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"THE STUDIES ON LINEAR STOCHASTIC AND LINEAR FRACTIONAL PROGRAMMING", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.5, Issue 1, page no.1210-1217, January-2018, Available :http://www.jetir.org/papers/JETIR1801228.pdf

• Dr. Ashutosh Kumar Srivastawa

Optimizing the ratio of two linear functions subject to some constraints in which at least one of the problem data is random is called linear stochastic fractional programming problem (LSFPP). In this paper, a method combining the LSFP with branch-and-bound technique is proposed. A chance-constrained linear fractional programming problem has been considered. Various cases of randomness have been taken into account. Once a real number solution is obtained by LSFP, the branch-and-bound technique is used to obtain the integer solution. The best feasible solution among the trials is taken as the final solution. This method works well if the problem is complex and the constraints are non-linear. A machine manufacturing problem has been considered where the above models have been applied. Processing time are considered independently distributed normal variables.

Stochastic, Fractional, Cluster and Non Linear.

"THE STUDIES ON LINEAR STOCHASTIC AND LINEAR FRACTIONAL PROGRAMMING", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.5, Issue 1, page no. pp1210-1217, January-2018, Available at : http://www.jetir.org/papers/JETIR1801228.pdf