Rotation algorithm on constructing DEA production frontier

YAN Qing-you, TAO Jie, YAO Xin

Systems Engineering - Theory & Practice ›› 2014, Vol. 34 ›› Issue (1) : 94-103.

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Systems Engineering - Theory & Practice ›› 2014, Vol. 34 ›› Issue (1) : 94-103. DOI: 10.12011/1000-6788(2014)1-94

Rotation algorithm on constructing DEA production frontier

  • YAN Qing-you, TAO Jie, YAO Xin
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Abstract

Traditional method of constructing production frontier in data envelopment analysis seems to be much more complex, in order to solve this problem, we propose a new DEA production frontier algorithm, which is called the rotation algorithm. We explain the meaning of rotation algorithm. Respectively, from the two-dimensional and high-dimensional perspective, we build the production frontier of traditional four DEA models, and prove the theoretical basis of the algorithm. Through practical examples, we prove that, compared to traditional methods, such as vertex and extreme direction method, Graham scanning method, rotation algorithm is much simpler and has a very wide practical value. Finally, we apply the rotation algorithm to practice——Construct a new DEA model dealing with negative data in decision making units, which the traditional DEA model cannot handle.

Key words

DEA / production frontier / convex hull / negative data

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YAN Qing-you , TAO Jie , YAO Xin. Rotation algorithm on constructing DEA production frontier. Systems Engineering - Theory & Practice, 2014, 34(1): 94-103 https://doi.org/10.12011/1000-6788(2014)1-94

References

[1] Charnes A, Cooper W W, Rhodes E. Measuring the efficiency of decision making units[J]. European Journal of Operation Research, 1978, 2: 429-444.
[2] Seiford L M, Thrall R M. Recent development in DEA: The mathematical programming approach to frontier analysis[J]. Journal of Econometrics, 1990, 46: 7-38.
[3] Wei Q L, Yan H, Hao G. Characteristics and structures of weak efficient surfaces of production possibility sets[J]. Journal of Mathematical Analysis and Applications, 2007, 327(2): 1055-1074.
[4] Wei Q L, Yan H. A method of transferring polyhedron between the intersection-form and the sum-form[J]. Computers and Mathematics with Applications, 2001, 41: 1327-1342.
[5] Graham R L. An efficient algorithm for determining the convex hull of a finite planar set[J]. Information Processing Letters, 1972, 1(4): 132-133.
[6] Jarvis R A. On the identification of the convex hull of a finite set of points in the plane[J]. Information Processing Letters, 1973, 2(1): 18-21.
[7] Eddy W F. A new convex hull algorithm for planar sets[J]. ACM Transactions on Mathematical Software (TOMS), 1997, 3(4): 398-403.
[8] Shamos M I. Geometric complexity[C]// Proceedings of Seventh Annual ACM Symposium on Theory of Computing, ACM, 1975: 224-233.
[9] Preparata F P. An optimal real-time algorithm for planar convex hulls[J]. Communications of the ACM, 1979, 22(7): 402-405.
[10] Chand D R, Kapur S S. An algorithm for convex polytopes[J]. Journal of the ACM (JACM), 1970, 17(1): 78-86.
[11] Chan T M. Optimal output-sensitive convex hull algorithms in two and three dimensions[J]. Discrete and Computational Geometry, 1996, 16(4): 361-368.
[12] Banker R D, Charnes A, Cooper W W. Some models for estimating technical and scale inefficiencies in data envelopment analysis[J]. Management Science, 1984, 30(9): 1078-1092.
[13] Cooper W W, Seiford L M, Tone K. Data envelopment analysis: A comprehensive text with models, applications, references and DEA-solver software[M]. Berlin: Springer, 2007.
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