Inverse Data Envelopment Analysis Model to Improve Efficiency by Increasing Outputs

Mohammad Taghi Yahyapour Shikhzahedi; Alireza Amirteimoori; Sohrab Kordrostami; Seyyed Ahmad Edalatpanah

doi:10.31181/dmame722024788

Authors

Mohammad Taghi Yahyapour Shikhzahedi Department of Mathematics, Lahijan Branch, Islamic Azad University Lahijan, Iran https://orcid.org/0000-0003-2522-7001
Alireza Amirteimoori Department of Applied Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran https://orcid.org/0000-0003-4160-8509
Sohrab Kordrostami Department of Mathematics, Lahijan Branch, Islamic Azad University Lahijan, Iran https://orcid.org/0000-0003-0081-8008
Seyyed Ahmad Edalatpanah Department of Applied Mathematics, Ayandegan Institute of Higher Education, Tonekabon, Iran https://orcid.org/0000-0002-1406-7068

DOI:

https://doi.org/10.31181/dmame722024788

Keywords:

Inverse data envelopment analysis (IDEA), Cost efficiency, Input estimation, Decision-making units (DMUs), Performance assessment

Abstract

Inverse Data Envelopment Analysis (IDEA) has gained significant attention among researchers as an analytical tool for assessing efficiency. Estimating input values while ensuring cost efficiency through changes in output quantities is complex and sensitive. In contrast to conventional data envelopment analysis methods, IDEA enables the quantification of input/output variations resulting from output/input reductions or expansions while preserving the measurement efficiency level. This paper aims to introduce a novel approach for estimating input values by incrementally increasing the value of each output of decision-making units (DMUs) during the evaluation process, thereby maintaining or improving cost efficiency. By utilizing IDEA and manipulating the output values of the DMU under evaluation, the input values are estimated while ensuring constant or enhanced cost efficiency. A simple numerical example and a case study from a Turkish automotive company are presented to validate the proposed method. The obtained results demonstrate significant improvements and hold promising prospects, indicating the potential applicability of this approach to other similar problems and research areas.

Downloads

Download data is not yet available.

References

Cooper, W.W., Seiford, L.M. & Tone, K. (2007). Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software. 2nd Edition, Springer, New York.

Charnes, A., Cooper, W.W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research. 2, 429–444. https://doi.org/10.1016/0377-2217(78)90138-8

Zhang, X.-S., & Cui, J.-C. (1999). A project evaluation system in the state economic information system of China An operations research practice in public sectors. International Transactions in Operational Research. 6, 441–452. https://doi.org/10.1111/j.1475-3995.1999.tb00166.x

Wei, Q., Zhang, J., & Zhang, X. (2000). An inverse DEA model for inputs/outputs estimate. European Journal of Operational Research. 121, 151–163. https://doi.org/10.1016/S0377-2217(99)00007-7

Yan, H., Wei, Q., & Hao, G. (2002). DEA models for resource reallocation and production input/output estimation. European Journal of Operational Research. 136, 19–31. https://doi.org/10.1016/S0377-2217(01)00046-7

Hadi-Vencheh, A., Foroughi, A. A., & Soleimani-damaneh, M. (2008). A DEA model for resource allocation. Economic Modelling, 25(5), 983-993. https://doi.org/10.1016/j.econmod.2008.01.003

Lertworasirikul, S., Charnsethikul, P., & Fang, S. C. (2011). Inverse data envelopment analysis model to preserve relative efficiency values: The case of variable returns to scale. Computers & Industrial Engineering, 61(4), 1017-1023.. https://doi.org/10.1016/j.cie.2011.06.014

Farrell, M. J. (1957). The measurement of productive efficiency. Journal of the Royal Statistical Society Series A: Statistics in Society, 120(3), 253-281. https://doi.org/10.2307/2343100

Fukuyama, H., Weber, W.L. (2002). Estimating output allocative efficiency and productivity change: Application to Japanese banks. European Journal of Operational Research. 137, 177–190. https://doi.org/10.1016/S0377-2217(01)00054-6

Lin, M. I., Lee, Y. D., & Ho, T. N. (2011). Applying integrated DEA/AHP to evaluate the economic performance of local governments in China. European journal of operational research, 209(2), 129-140. https://doi.org/10.1016/j.ejor.2010.08.006

Banihashem, S., Sanei, M., Mohamadian Manesh, Z. (2013). Cost, revenue and profit efficiency in supply chain. African Journal of Business Management. 7, 4280–4287.

