Title: Multi-objective fuzzy quadratic probabilistic programming problem involving fuzzy Cauchy random variable
Authors: Narmada Ranarahu; Jayanta Kumar Dash; Srikumar Acharya
Addresses: Department of Mathematics, Institute of Technical Education and Research, Siksha O Anusandhan University, Khandagiri Square, Bhubaneswar, Odisha, India ' Department of Mathematics, Institute of Technical Education and Research, Siksha O Anusandhan University, Khandagiri Square, Bhubaneswar, Odisha, India ' Department of Mathematics, School of Applied Sciences, KIIT University, Bhubaneswar-24, Odisha, India
Abstract: In this paper, we have proposed a method for solving a multi-objective quadratic probabilistic programming problem, where the objective functions are multi-objective and quadratic in nature. The right hand side parameters are fuzzy Cauchy distributed independent random variable with location parameter δ and scale parameter β. The proposed mathematical programming problem is solved using two steps. First, the fuzziness is removed by using alpha cut technique and randomness is removed by chance constrained method. In second step, weighting method is used to solve the transformed multi-objective quadratic mathematical programming. This mathematical model is solved by existing methodology or software. A numerical example is presented to illustrate the efficiency and feasibility of the proposed method.
Keywords: stochastic programming; multi-objective programming; fuzzy programming; Cauchy random variables; optimisation techniques.
International Journal of Operational Research, 2018 Vol.32 No.4, pp.495 - 513
Received: 01 Dec 2015
Accepted: 12 Nov 2016
Published online: 27 Jul 2018 *