PENGEMBANGAN SEBUAH METODE INTERAKTIF UNTUK PENYELESAIAN MASALAH PROGRAM LINIER BILANGAN BULAT KELAS STOKASTIK MULTIOBJEKTIF

Suparni Suparni ()

Abstract


Decision problems of stochastic or probabilistic optimization arise when certain coefficient of an optimization model are not fixed or known but are instead, to some extent, stochastic (or random or probabilistic) quantities. This paper focused on multi objective stochastic optimization. We propose a method for solving a multi objective chance constraints integer programming problem based on interactive approach. We assume that there is randomness in the right-hand sides of the constraints only and that the random variables are normally distributed.

Keywords


Pemrograman linear integer multiobjek; teknik chance-constrained; pendekatan interaktif

Full Text:

PDF

References


Balinski, M., “An Algorithm for Finding All Vertices of Convex Polyhedral Sets”, SIAM Journal, Vol. 9, No. 1, 1961.

Chankong, V. and Haimes, Y. Y., “Multiobjective Decision-Making: Theory and Methodology” (North Holland Series in System Science and Engineering), 1983.

El-Banna, A. Z. and Youness, E. A., “On Some Basic Notions of Stochastic Multiobjective Problems with Random Parameters in the Constraint”s, Microelectronics. Reliability, Vol. 33, No. 13, 1993, 1981-1986.

Guddat. J., Vasquez, F., Tammer, K. and Wendler, K., “Multiobjective and Stochastic Optimization Based on Parametric Optimization”, Akademie-Verlage, Berlin, 1985.

Osama, Ez-Eldin., “On Stochastic Multiobjective Integer Linear Programming Problems”, M.SC. Thesis, Helwan University, Cairo, Egypt, 2000.

Osman, M. S. A., “Qualitative Analysis of Basic Notions in Parametric Convex Programming I” (Parameters in the Constraints), Applied. Math. CSSR Akad. Ved. Prague, 22, 1977.

Osman, M. S. A., “Qualitative Analysis of Basic Notions in Parametric Convex Programming II” (Parameters in the Objective Function), Applied. Math. CSSR Akad. Ved. Prague, 22, 1977.

Osman, M. S. A. and Saad, O. M., “On the Solution of Chance-Constrained Multiobjective Linear Programming Problems with A Parametric Study,” Proceedings of the First International Conference on Operations Research and its Applications, Higher Technological Institute, Ramadan Tenth. City, Egypt, 1994.

Saad, O. M. and Kittani, H. F., “Multiobjective integer linear programming problems under randomness”, IAPQR TRANSACTIONS, Vol.28, No.2, 2003, 101-108.

Saad, O. M., “Optimization under uncertainty: A State-of-the-Art, Paper accepted for publication in Applied Mathematics and Computation”, 2006.

Saaty T. L., The Analytic Hierarchy Process. McGraw-Hill. New York, 1980

Saaty T. L., Hightlights and critical pints in the theory and applications of the analytic hierarchy process. EJOR, 74(3) (1994).

Seppälä, Y., “On Accurate Linear Approximations for Chance-Constrained Programming”, Journal of Operational. Research. Society, Vol. 39, No. 7, 1998.

Sharif, W.H. and Saad, O.M., “On stability in multiobjective integer linear programming: A stochastic approach”, American Journal of Applied Sciences, Vol. 2, No. 12, 2005.

Stochastic Programming Web Site, (2002), http:// Stoprog.org, Current as of July 2002.

Taha, H. A., “Integer Programming: Theory, Applications and Computations”, Academic Press, New York, 1975.

Vogel, S., “On Stability in Multiobjective Programming-A Stochastic Approach”, Mathematical Programming, 60, 1992.




DOI: https://doi.org/10.24952/logaritma.v6i01.1243

Refbacks

  • There are currently no refbacks.


Copyright (c) 2018 Suparni Suparni

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Logaritma : Jurnal Ilmu-ilmu Pendidikan dan Sains

Tadris Matematika FTIK UIN Syekh Ali Hasan Ahmad Addary Padangsidimpuan

ISSN: 2338-8706  (print), 2580-7145 (online)

Jl. T. Rizal Nurdin Km. 4,5 Sihitang Padangsidimpuan

Sumatera Utara 22733 Indonesia

Phone: 0634-22080 Fax: 0634-24022

Email: logaritma.tmm@gmail.com