Khodabakhshi, M., & Aryavash, K. (2014). The fair allocation of common fixed cost or revenue using DEA concept. Annals of Operations Research, 214, 187-194.. https://doi.org/10.1007/s10479-012-1117-2

Mozaffari, M. R., Kamyab, P., Jablonsky, J., & Gerami, J. (2014). Cost and revenue efficiency in DEA-R models. Computers & industrial engineering, 78, 188-194. https://doi.org/10.1016/j.cie.2014.10.001

Sahoo, B. K., Mehdiloozad, M., & Tone, K. (2014). Cost, revenue and profit efficiency measurement in DEA: A directional distance function approach. European journal of operational research, 237(3), 921-931. https://doi.org/10.1016/j.ejor.2014.02.017

Fang, L., Li, H. (2015). Centralized resource allocation based on the cost–revenue analysis. Computers & Industrial Engineering. 85, 395–401. https://doi.org/10.1016/j.cie.2015.04.018

Aparicio, J., Borras, F., Pastor, J.T., Vidal, F. (2015). Measuring and decomposing firm׳s revenue and cost efficiency: The Russell measures revisited. Int J Prod Econ. 165, 19–28. https://doi.org/10.1016/j.ijpe.2015.03.018

Ghiyasi, M. (2017). Inverse DEA based on cost and revenue efficiency. Computers & Industrial Engineering. 114, 258–263. https://doi.org/10.1016/j.cie.2017.10.024

Amin, G.R., Al-Muharrami, S., Toloo, M. (2019). A combined goal programming and inverse DEA method for target setting in mergers. Expert Systems with Applications, 115, 412–417. https://doi.org/10.1016/j.eswa.2018.08.018

Hassanzadeh, A., Yousefi, S., Farzipoor Saen, R., & Hosseininia, S. S. S. (2018). How to assess sustainability of countries via inverse data envelopment analysis?. Clean Technologies and Environmental Policy, 20, 29-40. https://doi.org/10.1007/s10098-017-1450-x

Khoshfetrat, S., Ghiyasi, M. (2019). Preserve the Relative Efficiency Values: An Inverse Data Envelopment Analysis with Imprecise Data. International Journal of Procurement Management. 12, 1. https://doi.org/10.1504/IJPM.2019.10012454

Guijarro, F., Martínez-Gómez, M., Visbal-Cadavid, D. (2020). A model for sector restructuring through genetic algorithm and inverse DEA. Expert Systems with Applications, 154, 113422. https://doi.org/10.1016/j.eswa.2020.113422

Soleimani-Chamkhorami, K., Hosseinzadeh Lotfi, F., Jahanshahloo, G.R., Rostamy-Malkhalifeh, M. (2020). Preserving cost and revenue efficiency through inverse data envelopment analysis models. INFOR: Information Systems and Operational Research. 58, 561–578. https://doi.org/10.1080/03155986.2019.1627780

Khoshfetrat, S., Ghiyasi, M. (2020). Using Multi-Objective Linear Programming (MOLP) and Data Envelopment Analysis (DEA) models in Non-discretionary Performance Measurement. International Journal of Data Envelopment Analysis (IJDEA). 8, 17–38.

Gatimbu, K. K., Ogada, M. J., & Budambula, N. L. (2020). Environmental efficiency of small-scale tea processors in Kenya: an inverse data envelopment analysis (DEA) approach. Environment, Development and Sustainability, 22, 3333-3345. https://doi.org/10.1007/s10668-019-00348-x

Zhang, G., Cui, J. (2020). A general inverse DEA model for non-radial DEA. Computers & Industrial Engineering. 142, 106368. https://doi.org/10.1016/j.cie.2020.106368

Monzeli, A., Daneshian, B., Tohidi, G., Sanei, M., & Razavian, S. (2020). Efficiency study with undesirable inputs and outputs in DEA. Journal of fuzzy extension and applications, 1(1), 73-80. https://doi.org/10.22105/jfea.2020.248018.1005

Moghaddas, Z., Tosarkani, B. M., & Yousefi, S. (2022). Resource reallocation for improving sustainable supply chain performance: an inverse data envelopment analysis. International Journal of Production Economics, 252, 108560. https://doi.org/10.1016/j.ijpe.2022.108560

