Title: Computation of a multi-objective fuzzy stochastic transportation problem

Authors: Srikumar Acharya; Narmada Ranarahu; Jayanta Kumar Dash; Mitali Madhumita Acharya

Addresses: Department of Mathematics, SAS, KIIT University, Bhubaneswar-24, Odisha, India ' 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, SAS, KIIT University, Bhubaneswar-24, Odisha, India

Abstract: This paper is concerned with the solution methodology of a multi-objective transportation problem where fuzziness and randomness occur under one roof. In the present transportation problem, supplies and demands are considered as fuzzy random variable. In the first step of the solution procedure, fuzziness is removed by using alpha-cut technique to obtain multi-objective stochastic transportation problem. By using the chance constrained technique, the multi-objective stochastic transportation problem is transformed to equivalent crisp multi-objective transportation problem. Then, introducing the concept of membership function, multi-objective deterministic transportation problem is converted into single objective mathematical programming problem. Finally, it is solved with the help of existing technique. A numerical example and a case study are provided in order to illustrate the methodology.

Keywords: stochastic programming; multi-objective programming; fuzzy programming; normal random variables; optimisation techniques; multi-objective transport problems; fuzzy random variables.

DOI: 10.1504/IJFCM.2014.067129

International Journal of Fuzzy Computation and Modelling, 2014 Vol.1 No.2, pp.212 - 233

Received: 03 Jul 2013
Accepted: 02 Jun 2014

Published online: 07 Feb 2015 *

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