finding the defining hyperplanes of production possibility set with variable returns to scale using the linear independent vectors

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Rafati ‎Maleki N.; ROSTAMY MALKHALIFEH M.

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Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2018 | Volume:4 | Issue:15 Page(s): 53-65

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Title

finding the defining hyperplanes of production possibility set with variable returns to scale using the linear independent vectors

Author(s)

Rafati ‎Maleki N. | ROSTAMY MALKHALIFEH M. | Issue Writer Certificate

Keywords

Data Envelopment AnalysisQ1

Decision Making UnitQ1

Production Possibility SetQ1

Defining HyperplaneQ1

Pareto-EfficientQ1

Abstract

The Production Possibility Set (PPS) is defined as the set of all inputs and outputs of a system in which inputs can produce outputs. In Data Envelopment Analysis (DEA), it is highly important to identify the Defining Hyperplanes and especially the strong Defining Hyperplanes of the empirical PPS. Although DEA models can determine the efficiency of a Decision Making Unit (DMU), but they cannot present efficient frontiers of PPS completely. The notion of Defining Hyperplanes is crucial to marginal discussions, marginal rates, marginal rates of substitution, sensitivity analysis, returns to scale, and in particular, the efficiency analysis of DMUs. In this paper, we propose a new method to determine all strong efficient(Pareto-Efficient) DMUs and strong Defining Hyperplanes of the PPS with variable returns to scale which strong efficient DMUs are located on them. Furthermore, we apply the proposed method to find the normal vectors or gradient of the strong Defining Hyperplanes of the PPS including strong efficient DMUs. Consequently, the equations of these hyperplanes are determined. To illustrate the ability of the proposed method, some numerical examples are finally provided. Our method can be easily implemented using existing packages for operation research, such as GAMS.

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APA: Copy

Rafati ‎Maleki, N., & ROSTAMY MALKHALIFEH, M.. (2018). finding the defining hyperplanes of production possibility set with variable returns to scale using the linear independent vectors. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 4(15 ), 53-65. SID. https://sid.ir/paper/257286/en

Vancouver: Copy

Rafati ‎Maleki N., ROSTAMY MALKHALIFEH M.. finding the defining hyperplanes of production possibility set with variable returns to scale using the linear independent vectors. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2018;4(15 ):53-65. Available from: https://sid.ir/paper/257286/en

IEEE: Copy

N. Rafati ‎Maleki, and M. ROSTAMY MALKHALIFEH, “finding the defining hyperplanes of production possibility set with variable returns to scale using the linear independent vectors,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 4, no. 15 , pp. 53–65, 2018, [Online]. Available: https://sid.ir/paper/257286/en

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