Oukil, A., Nourani, A., Bencheikh, A., & Soltani, A. A. (2022). Using inverse data envelopment analysis to evaluate potential impact of mergers on energy use optimization-Application in the agricultural production. Journal of Cleaner Production, 381, 135199. https://doi.org/10.1016/j.jclepro.2022.135199

Boubaker, S., Le, T.D.Q., Ngo, T. (2023). Managing bank performance under COVID‐19: A novel inverse DEA efficiency approach. International Transactions in Operational Research. 30, 2436–2452. https://doi.org/10.1111/itor.13132

Orisaremi, K.K., Chan, F.T.S., Chung, S.H., Fu, X. (2022). A sustainable lean production framework based on inverse DEA for mitigating gas flaring. Expert Systems with Applications, 206, 117856. https://doi.org/10.1016/j.eswa.2022.117856

Younesi, A., Lotfi, F.H., Arana-Jiménez, M. (2023). Using slacks-based model to solve inverse DEA with integer intervals for input estimation. Fuzzy Optimization and Decision Making. https://doi.org/10.1007/s10700-022-09403-1

Khoshandam, L., Nematizadeh, M. (2023). An inverse network DEA model for two-stage processes in the presence of undesirable factors. Journal of Applied Research on Industrial Engineering (JARIE). https://doi.org/10.22105/jarie.2023.351161.1492

Amin, G.R., Ibn Boamah, M. (2023). Modeling business partnerships: A data envelopment analysis approach. European Journal of Operational Research. 305, 329–337. https://doi.org/10.1016/j.ejor.2022.05.036

Mishra, A.R., Saha, A., Rani, P., Pamucar, D., Dutta, D., Hezam, I.M. (2022) Sustainable supplier selection using HF-DEA-FOCUM-MABAC technique: a case study in the Auto-making industry. Soft computing, 26, 8821–8840. https://doi.org/10.1007/s00500-022-07192-8

Zahra Montazeri, F. (2020). An Overview of Data Envelopment Analysis Models in Fuzzy Stochastic Environments. Journal of Fuzzy Extension and Applications www.journal-fea.com J. Fuzzy. Ext. Appl. 1, 272–278. https://doi.org/10.22105/JFEA.2021.281500.1061

Zervopoulos, P.D., Triantis, K., Sklavos, S., Kanas, A. (2023). An alternative Bayesian data envelopment analysis approach for correcting bias of efficiency estimators. Journal of the Operational Research Society. 74, 1021–1041. https://doi.org/10.1080/01605682.2022.2053309

Popović, M., Andrić Gušavac, B., Marinković, S., Pamučar, D. (2023). Selecting location of IT business units using unique DEA-MACBETH-OPA framework. Soft computing, https://doi.org/10.1007/s00500-023-08451-y

Sıcakyuz, C. (2023). Bibliometric Analysis of Data Envelopment Analysis in Supply Chain Management. Journal of Operational and Strategic Analytics, 1, 14–24 https://doi.org/10.56578/josa010103

Sinha, R.P., Edalatpanah, S.A. (2023). Efficiency and Fiscal Performance of Indian States: An Empirical Analysis Using Network DEA. Journal of Operational and Strategic Analytics. 1, 1–7. https://doi.org/10.56578/josa010101

Stević, Ž., Miškić, S., Vojinović, D., Huskanović, E., Stanković, M., Pamučar, D. (2022). Development of a Model for Evaluating the Efficiency of Transport Companies: PCA–DEA–MCDM Model. Axioms, 11, 140. https://doi.org/10.3390/axioms11030140

Tavassoli, M., & Saen, R. F. (2023). Sustainability measurement of combined cycle power plants: a novel fuzzy network data envelopment analysis model. Annals of Operations Research, 1-41. https://doi.org/10.1007/s10479-023-05170-3

Tone, K. (2002). A strange case of the cost and allocative efficiencies in DEA. Journal of the Operational Research Society, 53, 1225–1231. https://doi.org/10.1057/palgrave.jors.2601438

Toloo, M., Ertay, T. (2014). The most cost efficient automotive vendor with price uncertainty: A new DEA approach. Measurement, 52, 135–144. https://doi.org/10.1016/j.measurement.2014.03.002