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Interactive compromise hypersphere method and its applications

Published online by Cambridge University Press:  26 September 2012

Sebastian Sitarz
Sebastian Sitarz*
Affiliation:
Institute of Mathematics, University of Silesia, ul. Bankowa 14, 40-007 Katowice, Poland. [email protected]
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Abstract

The paper focuses on multi-criteria problems. It presents the interactive compromise hypersphere method with sensitivity analysis as a decision tool in multi-objective programming problems. The method is based on finding a hypersphere (in the criteria space) which is closest to the set of chosen nondominated solutions. The proposed modifications of the compromise hypersphere method are based on using various metrics and analyzing their influence on the original method. Applications of the proposed method are presented in four multi-criteria problems: the assignment problem, the knapsack problem, the project management problem and the manufacturing problem.

Keywords

Multi-criteria problemsmultiple objective linear programmingsensitivity analysisdecision makingcompromise programming
Type
Research Article
Information
RAIRO - Operations Research , Volume 46 , Issue 3 , July 2012 , pp. 235 - 252
Copyright
© EDP Sciences, ROADEF, SMAI, 2012

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References

Références

G.T. Anthony, B. Bittner, B.P. Butler, M.G. Cox, R. Elligsen, A.B. Forbes, H. Gross, S.A. Hannaby, P.M. Harris and J. Kok, Chebychev reference software for evaluation of coordinate measuring machine data, Report EUR 15304 EN, National Physical Laboratory, Teddington, United Kingdom (1993).
Ballestero, E., Selecting the CP metric : A risk aversion approach. Eur. J. Oper. Res. 97 (1996) 593–596. Google Scholar
Bazgan, C., Hugot, H. and Vanedrpooten, D., Solving efficiently the 0-1 multi-objective knapsack problem. Comput. Oper. Res. 36 (2009) 260–279. Google Scholar
B.P. Butler, A.B. Forbes and P.M. Harris, Algorithms for geometric tolerance assessment. NPL Report DITC 228/94, National Physical Laboratory, Teddington, United Kingdom (1994).
E. Carrizosa, E. Conde, A. Pacual, D. Romero-Morales, Closest solutions in ideal-point methods, in Advances in multiple objective and goal programming, edited by R. Caballero, F. Ruiz and R.E. Steuer. Springer Verlag, Berlin, LNEMS 455 (1996) 274–281.
Eben-Chaime, M., Parametric solution for linear bicriteria knapsack models. Manag. Sci. 42 (1996) 1565–1575. Google Scholar
M. Ehrgott, Multicriteria optimization. Springer Verlag, Berlin (2002).
O.M. Elmabrouk, A linear programming technique for the pptimization of the activities in maintenance projects. Int. J. Eng. Technol. IJET-IJENS 11 (2011).
Evans, J.P. and Steuer, R.E., A revised simplex method for linear multiple objective programs. Math. Programm. 5 (1973) 54–72. Google Scholar
Gal, T. and Wolf, K., Stability in vector maximization – a survey. Eur. J. Oper. Res. 25 (1986) 169–182. Google Scholar
Gandibleux, X. and Freville, A., Tabu search based procedure for solving the 0/1 multiobjective knapsack problem : The two objective case. J. Heuristics 6 (2000) 361–383. Google Scholar
S.I. Gass, An illustrated guide to linear programming. Mc Graw-Hill Book Company, New York (1970).
S.I. Gass, Linear programming, methods and applications. Mc Graw-Hill Book Company, New York (1975).
Gass, S.I. and Roy, P.G., The compromise hypersphere for multiobjective linear programming. Eur. J. Oper. Res. 144 (2003) 459–479. Google Scholar
