Department of Mathematics
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Item Performance Evaluation by SBM DEA Model Under Fuzzy Environments Using Expected Credits(Springer, 2023-03) Agarwal, Shivi; Mathur, TrilokPerformance evaluation is always the interest of the manager in every sector like banks, supply chain management, etc. Data envelopment analysis (DEA) is an operations research methodology based on linear programming, which is used to evaluate the performance of decision-making units (DMUs). The available data in real-life scenarios may be present in the vague form. Therefore, the crisp DEA model cannot be used for efficiency evaluation. In the present study, the slacks based model (SBM) DEA model is integrated with the fuzzy set theory to overcome the problem. The expected credits approach is used to solve the fuzzy SBM DEA model in the proposed study. The relative efficiency of the Indian oil refineries is calculated using this methodology, and the rank of the companies is computed from their relative efficiency.Item A Novel Fuzzy Non-radial Data Envelopment Analysis: An Application in Transportation(EDP Sciences, 2021-08) Mathur, Trilok; Agarwal, ShiviThe slack-based measure (SBM) DEA model is a non-radial model used to calculate the relative efficiency, input, and output targets of the different decision-making units (DMUs) based on their best peers or efficient frontier. The conventional SBM DEA model used crisp inputs and outputs. But, it can be observed in real-life problems that sometimes the available data is in linguistic forms such as “few”, “many”, “small”, or missing data. The DEA technique is frontier based, and therefore, imprecise data may lead to untenable results. Fuzzy theory, which is already established to handle uncertain data, can overcome this problem. Furthermore, the sensitivity and stability analysis have been checked the robustness of fuzzy DEA models. In this study, sensitivity and stability analysis of the fuzzy SBM DEA has been performed. The lower and upper sensitive bounds for inputs and outputs variables have been obtained for both the inefficient and efficient DMUs to calculate the input and output targets. Finally, a real-life transportation problem for the validity of the study is presented for its depiction.Item A novel fuzzy non-radial data envelopment analysis: An application in transportation(EDP Sciences, 2021-07) Mathur, Trilok; Agarwal, ShiviThe slack-based measure (SBM) DEA model is a non-radial model used to calculate the relative efficiency, input, and output targets of the different decision-making units (DMUs) based on their best peers or efficient frontier. The conventional SBM DEA model used crisp inputs and outputs. But, it can be observed in real-life problems that sometimes the available data is in linguistic forms such as “few”, “many”, “small”, or missing data. The DEA technique is frontier based, and therefore, imprecise data may lead to untenable results. Fuzzy theory, which is already established to handle uncertain data, can overcome this problem. Furthermore, the sensitivity and stability analysis have been checked the robustness of fuzzy DEA models. In this study, sensitivity and stability analysis of the fuzzy SBM DEA has been performed. The lower and upper sensitive bounds for inputs and outputs variables have been obtained for both the inefficient and efficient DMUs to calculate the input and output targets. Finally, a real-life transportation problem for the validity of the study is presented for its depiction.Item A novel fuzzy non-radial data envelopment analysis: An application in transportation(RAIRO-Oper. Res, 2021-07) Agarwal, Shivi; Mathur, TrilokThe slack-based measure (SBM) DEA model is a non-radial model used to calculate the relative efficiency, input, and output targets of the different decision-making units (DMUs) based on their best peers or efficient frontier. The conventional SBM DEA model used crisp inputs and outputs. But, it can be observed in real-life problems that sometimes the available data is in linguistic forms such as “few”, “many”, “small”, or missing data. The DEA technique is frontier based, and therefore, imprecise data may lead to untenable results. Fuzzy theory, which is already established to handle uncertain data, can overcome this problem. Furthermore, the sensitivity and stability analysis have been checked the robustness of fuzzy DEA models. In this study, sensitivity and stability analysis of the fuzzy SBM DEA has been performed. The lower and upper sensitive bounds for inputs and outputs variables have been obtained for both the inefficient and efficient DMUs to calculate the input and output targets. Finally, a real-life transportation problem for the validity of the study is presented for its depiction.