JSEA  Vol.2 No.4 , November 2009
A New Interactive Method to Solve Multiobjective Linear Programming Problems
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.

Cite this paper
nullM. 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.
[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.