Sebastian Sitarz

Reduced Multiplicative Tolerance Ranking and Applications

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Author(s)

Sebastian Sitarz ^1,*

1. Institute of Mathematics, University of Silesia, Katowice, Poland

* Corresponding author.

DOI: https://doi.org/10.5815/ijisa.2013.03.05

Received: 1 Apr. 2012 / Revised: 26 Aug. 2012 / Accepted: 19 Nov. 2012 / Published: 8 Feb. 2013

Index Terms

Multi-Criteria Analysis, Sensitivity Analysis, Multi-Objective Linear Programming, Decision Making

Abstract

In this paper a reduced multiplicative tolerance - a measure of sensitivity analysis in multi-objective linear programming (MOLP) is presented. By using this new measure a method for ranking the set of efficient extreme solutions is proposed. The idea is to rank these solutions by values of the reduced tolerance. This approach can be applied to many MOLP problems, where sensitivity analysis is important for a decision maker. In the paper, applications of the presented methodology are shown in the market model and the transportation problem.

Cite This Paper

Sebastian Sitarz, "Reduced Multiplicative Tolerance Ranking and Applications", International Journal of Intelligent Systems and Applications(IJISA), vol.5, no.3, pp.50-57, 2013. DOI:10.5815/ijisa.2013.03.05

Reference

[1]Aneya Y. P., Nair P. K. (1979). Bicriteria transportation problem, Management Science 25 (1), 73-78.

[2]Benson H. P. (1985). Multiple objective linear programming with parametric criteria coefficients. Management Science 31 (4), 461-474.

[3]Chanas, S., Kuchta, D. (1996), Multiobjective programming in optimization of interval objective functions a generalized approach, European Journal of Operational Research 94, 594–598.

[4]Ekeland I. (1979). Elements d’economic mathematic, Hermann, Paris.

[5]Evans, J.P., Steuer, R.E. (1973). A revised simplex method for linear multiple objective programs. Mathematical Programming 5, 54–72.

[6]Gal T. (1995). Postoptimal Analyses, Parametric Programming and Related Topics. Walter de Gruyter, Berlin.

[7]Gass S. I., Roy P. G. (2003). The compromise hypersphere for multiobjective linear programming, European Journal of Operational Research 144 , 459–479.

[8]Hansen P., Labbe M., Wendell R.E. (1989). Sensitivity Analysis in Multiple Objective Linear Programming: The Tolerance Approach. European Journal of Operational Research 38, 63-69.

[9]Hladik M. (2008). Computing the tolerances in multiobjective linear programming. Optimization. Methods & Software, 23 (5), 731–739.

[10]Hladik M. (2008). Additive and multiplicative tolerance in multiobjective linear programming, Operations Research Letters 36, 393–396.

[11]Hladik M., Sitarz S. (2010). Maximal and supremal tolerances in multiobjective linear programming. Technical report KAM-DIMATIA, Series: 2010-989, Department of Applied Mathematics, Charles University, Prague.

[12]Murad, A., Al-Ali, A., Ellaimony, E., Abdelwali, H., (2010). On bi-criteria two-stage transportation problem: A case study. Transport Problems 5 (3), 103–114.

[13]Pandian P., Anuradha D. (2011). A new method for solving bi-objective transportation problems, Australian Journal of Basic and Applied Sciences, 5(10): 67-74.

[14]Sitarz S. (2008). Postoptimal analysis in multicriteria linear programming. European Journal of Operational Research. 191, 7-18.

[15]Sitarz S. (2010). Standard sensitivity analysis and additive tolerance approach in MOLP. Annals of Operations Research, 181(1), 219-232.

[16]Sitarz S. (2011). Sensitivity analysis of weak efficiency in multiple objective linear programming. Asia-Pacific Journal of Operational Research, 28(4), 445-455.

[17]Sitarz S. (2012). Mean value and volume-based sensitivity analysis for Olympic rankings, European Journal of Operational Research, 216, 232-238.

[18]Sitarz S. (2012). Parametric LP for sensitivity analysis of efficiency in MOLP problems, Optimization Letters, [in press], doi: 10.1007/s11590-012-0541-1.

[19]Steuer R. (1986). Multiple Criteria Optimization Theory: Computation and Application. John Willey, New York.

[20]Wendell R. E. (1982) A preview of a tolerance approach to sensitivity analysis in linear programming, Discrete Mathemtaics, 38, 121-124.

[21]Yu, P.-L., Zeleny, M. (1975). The set of all nondominated solutions in linear cases and a multicriteria simplex method. Journal of Mathematical Analysis and Applications 49 (2), 430–468.

[22]Zeleny, M. (1982). Multiple Criteria Decision Making. McGraw-Hill Book Company, New York.

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