Interactive compromise hypersphere method and its applications

Sebastian Sitarz

RAIRO - Operations Research (2012)

  • Volume: 46, Issue: 3, page 235-252
  • ISSN: 0399-0559

Abstract

top
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.

How to cite

top

Sitarz, Sebastian. "Interactive compromise hypersphere method and its applications." RAIRO - Operations Research 46.3 (2012): 235-252. <http://eudml.org/doc/222505>.

@article{Sitarz2012,
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.},
author = {Sitarz, Sebastian},
journal = {RAIRO - Operations Research},
keywords = {Multi-criteria problems; multiple objective linear programming; sensitivity analysis; decision making; compromise programming; multi-criteria problems},
language = {eng},
month = {9},
number = {3},
pages = {235-252},
publisher = {EDP Sciences},
title = {Interactive compromise hypersphere method and its applications},
url = {http://eudml.org/doc/222505},
volume = {46},
year = {2012},
}

TY - JOUR
AU - Sitarz, Sebastian
TI - Interactive compromise hypersphere method and its applications
JO - RAIRO - Operations Research
DA - 2012/9//
PB - EDP Sciences
VL - 46
IS - 3
SP - 235
EP - 252
AB - 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.
LA - eng
KW - Multi-criteria problems; multiple objective linear programming; sensitivity analysis; decision making; compromise programming; multi-criteria problems
UR - http://eudml.org/doc/222505
ER -

References

top
  1. 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).  
  2. E. Ballestero, Selecting the CP metric : A risk aversion approach. Eur. J. Oper. Res.97 (1996) 593–596.  
  3. C. Bazgan, H. Hugot and D. Vanedrpooten, Solving efficiently the 0-1 multi-objective knapsack problem. Comput. Oper. Res.36 (2009) 260–279.  
  4. 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).  
  5. 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.  
  6. M. Eben-Chaime, Parametric solution for linear bicriteria knapsack models. Manag. Sci.42 (1996) 1565–1575.  
  7. M. Ehrgott, Multicriteria optimization. Springer Verlag, Berlin (2002).  
  8. O.M. Elmabrouk, A linear programming technique for the pptimization of the activities in maintenance projects. Int. J. Eng. Technol. IJET-IJENS11 (2011).  
  9. J.P. Evans and R.E. Steuer, A revised simplex method for linear multiple objective programs. Math. Programm.5 (1973) 54–72.  
  10. T. Gal and K. Wolf, Stability in vector maximization – a survey. Eur. J. Oper. Res.25 (1986) 169–182.  
  11. X. Gandibleux and A. Freville, Tabu search based procedure for solving the 0/1 multiobjective knapsack problem : The two objective case. J. Heuristics6 (2000) 361–383.  
  12. S.I. Gass, An illustrated guide to linear programming. Mc Graw-Hill Book Company, New York (1970).  
  13. S.I. Gass, Linear programming, methods and applications. Mc Graw-Hill Book Company, New York (1975).  
  14. S.I. Gass and P.G. Roy, The compromise hypersphere for multiobjective linear programming. Eur. J. Oper. Res.144 (2003) 459–479.  
  15. S.I. Gass, H.H. Harary and C. Witzgall, Fitting circles and spheres to coordinate measuring machine data. Int. J. Flexible Manuf.10 (1998) 5–25.  
  16. C. Gomes da Silva, J. Climaco and J. Rui Figueria, Core problem in bi-criteria  {0,1} -knapsack problem. Comput. Oper. Res.35 (2008) 2292–2306.  
  17. P. Hansen, M. Labbe and R.E. Wendell, Sensitivity analysis in multiple objective linear programming : the tolerance approach. Eur. J. Oper. Res.38 (1989) 63–69.  
  18. M. Hladik, Additive and multiplicative tolerance in multiobjective linear programming. Oper. Res. Lett.36 (2008) 393–396.  
  19. J. Knutson and I. Bitz, Project Management. Amacom, New York (1991).  
  20. S. Opricovic and G.H. Tzeng, Compromise solution by MCDM methods : a comparative analysis of VIKOR and TOPSIS. Eur. J. Oper. Res.156 (2004) 445–455.  
  21. S. Opricovic and G.H. Tzeng, Extended VIKOR method in comparison with outranking methods. Eur. J. Oper. Res.178 (2007) 514–529.  
  22. S. Sitarz, Hybrid methods in multi-criteria dynamic programming. Appl. Math. Comput.180 (2006) 38–45.  
  23. S. Sitarz, Postoptimal analysis in multicriteria linear programming. Eur. J. Oper. Res.191 (2008) 7–18.  
  24. S. Sitarz, Ant algorithms and simulated annealing for multicriteria dynamic programming. Comput. Oper. Res.36 (2009) 433–441.  
  25. S. Sitarz, Standard sensitivity analysis and additive tolerance approach in MOLP. Ann. Oper. Res.181 (2010) 219–232.  
  26. S. Sitarz, Dynamic programming with ordered structures : theory, examples and applications. Fuzzy Sets and Systems161 (2010) 2623–2641.  
  27. S. Sitarz, Sensitivity analysis of weak efficiency in MOLP. Asia-Pacific J. Oper. Res.28 (2011) 445–455.  
  28. S. Sitarz, Mean value and volume-based sensitivity analysis for Olympic rankings. Eur. J. Oper. Res.216 (2012) 232–238.  
  29. R.E. Steuer and E. ChooAn Interactive weighted Tchebycheff procedure for multiple objective programming. Math. Programm.26 (1981) 326–344.  
  30. R. Steuer, Multiple criteria optimization theory : computation and application. John Willey, New York (1986).  
  31. D. Tuyttens, J. Teghem, P. Fortemps and K. Van Nieuwenhuyse, Performance of the MOSA method for the bicriteria assignment problem. J. Heuristics6 (2000) 259–310.  
  32. T. Trzaskalik and S. Sitarz, Discrete dynamic programming with outcomes in random variable structures. Eur. J. Oper. Res.177 (2007) 1535–1548.  
  33. E.L. Ulungu and J. Teghem, Multicriteria assignment problem – a new method. Technical Report, Faculte Polytechnique de Mons, Belgium (1992).  
  34. 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).  
  35. D.J. White, A special Multi-objective assigmnet problem. J. Oper. Res. Soc.35 (1984) 759–767.  
  36. A. Woolf and B. Murray, Faster construction projects with CPM Scheduling. McGraw Hill (2007).  
  37. P.L. Yu and M. Zeleny, The set of all nondominated solutions in linear cases and a multicriteria simplex method. J. Math. Anal. Appl.49 (1975) 430–468.  
  38. M. Zeleny, Multiple Criteria Decision Making. McGraw-Hill Book Company, New York (1982).  
  39. S. Zionts and J. Wallenius, An interactive multiple objective linear programming method for a class of underlying nonlinear utility functions. Manag. Sci.29 (1983) 519–529.  

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.