Computation of Multi-choice Multi-objective Fuzzy Probabilistic Transportation Problem

Ranarahu, Narmada; Dash, J. K.; Acharya, Srikumar

doi:10.1007/978-981-13-1954-9_6

Cited by 5 publications

(1 citation statement)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The concept of fuzzy set theory was first introduced by Zadeh [3]. Solution methodology of different types of multi-objective fuzzy probabilistic programming problems have developed by several researchers [4][5][6][7][8][9]. After this motivation, Mendel et al [10] discussed how type-2 fuzzy is different from type-1 fuzzy.…”

Section: Introductionmentioning

confidence: 99%

Type-2 Fuzzy Stochastic Transportation Problem with Gamma Distribution

Chaini

Ranarahu

2023

IJFIS

View full text Add to dashboard Cite

The transportation problem in real-life is an uncertain problem. Particularly when goods are transported from the source to destinations with the best transportation setup that satisfies the decision maker's preferences by taking into account the competing objectives/criteria such as maintaining exact relationships between a few linear parameters, such as actual transportation fee/total transportation cost, delivery fee/desired path, total return/total investment, etc. Due to the uncertainty of nature, such a relationship is not deterministic. In this stochastic transportation problem supplies are considered as fuzzy random variables, which follow fuzzy gamma distribution, with shape parameter α and scale parameter β. Here β is a perfectly normal interval type-2 fuzzy random variable. This paper proposes a solution methodology for solving the fuzzy stochastic transportation problem, where fuzziness and randomness occur under one roof. Therefore, we converted it to an equivalent deterministic mathematical programming problem by applying the following two steps. In the first step of the solution procedure, fuzziness is removed by using alpha-cut technique to obtain stochastic transportation problem. In the second step, the stochastic transportation problem is converted to an equivalent crisp transportation problem using the chance constrained technique. This mathematical model is solved by existing methodology or software. In order to illustrate the methodology a case study is provided.

show abstract