A New Interactive Method to Solve Multiobjective Linear Programming Problems
Mahmood REZAEI SADRABADI, Seyed Jafar SADJADI
.
DOI: 10.4236/jsea.2009.24031   PDF   HTML     6,536 Downloads   12,715 Views   Citations

Abstract

Multiobjective Programming (MOP) has become famous among many researchers due to more practical and realistic applications. A lot of methods have been proposed especially during the past four decades. In this paper, we develop a new algorithm based on a new approach to solve MOP by starting from a utopian point, which is usually infeasible, and moving towards the feasible region via stepwise movements and a simple continuous interaction with decision maker. We consider the case where all objective functions and constraints are linear. The implementation of the pro-posed algorithm is demonstrated by two numerical examples.

Share and Cite:

M. REZAEI SADRABADI and S. SADJADI, "A New Interactive Method to Solve Multiobjective Linear Programming Problems," Journal of Software Engineering and Applications, Vol. 2 No. 4, 2009, pp. 237-247. doi: 10.4236/jsea.2009.24031.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] F. B. Abdelaziz, “Multiple objective programming and goal programming: New trends and applications,” Euro-pean Journal of Operational Research, Vol. 177, pp. 1520–1522, 2007.
[2] M. M. Wiecek, “Multiple criteria decision making for engineering,” Omega, Vol. 36, pp. 337–339, 2008.
[3] J. Kim and S. K. Kim, “A CHIM-based interactive Tche-bycheff procedure for multiple objective decision mak-ing,” Computers & Operations Research, Vol. 33, pp. 1557–1574, 2006.
[4] M. Sun, “Some issues in measuring and reporting solu-tion quality of interactive multiple objective programming procedures,” European Journal of Operational Research, Vol. 162, pp. 468–483, 2005.
[5] M. Zeleny, “Multiple criteria decision making,” MC Graw-Hill, New York, 1982.
[6] R. Kenney and H. Raiffa, “Decisions with multiple objec-tives: Preferences and value trade-offs,” J. Wiley, New York, 1976.
[7] C. Romero, “Handbook of critical issues in goal pro-gramming,” Pergamon Press, Oxford, 1991.
[8] M. Ida, “Efficient solution generation for multiple objec-tive linear programming based on extreme ray generation method,” European Journal of Operational Research, Vol. 160, pp. 242–251, 2005.
[9] L. Pourkarimi, M. A. Yaghoobi and M. Mashinchi, “De-termining maximal efficient faces in multiobjective linear programming problem,” Journal of Mathematical Analy-sis and Applications, Vol. 354, pp. 234–248, 2009.
[10] R. E. Steuer and C. A. Piercy, “A regression study of the number of efficient extreme points in multiple objective linear programming,” European Journal of Operational Research, Vol. 162, pp. 484–496, 2005.
[11] E. A. Youness and T. Emam, “Characterization of effi-cient solutions for multi-objective optimization problems involving semi-strong and generalized semi-strong e-convexity,” Acta Mathematica Scientia, Vol. 28B(1), pp. 7–16, 2008.
[12] S. I. Gass and P. G. Roy, “The compromise hypersphere for multiobjective linear programming,” European Jour-nal of Operational Research, Vol. 144, pp. 459–479, 2003.
[13] J. Chen and S. Lin, “An interactive neural network-based approach for solving multiple criteria decision making problems,” Decision Support Systems, Vol. 36, pp. 137–146, 2003.
[14] A. Engau, “Tradeoff-based decomposition and deci-sion-making in multiobjective programming,” European Journal of Operational Research, Vol. 199, pp. 883–891, 2009.
[15] L. R. Gardiner and R. E. Steuer, “Unified interactive mul-tiple objective programming,” European Journal of Op-erational Research, Vol. 74, pp. 391–406, 1994.
[16] C. Homburg, “Hierarchical multi-objective decision mak-ing,” European Journal of Operational Research, Vol. 105, pp. 155–161, 1998.
[17] C. L. Hwang and A. S. M. Masud, “Multiple objective decision making methods and applications,” Springer- Verlag, Amsterdam, 1979.
[18] B. Malakooti and J. E. Alwani, “Extremist vs. centrist decision behavior: Quasi-convex utility functions for in-teractive multi-objective linear programming problems,” Computers & Operations Research, Vol. 29, pp. 2003– 2021, 2002.
[19] G. R. Reeves and K. R. MacLeod, “Some experiments in Tchebycheff-based approaches for interactive multiple objective decision making,” Computers & Operations Research, Vol. 26, pp. 1311–1321, 1999.
[20] R. E. Steuer, J. Silverman, and A. W. Whisman, “A com-bined Tchebycheff/aspiration criterion vector interactive multi-objective programming procedure,” Computers & Operations Research, Vol. 43, pp. 641–648, 1995.
[21] M. Sun, A. Stam, and R. E. Steuer, “Interactive multiple objective programming using Tchebycheff programs and artificial neural networks,” Computers & Operations Re-search, Vol. 27, pp. 601–620, 2000.
[22] G. R. Reeves and J. J. Gonzalez, “A comparison of two interactive MCDM procedures,” European Journal of Operational Research, Vol. 41, pp. 203–209, 1989.
[23] A. R. P. Borges and C. H. Antunes, “A visual interactive tolerance approach to sensitivity analysis in MOLP,” European Journal of Operational Research, Vol. 142, pp. 357–381, 2002.
[24] J. T. Buchanan and H. G. Daellenbach, “A comparative evaluation of interactive solution methods for multiple objective decision models,” European Journal of Opera-tional Research, Vol. 29, pp. 353–359, 1987.
[25] A. A. Geoffrion, J. S. Dyer, and A. Feinberg, “An inter-active approach for multi-criterion optimization with an application to the operation of an academic department,” Management Science, Vol. 19, pp. 357–368, 1972.
[26] R. E. Steuer and E. U. Choo, “An interactive weighted Tchebycheff procedure for multiple objective program-ming,” Mathematical Programming, Vol. 26, pp. 326–344, 1983.
[27] S. Zionts and J. Wallenius, “An interactive multiple ob-jective linear programming method for a class of under-lying nonlinear utility functions,” Management Science, Vol. 29, pp. 519–529, 1983.
[28] D. Vanderpooten, “The interactive approach in MCDA: A technical framework and some basic conceptions,” Mathematical and Computer Modelling, Vol. 12, pp. 1213–1220, 1989.
[29] G. R. Reeves and L. Franz, “A simplified interactive mul-tiple objective linear programming procedure,” Com-puters and Operations Research, Vol. 12, pp. 589–601, 1985.

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.