Title: Computation of multi-choice multi-objective fuzzy probabilistic two stage programming problem

Authors: Prabhat Kumar Rout; Sudarsan Nanda; Srikumar Acharya

Addresses: School of Applied Sciences, KIIT University, Bhubaneswar, Odisha, India ' KIIT University, Bhubaneswar, Odisha, India ' School of Applied Sciences, KIIT University, Bhubaneswar, Odisha, India

Abstract: The aim of the paper is to present a multi-choice multi-objective fuzzy probabilistic two stage programming problem and its solution methodology. The mathematical programming problem suggested here is difficult to solve directly. Therefore, three major steps are suggested to solve the proposed mathematical programming problem. In first step, fuzzy chance constraint is transformed to its equivalent chance constraint programming problem using α – cut technique. Chance constraint technique is used to obtain a crisp model of multi-choice multi-objective two-stage programming problem. In the second step, two stage programming problem is converted to its equivalent deterministic model. In next step, importance is given to handle multi-choice parameter using least square approximation technique. At the end of third step, a multi-objective mathematical programming is obtained. Finally ∈-constraint approach is used to solve the transformed multi-objective mathematical programming. Using existing methodology and software the final solution of the proposed model is obtained. The proposed method is implemented with a numerical example.

Keywords: multi-objective; fuzzy probability; ∈-constraint; multi-choice programming; least square approximation.

DOI: 10.1504/IJCSM.2020.106393

International Journal of Computing Science and Mathematics, 2020 Vol.11 No.2, pp.168 - 191

Accepted: 07 Oct 2017
Published online: 06 Apr 2020 *

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