NDLI: LU Decomposition in DEA with an Application to Hospitals

Content Provider	Springer Nature Link
Author	Toloo, Mehdi Jalili, Rahele
Copyright Year	2015
Abstract	A fundamental problem that usually appears in linear systems is to find a vector $$\mathbf{x}$$ satisfying $$\mathbf{Bx}=\mathbf{b}$$ . This linear system is encountered in many research applications and more importantly, it is required to be solved in many contexts in applied mathematics. LU decomposition method, based on the Gaussian elimination, is particularly well suited for spars and large-scale problems. Linear programming (LP) is a mathematical method to obtain optimal solutions for a linear system that is more being considered in various fields of study in recent decades. The simplex algorithm is one of the mostly used mathematical techniques for solving LP problems. Data envelopment analysis (DEA) is a non-parametric approach based on linear programming to evaluate relative efficiency of decision making units (DMUs). The number of LP models that has to be solved in DEA is at least the same as the number of DMUs. Toloo et al. (Comput Econ 45(2):323–326, 2015) proposed an initial basic feasible solution for DEA models which practically reduces at least 50 % of the whole computations. The main contribution of this paper is in utlizing this solution to implement LU decomposition technique on the basic DEA models which is more accurate and numerically stable. It is shown that the number of computations in applying the Gaussian elimination method will be fairly reduced due to the special structure of basic DEA models. Potential uses are illustrated with applications to hospital data set.
Starting Page	473
Ending Page	488
Page Count	16
File Format	PDF
ISSN	09277099
Journal	Computational Economics
Volume Number	47
Issue Number	3
e-ISSN	15729974
Language	English
Publisher	Springer US
Publisher Date	2015-06-10
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Data envelopment analysis (DEA) Simplex algorithm LU decomposition Computational complexity Economic Theory/Quantitative Economics/Mathematical Methods Computer Application in Social and Behavioral Sciences Operation Research/Decision Theory Behavioral/Experimental Economics Math Applications in Computer Science
Content Type	Text
Resource Type	Article
Subject	Economics, Econometrics and Finance Computer Science Applications

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