Gass, S.I., Harary, H.H. and Witzgall, C., Fitting circles and spheres to coordinate measuring machine data. Int. J. Flexible Manuf. 10 (1998) 5–25. Google Scholar
Gomes da Silva, C., Climaco, J. and Rui Figueria, J., Core problem in bi-criteria  {0,1} -knapsack problem. Comput. Oper. Res. 35 (2008) 2292–2306. Google Scholar
Hansen, P., Labbe, M. and Wendell, R.E., Sensitivity analysis in multiple objective linear programming : the tolerance approach. Eur. J. Oper. Res. 38 (1989) 63–69. Google Scholar
Hladik, M., Additive and multiplicative tolerance in multiobjective linear programming. Oper. Res. Lett. 36 (2008) 393–396. Google Scholar
J. Knutson and I. Bitz, Project Management. Amacom, New York (1991).
Opricovic, S. and Tzeng, G.H., Compromise solution by MCDM methods : a comparative analysis of VIKOR and TOPSIS. Eur. J. Oper. Res. 156 (2004) 445–455. Google Scholar
Opricovic, S. and Tzeng, G.H., Extended VIKOR method in comparison with outranking methods. Eur. J. Oper. Res. 178 (2007) 514–529. Google Scholar
Sitarz, S., Hybrid methods in multi-criteria dynamic programming. Appl. Math. Comput. 180 (2006) 38–45. Google Scholar
Sitarz, S., Postoptimal analysis in multicriteria linear programming. Eur. J. Oper. Res. 191 (2008) 7–18. Google Scholar
Sitarz, S., Ant algorithms and simulated annealing for multicriteria dynamic programming. Comput. Oper. Res. 36 (2009) 433–441. Google Scholar
Sitarz, S., Standard sensitivity analysis and additive tolerance approach in MOLP. Ann. Oper. Res. 181 (2010) 219–232. Google Scholar
Sitarz, S., Dynamic programming with ordered structures : theory, examples and applications. Fuzzy Sets and Systems 161 (2010) 2623–2641. Google Scholar
Sitarz, S., Sensitivity analysis of weak efficiency in MOLP. Asia-Pacific J. Oper. Res. 28 (2011) 445–455. Google Scholar
Sitarz, S., Mean value and volume-based sensitivity analysis for Olympic rankings. Eur. J. Oper. Res. 216 (2012) 232–238. Google Scholar
Steuer, R.E. and Choo, E. An Interactive weighted Tchebycheff procedure for multiple objective programming. Math. Programm. 26 (1981) 326–344. Google Scholar
R. Steuer, Multiple criteria optimization theory : computation and application. John Willey, New York (1986).
Tuyttens, D., Teghem, J., Fortemps, P. and Van Nieuwenhuyse, K., Performance of the MOSA method for the bicriteria assignment problem. J. Heuristics 6 (2000) 259–310. Google Scholar
Trzaskalik, T. and Sitarz, S., Discrete dynamic programming with outcomes in random variable structures. Eur. J. Oper. Res. 177 (2007) 1535–1548. Google Scholar
E.L. Ulungu and J. Teghem, Multicriteria assignment problem – a new method. Technical Report, Faculte Polytechnique de Mons, Belgium (1992).
A.P. Wierzbicki, Reference point approaches, in Multicriteria Decision Making, edited by R. Gal, T.J. Stewart, T. Hanne. Kluwer, Boston, MA (Chap. 9) (1999).
White, D.J., A special Multi-objective assigmnet problem. J. Oper. Res. Soc. 35 (1984) 759–767. Google Scholar
A. Woolf and B. Murray, Faster construction projects with CPM Scheduling. McGraw Hill (2007).
Yu, P.L. and Zeleny, M., The set of all nondominated solutions in linear cases and a multicriteria simplex method. J. Math. Anal. Appl. 49 (1975) 430–468. Google Scholar
M. Zeleny, Multiple Criteria Decision Making. McGraw-Hill Book Company, New York (1982).
Zionts, S. and Wallenius, J., An interactive multiple objective linear programming method for a class of underlying nonlinear utility functions. Manag. Sci. 29 (1983) 519–529. Google Scholar