The multi-objective linear fractional programming is an interesting topic with many applications in different fields. Until now, various algorithms have been proposed in order to solve the multi-objective linear fractional programming (MOLFP) problem. An important point in most of them is the use of non-linear programming with a high computational complexity or the use of linear programming with preferences of the objective functions which are assigned by the decision maker. The current paper, through combining goal programming and data envelopment analysis (DEA), proposes an iterative method to solve MOLFP problems using only linear programming. Moreover, the proposed method provides an efficient solution which fairly optimizes each objective function when the decision maker has no information about the preferences of the objective functions. In fact, along with normalization of the objective functions, their relative preferences are fairly determined using the DEA. The implementation of the proposed method is demonstrated using numerical examples.
Keywords: Multi-Objective linear fractional programming, goal programming, data envelopment analysis, fair satisfaction
Jahanshahloo, G. R. 1 ; Talebian, B. 1 ; Hosseinzadeh Lotfi, F. 2 ; Sadeghi, J. 1
@article{RO_2017__51_1_199_0,
author = {Jahanshahloo, G. R. and Talebian, B. and Hosseinzadeh Lotfi, F. and Sadeghi, J.},
title = {Finding a solution for {Multi-Objective} {Linear} {Fractional} {Programming} problem based on goal programming and {Data} {Envelopment} {Analysis}},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {199--210},
year = {2017},
publisher = {EDP Sciences},
volume = {51},
number = {1},
doi = {10.1051/ro/2016014},
mrnumber = {3603502},
zbl = {1358.90125},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2016014/}
}
TY - JOUR AU - Jahanshahloo, G. R. AU - Talebian, B. AU - Hosseinzadeh Lotfi, F. AU - Sadeghi, J. TI - Finding a solution for Multi-Objective Linear Fractional Programming problem based on goal programming and Data Envelopment Analysis JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2017 SP - 199 EP - 210 VL - 51 IS - 1 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/ro/2016014/ DO - 10.1051/ro/2016014 LA - en ID - RO_2017__51_1_199_0 ER -
%0 Journal Article %A Jahanshahloo, G. R. %A Talebian, B. %A Hosseinzadeh Lotfi, F. %A Sadeghi, J. %T Finding a solution for Multi-Objective Linear Fractional Programming problem based on goal programming and Data Envelopment Analysis %J RAIRO - Operations Research - Recherche Opérationnelle %D 2017 %P 199-210 %V 51 %N 1 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/ro/2016014/ %R 10.1051/ro/2016014 %G en %F RO_2017__51_1_199_0
Jahanshahloo, G. R.; Talebian, B.; Hosseinzadeh Lotfi, F.; Sadeghi, J. Finding a solution for Multi-Objective Linear Fractional Programming problem based on goal programming and Data Envelopment Analysis. RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 1, pp. 199-210. doi: 10.1051/ro/2016014
, and , Some models for estimating technical scale ineffciencies in data envelopment analysis. Manage. Sci. 30 (1984) 1078–1092. | Zbl | DOI
, Equivalence of various linearization algorithms for linear fractional programming. Z. Oper. Res. 33 (1989) 39–43. | MR | Zbl
and , Programming with linear fractional functions. Nav. Res. Logist. Quart. 9 (1962) 181–186. | MR | Zbl | DOI
, , , and , Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions. J. Econom. 30 (1985) 91–107. | MR | Zbl | DOI
, , Fuzzy mathematical programming for multi objective linear fractional programming problem. Fuzzy Sets Syst. 125 (2002) 335–342. | MR | Zbl | DOI
, and , Measuring the efficiency of decision makingunits. Eur. J. Oper. Res. 2 (1987) 429–444. | MR | Zbl | DOI
, Computing non-dominated solutions in MOLFP. Eur. J. Oper. Res. 181 (2007) 1464–1475. | Zbl | DOI
and , A reference point technique to compute non-dominated solutions in MOLFP. J. Math. Sci. 161 (2009) 820–831. | MR | Zbl | DOI
, and , Conical partition algorithm for maximizing the sum of DC ratios. J. Global Optim. 31 (2005) 253–270. | MR | Zbl | DOI
, On nonlinear fractional programming. Manage. Sci. 13 (1967) 492–498. | MR | Zbl | DOI
, and , Multiple objective linear fractional programming- A fuzzy set theoretic approach. Fuzzy Sets Syst. 52 (1992) 39–45. | MR | Zbl | DOI
, A simple method for obtaining weakly efficient points in multiobjective linear fractional programming problems. Eur. J. Oper. Res. 126 (2000) 386–390. | MR | Zbl | DOI
and , Attrition games. Nav. Res. Logist. Quart. 3 (1956) 71–94. | MR | Zbl | DOI
and , Multiple objective linear fractional programming. Manage. Sci. 27 (1981) 1024–1039. | Zbl | DOI
and , Goal programming with linear fractional criteria. Eur. J. Oper. Res. 8 (1981) 58–65. | MR | Zbl | DOI
, , , and , A linear programming approach to test efficiency in multi-objective linear fractional programming problems. Appl. Math. Model. 34 (2010) 4179–4183. | MR | Zbl | DOI
, Fuzzy approaches for multiple objective linear fractional optimization. Fuzzy Sets Syst. 13 (1984) 11–23. | MR | Zbl | DOI
and , Target setting: an application to a bank branch network. Eur. J. Oper. Res. 98 (1997) 290–299. | Zbl | DOI
and , Radial DEA models without inputs or without outputs, theory and methodology. Eur. J. Oper. Res. 118 (1999) 46-51. | Zbl | DOI
, , A novel Data Envelopment Analysis model for solving supplier selection problems with undesirable outputs and lack of inputs. Int. J. Logist. Syst. Manage. 11 (2012) 285–305.
and , On a fuzzy set approach to solving multiple objective linear fractional programming problem. Fuzzy Sets Syst. 134 (2003) 397–405. | MR | Zbl | DOI
and , On the efficiency test in multi-objective linear fractional programming problems by Lotfi et al. 2010. Appl. Math. Model. 37 (2013) 7086–7093. | MR | Zbl | DOI
, and , An iterative approach to solve multiobjective linear fractional programming problems. Appl. Math. Model. 38 (2014) 38–49. | MR | Zbl | DOI
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