Ranking of Decision-Making Units with Multi-Period Two-Stage Network Structure: a Method Based on Relative Data Envelopment Analysis
محورهای موضوعی : Operation ResearchMaghsoud Ahmad khanlou Gharakhanlou 1 , Nima Azarmir shotorbani 2 , Ghasem Tohidi 3 , Shabnam Razavyan 4 , Rohollah Abbasi 5
1 - PhD Student, Department of Applied Mathematics, Islamic Azad University, Tabriz Branch. Tabriz - Iran
2 - Assistant Professor, Department of Applied Mathematics, Islamic Azad University, Tabriz Branch. Tabriz - Iran
3 - Associate Professor, Department of Mathematics, Islamic Azad University, Tehran Branch. Tehran- Iran.
4 - Associate Professor, Department of Mathematics, Islamic Azad University, South Tehran Branch. Tehran- Iran
5 - Assistant Professor, Department of Mathematics, Qom University. Qom- Iran
کلید واژه: Multi-period, Efficiency, network, Grading, relative data envelopment analysis,
چکیده مقاله :
Data envelopment analysis is always considered as a non-parametric method for measuring the efficiency of a set of decision units. The efficiency number obtained from standard models is a criterion for comparing the performance of each decision unit with other units. Despite the many strengths of these models, one of their weaknesses is the lack of distinction between efficient units. Also, these models do not pay attention to the internal structure of the units and have a black box view. To solve these problems, relational data envelopment analysis models are used, which are much more cost-effective in terms of time and cost; But these models are static and do not take time into evaluation. In this paper, a method has been proposed for grading of the decision making units with multi- period two stages network structure using relative data envelopment analysis. Three different perspective are introduced for assessment of efficiency in time periods via relative data envelopment analysis. Proportionate with each perspective, an efficiency number is obtained for any decision making unit. Then three efficiency numbers obtained in the mentioned method is combined with Shannon entropy method and a total efficiency criterion is defined for each unit. Finally, this measure is considered as the main indicator for the units grading. The results of implementation of the mentioned algorithm on the real example and comparison with the similar methods clarify the strength of this algorithm.
Data envelopment analysis is always considered as a non-parametric method for measuring the efficiency of a set of decision units. The efficiency number obtained from standard models is a criterion for comparing the performance of each decision unit with other units. Despite the many strengths of these models, one of their weaknesses is the lack of distinction between efficient units. Also, these models do not pay attention to the internal structure of the units and have a black box view. To solve these problems, relational data envelopment analysis models are used, which are much more cost-effective in terms of time and cost; But these models are static and do not take time into evaluation. In this paper, a method has been proposed for grading of the decision making units with multi- period two stages network structure using relative data envelopment analysis. Three different perspective are introduced for assessment of efficiency in time periods via relative data envelopment analysis. Proportionate with each perspective, an efficiency number is obtained for any decision making unit. Then three efficiency numbers obtained in the mentioned method is combined with Shannon entropy method and a total efficiency criterion is defined for each unit. Finally, this measure is considered as the main indicator for the units grading. The results of implementation of the mentioned algorithm on the real example and comparison with the similar methods clarify the strength of this algorithm.
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