A Decision Aid Approach for Optimisation Problems Involving Several Economic Functions

DOI: 10.4236/ajor.2012.23040   PDF   HTML   XML   3,259 Downloads   5,677 Views   Citations

Abstract

Many concrete real life problems ranging from economic and business to industrial and engineering may be cast into a multi-objective optimisation framework. The redundancy of existing methods for solving this kind of problems susceptible to inconsistencies, coupled with the necessity for checking inherent assumptions before using a given method, make it hard for a nonspecialist to choose a method that fits well the situation at hand. Moreover, using blindly a method as proponents of the hammer principle (when you only have a hammer, you want everything in your hand to be a nail) is an awkward approach at best and a caricatural one at worst. This brings challenges to the design of a tool able to help a Decision Maker faced with these kinds of problems. The help should be at two levels. First the tool should be able to choose an appropriate multi-objective programming technique and second it should single out a satisfying solution using the chosen technique. The choice of a method should be made according to the structure of the problem and to the Decision Maker’s judgment value. This paper is an attempt to satisfy that need. We present a Decision Aid Approach that embeds a sample of good multi-objective programming techniques. The system is able to assist the Decision Maker in the above mentioned two tasks.

Share and Cite:

M. Rangoaga, M. Luhandjula and S. Ruzibiza, "A Decision Aid Approach for Optimisation Problems Involving Several Economic Functions," American Journal of Operations Research, Vol. 2 No. 3, 2012, pp. 331-338. doi: 10.4236/ajor.2012.23040.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] K. Deb, “Multi-Objective Optimization Using Evolutionary Algorithms,” John Wiley and Sons, New York, 2001.
[2] C. L. Hwang and A. S. M. Masud, “Multiple Objective Decision Making: Methods and Applications: A State-of- the-Art Survey,” Lecture notes in economics and mathematical systems, Vol. 164, Springer-Verlag, Berlin, Heidelberg, 1979. doi:10.1007/978-3-642-45511-7
[3] K. M. Miettinen and M. M. Makela, “Interactive Bundle- Based Method for Non-Differentiable Multi-Objective Optimization: NIMBUS,” Optimization, Vol. 34, No. 3, 1995, pp. 231-246. doi:10.1080/02331939508844109
[4] K. C. Kiwiel, “A Descent Method for Non-Smooth Convex Multi-Objective Minimization,” Large Scale Systems, Vol. 8, 1985, pp. 119-129.
[5] B. Render and R.M. Stair, “Quantitative Analysis for Management,” sixth edition, Prentice Hall, New Jersey, 1997.
[6] G. B. Dantzig, “A Complementary Algorithm for an Optimal Capital Path with Invariant Proportions,” International Institute for Applied Systems Analysis, 1973.
[7] D. G. Luenberger, “Introduction to Linear and Nonlinear Programming,” Addison-Wesley Publishing Company, Menlo-Park, 1973.
[8] N. Karmarkar, “A New Polynomial Time Algorithm for Linear Programming,” Combinatorica, Vol. 4, No. 4, 1984, pp. 373-395. doi:10.1007/BF02579150
[9] W. L. Winston, “Operations Research: Applications and Algorithms,” Third Edition, International Thomson Publishing, California, 1994.
[10] M. Avriel “Nonlinear Programming Analysis and Methods,” Prentice-Hall, New Jersey, 1976.
[11] L. Scharage, “Optimization Modeling with LINGO,” Sixth Edition, LINDO Systems Inc, Chicago, 2006.
[12] K. M. Miettinen and M. M. Makela, “Synchronous Approach in Interactive Multi-Objective Optimization,” European Journal of Operational Research, Vol. 170, No. 3, 2006, pp. 909-922. doi:10.1016/j.ejor.2004.07.052
