Geodesic
Finding a solution for Multi-Objective Linear Fractional Programming problem based on goal programming and Data Envelopment Analysis
Jahanshahloo, G. R.1 ; Talebian, B.1 ; Hosseinzadeh Lotfi, F.2  ; Sadeghi, J.1
1 Faculty of Mathematics and Computer Sciences, Kharazmi University, Tehran, Iran.
2 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 1, pp. 199-210.

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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.

DOI : 10.1051/ro/2016014
Classification : 90C29, 90C32, 90C05
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

1 Faculty of Mathematics and Computer Sciences, Kharazmi University, Tehran, Iran.
2 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran. 
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     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},
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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. http://geodesic.mathdoc.fr/articles/10.1051/ro/2016014/

R.D. Banker, A. Charnes and W.W. Cooper, Some models for estimating technical scale ineffciencies in data envelopment analysis. Manage. Sci. 30 (1984) 1078–1092. | Zbl | DOI

S.K. Bhatt, Equivalence of various linearization algorithms for linear fractional programming. Z. Oper. Res. 33 (1989) 39–43. | MR | Zbl

A. Charnes and W.W. Cooper, Programming with linear fractional functions. Nav. Res. Logist. Quart. 9 (1962) 181–186. | MR | Zbl | DOI

A. Charnes, W.W. Cooper, B. Golany, L. Seiford and J. Stutz, Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions. J. Econom. 30 (1985) 91–107. | MR | Zbl | DOI

M. Chakraborty, Sandipan Gupta, Fuzzy mathematical programming for multi objective linear fractional programming problem. Fuzzy Sets Syst. 125 (2002) 335–342. | MR | Zbl | DOI

A. Charnes, W.W. Cooper and E. Rhodes, Measuring the efficiency of decision makingunits. Eur. J. Oper. Res. 2 (1987) 429–444. | MR | Zbl | DOI

J.P. Costa, Computing non-dominated solutions in MOLFP. Eur. J. Oper. Res. 181 (2007) 1464–1475. | Zbl | DOI

J.P. Costa and J.M. Alves, A reference point technique to compute non-dominated solutions in MOLFP. J. Math. Sci. 161 (2009) 820–831. | MR | Zbl | DOI

Y. Dai, J. Shi and S. Wang, Conical partition algorithm for maximizing the sum of DC ratios. J. Global Optim. 31 (2005) 253–270. | MR | Zbl | DOI

W. Dinkelbach, On nonlinear fractional programming. Manage. Sci. 13 (1967) 492–498. | MR | Zbl | DOI

D. Dutta, R.N. Tiwari and J.R. Rao, Multiple objective linear fractional programming- A fuzzy set theoretic approach. Fuzzy Sets Syst. 52 (1992) 39–45. | MR | Zbl | DOI

B.D. Gueorguieva, 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

J.R. Isbell and W.H. Marlow, Attrition games. Nav. Res. Logist. Quart. 3 (1956) 71–94. | MR | Zbl | DOI

J.S.H. Kornbluth and R.E. Steuer, Multiple objective linear fractional programming. Manage. Sci. 27 (1981) 1024–1039. | Zbl | DOI

J.S.H. Kornbluth and R.E. Steuer, Goal programming with linear fractional criteria. Eur. J. Oper. Res. 8 (1981) 58–65. | MR | Zbl | DOI

F.H. Lotfi, A.A. Noora, G.R. Jahanshahloo, M. Khodabakhshi and A. Payan, A linear programming approach to test efficiency in multi-objective linear fractional programming problems. Appl. Math. Model. 34 (2010) 4179–4183. | MR | Zbl | DOI

M.K. Luhandjula, Fuzzy approaches for multiple objective linear fractional optimization. Fuzzy Sets Syst. 13 (1984) 11–23. | MR | Zbl | DOI

C.A.K. Lovell and J.T. Pastor, Target setting: an application to a bank branch network. Eur. J. Oper. Res. 98 (1997) 290–299. | Zbl | DOI

C.A.K. Lovell and J.T. Pastor, Radial DEA models without inputs or without outputs, theory and methodology. Eur. J. Oper. Res. 118 (1999) 46-51. | Zbl | DOI

M. Mahdiloo, R. Farzipoor Saen And M. Tavana, 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.

I.M. Stancu-Minasian and B. Pop, On a fuzzy set approach to solving multiple objective linear fractional programming problem. Fuzzy Sets Syst. 134 (2003) 397–405. | MR | Zbl | DOI

B. Stanojević and M. Stanojević, 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

E. Valipour, M.A. Yaghoobi and M. Mashinchi, An iterative approach to solve multiobjective linear fractional programming problems. Appl. Math. Model. 38 (2014) 38–49. | MR | Zbl | DOI

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