International Journal of Information Technology and Computer Science(IJITCS)

ISSN: 2074-9007 (Print), ISSN: 2074-9015 (Online)

Published By: MECS Press

IJITCS Vol.6, No.3, Feb. 2014

Approaches to Sensitivity Analysis in MOLP

Full Text (PDF, 355KB), PP.54-60

Views:77   Downloads:1


Sebastian Sitarz

Index Terms

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


The paper presents two approaches to the sensitivity analysis in multi-objective linear programming (MOLP). The first one is the tolerance approach and the other one is the standard sensitivity analysis. We consider the perturbation of the objective function coefficients. In the tolerance method we simultaneously change all of the objective function coefficients. In the standard sensitivity analysis we change one objective function coefficient without changing the others. In the numerical example we compare the results obtained by using these two different approaches.

Cite This Paper

Sebastian Sitarz,"Approaches to Sensitivity Analysis in MOLP", International Journal of Information Technology and Computer Science(IJITCS), vol.6, no.3, pp.54-60, 2014. DOI: 10.5815/ijitcs.2014.03.07


[1]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.

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

[3]Vetschera R. (1997). Volume-Based Sensitivity Analysis for Multi-Criteria Decision Models. In: Göpfert A., Seeländer J., Tammer Chr. (Eds.). Methods of Multicriteria Decision Theory. Hänsel-Hohenhausen, Egelsbach.

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

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

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

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

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

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

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

[11]Sitarz S. (2013). Parametric LP for sensitivity analysis of efficiency in MOLP problems, Optimization Letters, [in press], doi: 10.1007/s11590-012-0541-1.

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

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

[14]Hladik M., Sitarz S., Maximal and supremal tolerances in multiobjective linear programming, European Journal of Operational Research, 228 (1), 93-101, 2013

[15]Oliveira C., Antunes C. H. (2007). Multiple objective linear programming models with interval coefficients – an illustrated overview, European Journal of Operational Research 181/3, 1434-1463.

[16]Gass S. I. (1970). An illustrated guide to linear programming. Mc Graw-Hill Book Company, New York. 

[17]Gass S. I. (1975). Linear Programming, Methods and Applications. Mc Graw-Hill Book Company, New York. 

[18]Benson H., Morin T. L. (1987). A bicriteria mathematical programming model for nutrition planning in developing nations. Managemant Science 33 (12), 1593-1601.

[19]Kwasniewski J., (1999). Optimal Nutrition. WGP, Warsaw. 

[20]Sitarz S. (2006), Hybrid methods in multi-criteria dynamic programming, Applied Mathematics and Computation, 180/1, 38-45.

[21]Sitarz S. (2009). Ant algorithms and simulated annealing for multicriteria dynamic programming, Computers & Operations Research, 36 (2), 433-441.

[22]Steuer R., Choo E (1981). An Interactive weighted Tchebycheff procedure for multiple objective programming, Mathematical Programming 26, 326-344.

[23]Opricovic S., Tzeng G.H. (2004). Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS, European Journal of Operational Research, 156, 445-455.

[24]Opricovic S., Tzeng G.H. (2007). Extended VIKOR method in comparison with outranking methods, European Journal of Operational Research, 178 (2), 514-529.

[25]Sitarz S. (2010). Dynamic Programming with Ordered Structures: Theory, Examples and Applications, Fuzzy Sets and Systems, 161, 2623–2641.

[26]Trzaskalik T., Sitarz S. (2007). Discrete dynamic programming with outcomes in random variable structures, European Journal of Operational Research, 177 (3), 1535-1548.