[13] G. W. Evans, “An Overview of Techniques for Solving Multi-Objective Mathematical Programs,” Management Science, Vol. 30, No. 11, 1984, pp. 1268-1282. doi:10.1287/mnsc.30.11.1268
[14] K. M. Miettinen and M. M. Makela, “Optimization System www Nimbus,” Vol. 9, Laboratory of Scientific Computing, Department of Mathematics, University of Jyvaskyla, Finland, 1998.
[15] R. Caballero, M. Luque, J. Molina and F. Ruiz, “Mopen: A Computational Package for Linear Multi-Objective and Goal Programming Problems,” Decision Support Systems, Vol. 41, No. 1, 2005, pp. 160-175. doi:10.1016/j.dss.2004.06.002
[16] M. Ehrgott, “Multicriteria Optimization,” Second Edition, Springer, Auckland, 2005.
[17] K. M. Miettinen, “Nonlinear Multi-Objective Optimization,” First Edition, Kluwer Academic Publishers, Boston, 1999.
[18] K. C. Kiwiel, “Proximity Control in Bundle Methods for Methods for Convex Non-Differentiable Minimization,” Mathematical Programming, Vol. 46, No. 1-3, 1990, pp. 105-122. doi:10.1007/BF01585731
[19] F. Amador and C Romero, “Redundancy in Lexicographic Goal Programming: An Empiricalapproach,” European Journal of Operational Research, Vol. 41, No. 3, 1989, pp. 347-354. doi:10.1016/0377-2217(89)90255-5
[20] R. Chelouah and P. Siarry, “A Hybrid Method Combining Continuous Tabu Search and Nelder-Mead Simplex Algorithms for the Global Optimization of Multiminima Functions,” European Journal of Operational Research, Vol. 161, No. 3, 2005, pp. 636-654. doi:10.1016/j.ejor.2003.08.053
[21] M. Gershon, “The Role of Weights and Scales in the Application of Multi-Objective Decision Making,” European Journal of Operational Research, Vol. 15, No. 2, 1984, pp. 244-250. doi:10.1016/0377-2217(84)90214-5
[22] R. Benayoun, J. de Montgolfier and J. Tergny, “Linear Programming with Multiple Objective Functions: Step Method (Stem),” Mathematical Programming, Vol. 1, No. 1, 1971, pp. 366-375. doi:10.1007/BF01584098
[23] L. R. Gardiner and R. E. Steuer, “Unified Interactive Multiple Objective Programming,” European Journal of Operational Research, Vol. 74, 1984, pp. 371-406.
[24] J. T. Buchanan, “Multiple Objective Mathematical Programming: A Review,” New Zealand Operational Research, Vol. 14, No. 1, 1986, pp. 1-27.
[25] A. M. Geoffrion, “Proper Efficiency and the Theory of Vector Maximization,” Journal of Mathematical Analysis and Applications, Vol. 22, No. 3, 1968, pp. 619-630. doi:10.1016/0022-247X(68)90201-1
[26] M. I. Henig and Z. Ritz, “Multiplicative Decision Rules for Multi-Objective Decision Problems,” European Journal of Operational Research, Vol. 26, No. 1, 1986, pp. 134-141. doi:10.1016/0377-2217(86)90165-7
[27] A. K. Bhunia and J. Majumdar, “Elitist Genetic Algorithm for Assignment Problem with Imprecise Goal,” European Journal of Operational Research, Vol. 177, 2007, pp. 684-692. doi:10.1016/j.ejor.2005.11.034
[28] C. Botha, E. Ferreira, G. Geldenhuys and H. Ittman, “Selected Topics in Operations Research: Quantitative Management,” UNISA, Pretoria, 1998.
[29] C. D. Gelatt, S. Kirkpatrick and M. P. Vecchi, “Optimization by Simulated Annealing,” Science, Vol. 220, 1983, pp. 45-54.
[30] J. W. Barnes, F. W. Glover and M. Laguna, “Tabu Search Methods for a Single Machinescheduling Problem,” Journal of Intelligent Manufacturing, Vol. 2, No. 2, 1991, pp. 63-74. doi:10.1007/BF01471219
[31] M. J. Rangoaga, “A Decision Support System for MultiObjective Programming Problems,” Master’s Thesis, University of South Africa, Pretoria, 2009.
[32] H. S. Solutions, “Textpad,” 1992. http://wapedia.mobi/en/textpad
[33] S. S. Ruzibiza, “Solving Multi-Objective Mathematical Programming Problems with Fixed and Fuzzy Coefficients,” Master’s Thesis, Independent Institute of Lay Aventists of Kigali, Kigali, 2011.

  
comments powered by Disqus

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.