Document Type : Research Paper
Department of Applied Mathematic, Azarbaijan Shahid Madani University, Tabriz, Iran.
Department of Mathematical, Science and Research Branch, Islamic Azad University, Tehran, Iran.
In traditional cost-efficiency models, inputs and outputs, as well as input prices were known as constant values for each decision-making unit In our daily applications, however, market entry prices vary at different times. In other words, input prices for decision-making units (DMUs) are time dependent. Traditional methods cannot calculate the cost efficiency of DMUs with time-dependent prices. This paper proposes a new method to calculate the cost efficiency of DMUs in the presence of time-dependent prices. The proposed model is a parametric programming problem model depending on time. In the presented model, the inputs and outputs are functions in terms of time, which is not present in the models introduced by other researchers. New definitions for time-dependent cost efficiency have also been introduced. The cost efficiency of DMUs is measured over a given time and the units are ranked according to the time obtained. Finally, a numerical example has been presented to illustrate the proposed method.
- Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management science, 30(9), 1078-1092.
- Bazaraa, M. S., Jarvis, J. J., & Sherali, H. D. (2011). Linear programming and network flows. John Wiley & Sons.
- Camanho, A. S., & Dyson, R. G. (2005). Cost efficiency measurement with price uncertainty: a DEA application to bank branch assessments. European journal of operational research, 161(2), 432-446.
- Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European journal of operational research, 2(6), 429-444.
- Charnes, A., & Cooper, W. W. (1984). Preface to topics in data envelopment analysis. Annals of operations research, 2(1), 59-94.
- Dyvak, M., Melnyk, A., Rot, A., Hernes, M., & Pukas, A. (2022). Ontology of mathematical modeling based on interval data. Complexity, 2022. https://doi.org/10.1155/2022/8062969
- Edalatpanah, S. A. (2018). Neutrosophic perspective on DEA. Journal of applied research on industrial engineering, 5(4), 339-345.
- Fallahnejad, R., Asadi Rahmati, S., & Moradipour, K. (In Press). Decomposition of cost efficiency, given the set of price and cost production possibilities in data envelopment analysis. Journal of applied research on industrial engineering. http://www.journal-aprie.com/article_148535_6a05ccefae17e255435630d6d1731659.pdf
- Färe, R., Grosskopf, S., & Lovell, C. K. (1985). The measurement of efficiency of production (Vol. 6). Springer Science & Business Media.
- Färe, R., & Grosskopf, S. (1997). Intertemporal production frontiers: with dynamic DEA. Journal of the operational research society, 48(6), 656-656.
- Farrell, M. J. (1957). The measurement of productive efficiency. Journal of the royal statistical society: series A (General), 120(3), 253-281.
- Haralayya, B., & Aithal, P. S. (2021). Inter bank analysis of cost efficiency using mean. International journal of innovative research in science, engineering and technology (IJIRSET), 10(6), 6391-6397.
- Haralayya, B., & Aithal, P. S. (2021). Study on cost efficiency in Indian and other countries experience. Journal of advanced research in hr and organizational management, 8(1&2), 23-30.
- Hatami-Marbini, A., & Arabmaldar, A. (2021). Robustness of Farrell cost efficiency measurement under data perturbations: evidence from a US manufacturing application. European journal of operational research, 295(2), 604-620.
- Hosseinzadeh Lotfi, F., Jahanshahloo, G. R., Shahverdi, R., & Rostamy-Malkhalifeh, M. (2007). Cost efficiency and cost Malmquist productivity index with interval data. International mathematical forum, 2(9), 441-453.
- Jahanshahloo, G. R., Hosseinzadeh Lotfi, F., Alimardani Jondabeh, M., Banihashemi, S., & Lakzaie, L. (2008). Cost efficiency measurement with certain price on fuzzy data and application in insurance organization. math. sci, 2(1), 1-18.
- Khodabakhshi, M., & Cheraghali, Z. (2022). Ranking of Iranian executive agencies using audit court budget split indexes and data envelopment analysis. Journal of applied research on industrial engineering, 9(3), 312-322.
- Kholmuminov, S., & Wright, R. E. (2017). Cost efficiency analysis of public higher education institutions in Uzbekistan. Retrieved from https://pureportal.strath.ac.uk/en/publications/cost-efficiency-analysis-of-public-higher-education-institutions-
- Li, Z., Crook, J., & Andreeva, G. (2017). Dynamic prediction of financial distress using Malmquist DEA. Expert systems with applications, 80, 94-106.
- Maghbouli, M., & Moradi, F. (2021). The relation between emotional intelligence (EQ) and mathematics performance: a DEA-based approach. Journal of applied research on industrial engineering, 8(Special Issue), 1-14.
- Malmquist, S. (1953). Index numbers and indifference surfaces. Trabajos de estadística, 4(2), 209-242.
- Pourmahmoud, J. (2015). New model for ranking DMUs in DDEA as a special case. International journal industrial mathematics, 7(2), 187-192.
- Pourmahmoud, J., & Sharak, N. B. (2018). Measuring cost efficiency with new fuzzy DEA models. International journal of fuzzy systems, 20(1), 155-162.
- Pourmahmoud, J., & Sharak, N. B. (2020). Evaluating cost efficiency using fuzzy data envelopment analysis method. Iranian journal of operations research, 11(1), 25-42.
- Puri, J., & Yadav, S. P. (2016). A fully fuzzy DEA approach for cost and revenue efficiency measurements in the presence of undesirable outputs and its application to the banking sector in India. International journal of fuzzy systems, 18, 212-226.
- Soleimani-Chamkhorami, K., & Ghobadi, S. (2021). Cost-efficiency under inter-temporal dependence. Annals of operations research, 302(1), 289-312.
- Sun, J., Chen, M., Fu, Y., & Luo, H. (2021). Allocating fixed resources for DMUs with interval data. RAIRO-operations research, 55(2), 505-520.
- Taeb, Z., Hosseinzadeh Lotfi, F., & Abbasbandy, S. (2017). Determine the efficiency of time depended units by using data envelopment analysis. International journal of research in industrial engineering, 6(3), 193-201.
- Tone, K. (2002). A strange case of the cost and allocative efficiencies in DEA. Journal of the operational research society, 53(11), 1225-1231.