Optimizing Chance Constraint Multiple-Objective Fractional Mathematical Programming Problem Involving Dependent Random Variable
Download PDF
Authors: B. BELAY AND S. ACHARYA
DOI: 10.46793/KgJMat2502.239B
Abstract:
This manuscript suggests a methodology to solve chance constraint multiple-objective linear fractional mathematical programming problem in which the parameters are dependent random variables to each other. The proposed problem is formulated by taking few of the parameters as continuous dependent random variables. The proposed model cannot be solved directly by using existing methodology. Thus in order to solve the proposed model, an equivalent deterministic model is derived. The procedure to solve the proposed model is accomplished in two main steps. Initially, the proposed multiple-objective chance constraint linear fractional mathematical problem is transformed to deterministic equivalent multiple-objective linear fractional mathematical programming by the help of chance constrained method. In the second step, multiple-objective functions, which consist of fractional functions is solved by using lexicographic programming approach. Finally, an example is mentioned to illustrate the methodology.
Keywords:
Multiple-objective programming problem, chance constraint programming problem, fractional programming problem, lexicography method, dependent random variables.
References:
[1] S. Acharya, B. Belay and R. Mishra, Multi-objective probabilistic fractional programming problem involving two parameters cauchy distribution, Math. Model. Anal. 24(3) (2019),385–403. https://doi.org/10.3846/mma.2019.024
[2] M. P. Biswal, N. Biswal and D. Li, Probabilistic linear programming problems with exponential random variables, European J. Oper. Res. 111(3) (1998), 589–597. https://doi.org/10.1016/S0377-2217(97)90319-2
[3] M. Chakraborty and S. Gupta, Fuzzy mathematical programming for multi objective linear fractional programming problem, Fuzzy Sets and Systems 125(3) (2002), 335–342. https://doi.org/10.1016/S0165-0114(01)00060-4
[4] V. Charles, S. Ansari and M. Khalid, Multi-objective stochastic linear programming with general form of distributions, International Journal of Operational Research & Optimization 2(2) (2011), 261–278.
[5] A. Charnes and W. Cooper, Chance constraints and normal deviates, J. Amer. Statist. Assoc. 57(297) (1962), 134–148. https://doi.org/10.2307/2282444
[6] A. Charnes and W. W. Cooper, Programming with linear fractional functionals, Naval Research Logistics Quarterly 9(3–4) (1962), 181–186. https://doi.org/10.1002/nav.3800090303
[7] A. N. Dheyab, Finding the optimal solution for fractional linear programming problems with fuzzy numbers, Journal of Kerbala University 10(3) (2012), 105–110.
[8] D. Dutta, J. Rao and R. Tiwari, A restricted class of multi objective linear fractional programming problems, European J. Oper. Res. 68(3) (1993), 352–355. https://doi.org/10.1016/0377-2217(93)90191-O
[9] S. Jain, Modeling of Gauss elimination technique for multi-objective fractional programming problem, South Asian Journal of Mathematics 4(3) (2014), 148–153.
[10] M. Knott, Randomized decisions in chance-constrained programming, Journal of the Operational Research Society 36(10) (1985), 959–962. https://doi.org/10.1057/jors.1985.167
[11] J. S. Kornbluth and R. E. Steuer, Multiple objective linear fractional programming, Management Science 27(9) (1981), 1024–1039. https://doi.org/10.1287/mnsc.27.9.1024
[12] B. Lingaraj and H. Wolfe, Certainty equivalent of a chance constraint if the random variable follows a gamma distribution, The Indian Journal of Statistics 36(2) (1974), 204–208.
[13] M. K. Luhandjula, Fuzzy approaches for multiple objective linear fractional optimization, Fuzzy Sets and Systems 13(1) (1984), 11–23. https://doi.org/10.1016/0165-0114(84)90023-X
[14] R. Porchelvi, L. Vasanthi and R. Hepzibah, On solving multi objective fractional linear programming problems, International Journal of Current Research 6(8) (2014), 8095–8102.
[15] N. Sahoo and M. Biswal, Computation of probabilistic linear programming problems involving normal and log-normal random variables with a joint constraint, Computer Mathematics 82(11) (2005), 1323–1338. https://doi.org/10.1080/00207160500113058
[16] S. F. Tantawy, Solving a special class of multiple objective linear fractional programming problems, The ANZIAM Journal 56(1) (2014), 91–103.
Login:
