Document Type : Original Article
Department of Mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran.
Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran.
Data envelopment analysis based on mathematical programming for decision-making units determines the efficiency score in addition to the projection of inefficient DMUs on the efficient frontier. Centralized Allocation Resource (CRA) with a two-stage linear programming model captures the projection of DMUs on the efficient frontier. But since the input and output vectors of each DMU in the DEA are crucial, they may be random data that follow a particular distribution. Hence, many applied studies face random data. This paper shows a two-stage supply chain with random data and the CRA model with ratio data has been used to calculate the projection of DMUs. In the end, the supply chain of 11 Iranian Airlines with random data during the period of 2011-2017 was considered concerning sustainability factors.
- Farell, M. J. (1957). The measurement of productive efficiency. Journal of the royal statistical society, 120(3), 253-290.
- 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.
- Korhonen, P. J., & Siitari, P. A. (2007). Using lexicographic parametric programming for identifying efficient units in DEA. Computers & operations research, 34(7), 2177-2190.
- Korhonen, P. J., & Siitari, P. A. (2009). A dimensional decomposition approach to identifying efficient units in large-scale DEA models. Computers & operations research, 36(1), 234-244.
- Yu, M. M., Ting, S. C., & Chen, M. C. (2010). Evaluating the cross-efficiency of information sharing in supply chains. Expert systems with applications, 37(4), 2891-2897.
- Chen, C., & Yan, H. (2011). Network DEA model for supply chain performance evaluation. European journal of operational research, 213(1), 147-155.
- Seuring, S. (2013). A review of modeling approaches for sustainable supply chain management. Decision support systems, 54(4), 1513-1520.
- Izadikhah, M., & Saen, R. F. (2016). Evaluating sustainability of supply chains by two-stage range directional measure in the presence of negative data. Transportation research part D: transport and environment, 49, 110-126.
- Badiezadeh, T., Saen, R. F., & Samavati, T. (2018). Assessing sustainability of supply chains by double frontier network DEA: a big data approach. Computers & operations research, 98, 284-290.
- Bal, A., & Satoglu, S. I. (2019). The use of data envelopment analysis in evaluating Pareto optimal solutions of the sustainable supply chain models. Procedia manufacturing, 33, 485-492.
- Zhang, J., Wu, Q., & Zhou, Z. (2019). A two-stage DEA model for resource allocation in industrial pollution treatment and its application in China. Journal of cleaner production, 228, 29-39.
- Lozano, S., & Villa, G. (2004). Centralized resource allocation using data envelopment analysis. Journal of productivity analysis, 22(1), 143-161.
- Asmild, M., Paradi, J. C., & Pastor, J. T. (2009). Centralized resource allocation BCC models. Omega, 37(1), 40-49.
- Malekmohammadi, N., Lotfi, F. H., & Jaafar, A. B. (2009). Centralized resource allocation in DEA with interval data: an application to commercial banks in Malaysia. International journal of mathematical analysis, 3(13-16), 757-764.
- Hosseinzadeh Lotfi, F., Nematollahi, N., Behzadi, M. H., Mirbolouki, M., & Moghaddas, Z. (2012). Centralized resource allocation with stochastic data. Journal of computational and applied mathematics, 236(7), 1783-1788.
- Fang, L., & Li, H. (2015). Centralized resource allocation based on the cost–revenue analysis. Computers & industrial engineering, 85, 395-401.
- Hu, J. L., Chiu, C. N., Shieh, H. S., & Huang, C. H. (2010). A stochastic cost efficiency analysis of international tourist hotels in Taiwan. International journal of hospitality management, 29(1), 99-107.
- Azadi, M., & Saen, R. F. (2012). Supplier selection using a new russell model in the presence of undesirable outputs and stochastic data. Journal of applied sciences, 12(4), 336-344.
- Jin, J., Zhou, D., & Zhou, P. (2014). Measuring environmental performance with stochastic environmental DEA: the case of APEC economies. Economic modelling, 38, 80-86.
- Dong, Y., Hamilton, R., & Tippett, M. (2014). Cost efficiency of the Chinese banking sector: a comparison of stochastic frontier analysis and data envelopment analysis. Economic modelling, 36, 298-308.
- Izadikhah, M., & Saen, R. F. (2018). Assessing sustainability of supply chains by chance-constrained two-stage DEA model in the presence of undesirable factors. Computers & operations research, 100, 343-367.
- Liu, W., Wang, Y. M., & Lyu, S. (2017). The upper and lower bound evaluation based on the quantile efficiency in stochastic data envelopment analysis. Expert systems with applications, 85, 14-24.
- Tavassoli, M., Saen, R. F., & Zanjirani, D. M. (2020). Assessing sustainability of suppliers: a novel stochastic-fuzzy DEA model. Sustainable production and consumption, 21, 78-91.
- Despić, O., Despić, M., & Paradi, J. C. (2007). DEA-R: Ratio-based comparative efficiency model, its mathematical relation to DEA and its use in applications. Journal of productivity analysis, 28(1), 33-44.
- Emrouznejad, A., & Amin, G. R. (2009). DEA models for ratio data: convexity consideration. Applied mathematical modelling, 33(1), 486-498.
- Hatami-Marbini, A., & Toloo, M. (2019). Data envelopment analysis models with ratio data: a revisit. Computers & industrial engineering, 133, 331-338.
- Olesen, O. B., Petersen, N. C., & Podinovski, V. V. (2015). Efficiency analysis with ratio measures. European journal of operational research, 245(2), 446-462.
- Olesen, O. B., Petersen, N. C., & Podinovski, V. V. (2017). Efficiency measures and computational approaches for data envelopment analysis models with ratio inputs and outputs. European journal of operational research, 261(2), 640-655.
- Wei, C. K., Chen, L. C., Li, R. K., & Tsai, C. H. (2011). Using the DEA-R model in the hospital industry to study the pseudo-inefficiency problem. Expert systems with applications, 38(3), 2172-2176.