2002). Modeling undesirable factors in efficiency evaluation. European Journal of Operational Research, 142(1), 16-20.
Sueyoshi, T., & Goto M.(2012). Returns to Scale, Damages to Scale, Marginal Rate of Transform and Rate of Substitution in DEA Environmental Assessment. Energy Econ. 34(4), 905-917.
Syrjänen, M.J. (2004). Non-discretionary and discretionary factors and scale in data envelopment analysis. European Journal of Operational Research, 158(1), 20-33.
Industrial Management Journal
Volume 13, Issue 3
2022
Pages 492-513

Files

Share

How to cite

Statistics