Solving Stochastic Fuzzy Transportation Problem with Mixed Constraints Using the Weibull Distribution

The development in the industries has necessitated the growth of transportation methods. Due to the variation in the transportation systems, many problems seem to arise in the present times. One such problem is the stochastic fuzzy transportation problem (SFTP). The SFTP is a chance-constrained prog...

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Bibliographic Details
Published inJournal of mathematics (Hidawi) Vol. 2022; no. 1
Main Authors Buvaneshwari, T.K., Anuradha, D.
Format Journal Article
LanguageEnglish
Published Cairo Hindawi 2022
Hindawi Limited
Subjects
Constraints
Costs
Decision making
Fuzzy sets
Linear programming
Mathematical programming
Mathematics
Operating costs
Parameter sensitivity
Probability theory
Random variables
Randomness
Sensitivity analysis
Set theory
Statistical analysis
Supply & demand
Transportation problem
Transportation systems
Weibull distribution
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Summary:The development in the industries has necessitated the growth of transportation methods. Due to the variation in the transportation systems, many problems seem to arise in the present times. One such problem is the stochastic fuzzy transportation problem (SFTP). The SFTP is a chance-constrained programming (CCP) problem with probabilistic constraints where supply and demand are randomness, and the objective function is in fuzzy nature. In this paper, we have developed three models for the SFTP, where the constraints are mixed type following Weibull distribution (WD). The aim of the research work is to optimize the transportation cost in FTP under probabilistic mixed constraints. In order to achieve this, the cost coefficient of the fuzzy objective function is converted to alpha cut representation, and the probabilistic mixed constraints are converted to deterministic form by using the WD. The proposed models are illustrated by providing a numerical example, and the problem is solved using Lingo software. It is worth pointing out that these models are constructed from different points of view. The decision-maker’s (DM’s) preference has the final say in the usage of the models. A sensitivity analysis (SA) is performed to explore the sensitivity of the parameters in the proposed model.
ISSN:2314-4629
2314-4785
DOI:10.1155/2022/6892342