LU Decomposition in DEA with an Application to Hospitals

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27510%2F16%3A86098950" target="_blank" >RIV/61989100:27510/16:86098950 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s10614-015-9501-z" target="_blank" >http://dx.doi.org/10.1007/s10614-015-9501-z</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10614-015-9501-z" target="_blank" >10.1007/s10614-015-9501-z</a>

Jazyk výsledku

angličtina

Název v původním jazyce

LU Decomposition in DEA with an Application to Hospitals

Popis výsledku v původním jazyce

A fundamental problem that usually appears in linear systems is to find a vector satisfying . 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.

Název v anglickém jazyce

LU Decomposition in DEA with an Application to Hospitals

Popis výsledku anglicky

A fundamental problem that usually appears in linear systems is to find a vector satisfying . 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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BB - Aplikovaná statistika, operační výzkum

OECD FORD obor

—

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2016

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Computational Economics

ISSN

0927-7099

e-ISSN

—

Svazek periodika

47

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

16

Strana od-do

473-488

Kód UT WoS článku

000371796600007

EID výsledku v databázi Scopus

2-s2.0-84960391486