Title: A solid transportation problem with fuzzy random costs and constraints

Authors: Pravash Kumar Giri; Manas Kumar Maiti; Manoranjan Maiti

Addresses: Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Paschim-Medinipur, WB, India ' Department of Mathematics, Mahishadal Raj College, Mahishadal, Purba-Medinipur, WB 721628, India ' Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Paschim-Medinipur, WB, India

Abstract: Three Fuzzy Random Solid Transportation Problems (FRSTPs) are proposed, where both fuzziness and randomness occur simultaneously in costs and times. Among the models, the first one is a multi-objective model minimising both fuzzy-random total cost and time and other two are fuzzy-random single objective ones with fuzzy-random/fuzzy constraint on time. The fuzzy-random models are transformed to deterministic multi-objective constrained problems following Nanda, S., Panda, G., Dash, J.K., (2008) 'A new methodology for crisp equivalent of fuzzy chance constrained programming problem', Fuzzy Optim. Decision Making, Vol. 7, pp.5974. Finally Pareto optimal decisions are derived using an elitist Multi-Objective Genetic Algorithm (MOGA) with cyclic crossover, two-point mutation and a refining operation.

Keywords: fuzzy random variables; solid transport problem; fuzzy normal distribution; MOGA; fuzzy random constraints; multi-objective genetic algorithms; MOGA.

DOI: 10.1504/IJMOR.2012.049938

International Journal of Mathematics in Operational Research, 2012 Vol.4 No.6, pp.651 - 678

Available online: 19 Oct 2012 *

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