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Modelling linear fractional transportation problem in belief degree—based uncertain environment

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A linear fractional transportation problem in uncertain environment is studied in this paper where the uncertain parameters of the problem are of belief degreebased uncertainty. For the first time, this type of uncertainty is considered for the linear fractional transportation problem. Belief degreebased uncertainty is useful for the cases that no historical information of an uncertain event is available. Zigzag type uncertainty distribution is used to show the belief degreebased uncertainty of the parameters of the problem. As solution methodology, the uncertain linear fractional transportation problem is converted to a crisp form using three approaches of expected value model, expected value and chance-constrained model, and chance-constrained model, separately. An extensive computational study on a real illustrative example shows the efficiency of the proposed formulation and the conversion approaches. The sensitivity analysis over the example illustrates the high dependency of the objective function value to the changes of the confidence level values of the chance constraints in the expected value and chance-constrained programming approach and the chance-constrained programming approach.
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Keywords: Uncertainty theory; belief degree; chance-constrained programming; linear fractional transportation problem

Document Type: Research Article

Affiliations: 1: Department of Mathematics, Masjed-Soleiman Branch, Islamic Azad University, Masjed-Soleiman, Iran 2: Department of Industrial Engineering, Firouzabad Institute of Higher Education, Firouzabad, Fars, Iran

Publication date: May 4, 2019

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