TY - JOUR

T1 - An equivalent linear programming form of general linear fractional programming

T2 - A duality approach

AU - Toloo, Mehdi

N1 - Funding Information:
Funding: This study was supported by the Czech Science Foundation grant number 19-13946S.
Publisher Copyright:
© 2021 by the author. Licensee MDPI, Basel, Switzerland.

PY - 2021/7/2

Y1 - 2021/7/2

N2 - Linear fractional programming has been an important planning tool for the past four decades. The main contribution of this study is to show, under some assumptions, for a linear programming problem, that there are two different dual problems (one linear programming and one linear fractional functional programming) that are equivalent. In other words, we formulate a linear programming problem that is equivalent to the general linear fractional functional programming problem. These equivalent models have some interesting properties which help us to prove the related duality theorems in an easy manner. A traditional data envelopment analysis (DEA) model is taken, as an instance, to illustrate the applicability of the proposed approach.

AB - Linear fractional programming has been an important planning tool for the past four decades. The main contribution of this study is to show, under some assumptions, for a linear programming problem, that there are two different dual problems (one linear programming and one linear fractional functional programming) that are equivalent. In other words, we formulate a linear programming problem that is equivalent to the general linear fractional functional programming problem. These equivalent models have some interesting properties which help us to prove the related duality theorems in an easy manner. A traditional data envelopment analysis (DEA) model is taken, as an instance, to illustrate the applicability of the proposed approach.

KW - Data envelopment analysis (DEA)

KW - Duality

KW - Linear fractional programming

KW - Linear programming

UR - http://www.scopus.com/inward/record.url?scp=85110744242&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85110744242&partnerID=8YFLogxK

U2 - 10.3390/math9141586

DO - 10.3390/math9141586

M3 - Article

AN - SCOPUS:85110744242

VL - 9

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 14

M1 - 1586

ER -