Using the Outer Approximation Algorithm for Generating all Efficient Extreme Points of DEA

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GERAMI J.

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Journal: JOURNAL OF MATHEMATICAL EXTENSION Year:2018 | Volume:12 | Issue:2 Page(s): 33-62

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Title

Using the Outer Approximation Algorithm for Generating all Efficient Extreme Points of DEA

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GERAMI J. | Issue Writer Certificate

Keywords

Data Envelopment analysis

multiple objective

linear programming

outer approximation

Abstract

Identifying the efficient extreme units in a production possibility set is a very important matter in Data Envelopment analysis, as these observed, real units have the best performances. In this paper, we proposed a multiple objective programming model, in which the feasible region is the production possibility set under the assumption of variable returns to scale and the objective function consists of input and output variables. As we know, by increasing the dimensions of the problem, the set of efficient points would increase as well; thus, using the multiple objective linear programming problem-solving methods in a decision set would lead to computational problems and it would be much easier to work in the outcome set instead of the decision set. In this research, we show that the efficient points in the outcome set of the suggested multiple objective linear programming problems correspond with the efficient extreme points in Data Envelopment analysis. An outer approximation algorithm is presented for production of all efficient extreme points in the outcome set. This algorithm provides us with the equations for all efficient surfaces. In the outcome set, this algorithm would use few calculations to produce all the extreme points. Finally, we demonstrate the presented approach through numerical examples.

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APA: Copy

GERAMI, J.. (2018). Using the Outer Approximation Algorithm for Generating all Efficient Extreme Points of DEA. JOURNAL OF MATHEMATICAL EXTENSION, 12(2), 33-62. SID. https://sid.ir/paper/720602/en

Vancouver: Copy

GERAMI J.. Using the Outer Approximation Algorithm for Generating all Efficient Extreme Points of DEA. JOURNAL OF MATHEMATICAL EXTENSION[Internet]. 2018;12(2):33-62. Available from: https://sid.ir/paper/720602/en

IEEE: Copy

J. GERAMI, “Using the Outer Approximation Algorithm for Generating all Efficient Extreme Points of DEA,” JOURNAL OF MATHEMATICAL EXTENSION, vol. 12, no. 2, pp. 33–62, 2018, [Online]. Available: https://sid.ir/paper/720602/en

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