Multi-objective transportation problem under type-2 trapezoidal fuzzy numbers with parameters estimation and goodness of fit

The problem of transportation in real-life is an uncertain multi-objective decision-making problem. In particular, by taking into account the conflicting objectives, Decision-Makers (DMs) are looking for the best transport set up to determine the optimum shipping quantity subject to certain capacity...

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Autores principales:	Murshid Kamal, Ali Alarjani, Ahteshamul Haq, Faiz Noor Khan Yusufi, Irfan Ali
Formato:	article
Lenguaje:	EN
Publicado:	Vilnius Gediminas Technical University 2021
Materias:	multi-objective optimization transportation problem fuzzy goal programming multi-choice maximum likelihood estimation akaike information criterion bayesian information criterion stochastic programming Transportation engineering TA1001-1280
Acceso en línea:	https://doaj.org/article/cde807110ff646b2ba8ad7fbae381d9b
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spelling	oai:doaj.org-article:cde807110ff646b2ba8ad7fbae381d9b2021-11-25T13:01:50ZMulti-objective transportation problem under type-2 trapezoidal fuzzy numbers with parameters estimation and goodness of fit1648-41421648-348010.3846/transport.2021.15649https://doaj.org/article/cde807110ff646b2ba8ad7fbae381d9b2021-11-01T00:00:00Zhttps://journals.vgtu.lt/index.php/Transport/article/view/15649https://doaj.org/toc/1648-4142https://doaj.org/toc/1648-3480The problem of transportation in real-life is an uncertain multi-objective decision-making problem. In particular, by taking into account the conflicting objectives, Decision-Makers (DMs) are looking for the best transport set up to determine the optimum shipping quantity subject to certain capacity constraints on each route. This paper presented a Multi-Objective Transportation Problem (MOTP) where the objective functions are considered as Type-2 trapezoidal fuzzy numbers (T2TpFN), respectively. Demand and supply in constraints are in multi-choice and probabilistic random variables, respectively. Also considered the “rate of increment in Transportation Cost (TC) and rate of decrement in profit on transporting the products from ith sources to jth destinations due to” (or additional cost) of each product due to the damage, late deliveries, weather conditions, and any other issues. Due to the presence of all these uncertainties, it is not possible to obtain the optimum solution directly, so first, we need to convert all these uncertainties from the model into a crisp equivalent form. The two-phase defuzzification technique is used to transform T2TpFN into a crisp equivalent form. Multi-choice and probabilistic random variables are transformed into an equivalent value using Stochastic Programming (SP) approach and the binary variable, respectively. It is assumed that the supply and demand parameter follows various types of probabilistic distributions like Weibull, Extreme value, Cauchy and Pareto, Normal distribution, respectively. The unknown parameters of probabilistic distributions estimated using the maximum likelihood estimation method at the defined probability level. The best fit of the probability distributions is determined using the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), respectively. Using the Fuzzy Goal Programming (FGP) method, the final problem is solved for the optimal decision. A case study is intended to provide the effectiveness of the proposed work.Murshid KamalAli AlarjaniAhteshamul HaqFaiz Noor Khan YusufiIrfan AliVilnius Gediminas Technical Universityarticlemulti-objective optimizationtransportation problemfuzzy goal programmingmulti-choicemaximum likelihood estimationakaike information criterionbayesian information criterionstochastic programmingTransportation engineeringTA1001-1280ENTransport, Vol 36, Iss 4, Pp 317-338 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	multi-objective optimization transportation problem fuzzy goal programming multi-choice maximum likelihood estimation akaike information criterion bayesian information criterion stochastic programming Transportation engineering TA1001-1280
spellingShingle	multi-objective optimization transportation problem fuzzy goal programming multi-choice maximum likelihood estimation akaike information criterion bayesian information criterion stochastic programming Transportation engineering TA1001-1280 Murshid Kamal Ali Alarjani Ahteshamul Haq Faiz Noor Khan Yusufi Irfan Ali Multi-objective transportation problem under type-2 trapezoidal fuzzy numbers with parameters estimation and goodness of fit
description	The problem of transportation in real-life is an uncertain multi-objective decision-making problem. In particular, by taking into account the conflicting objectives, Decision-Makers (DMs) are looking for the best transport set up to determine the optimum shipping quantity subject to certain capacity constraints on each route. This paper presented a Multi-Objective Transportation Problem (MOTP) where the objective functions are considered as Type-2 trapezoidal fuzzy numbers (T2TpFN), respectively. Demand and supply in constraints are in multi-choice and probabilistic random variables, respectively. Also considered the “rate of increment in Transportation Cost (TC) and rate of decrement in profit on transporting the products from ith sources to jth destinations due to” (or additional cost) of each product due to the damage, late deliveries, weather conditions, and any other issues. Due to the presence of all these uncertainties, it is not possible to obtain the optimum solution directly, so first, we need to convert all these uncertainties from the model into a crisp equivalent form. The two-phase defuzzification technique is used to transform T2TpFN into a crisp equivalent form. Multi-choice and probabilistic random variables are transformed into an equivalent value using Stochastic Programming (SP) approach and the binary variable, respectively. It is assumed that the supply and demand parameter follows various types of probabilistic distributions like Weibull, Extreme value, Cauchy and Pareto, Normal distribution, respectively. The unknown parameters of probabilistic distributions estimated using the maximum likelihood estimation method at the defined probability level. The best fit of the probability distributions is determined using the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), respectively. Using the Fuzzy Goal Programming (FGP) method, the final problem is solved for the optimal decision. A case study is intended to provide the effectiveness of the proposed work.
format	article
author	Murshid Kamal Ali Alarjani Ahteshamul Haq Faiz Noor Khan Yusufi Irfan Ali
author_facet	Murshid Kamal Ali Alarjani Ahteshamul Haq Faiz Noor Khan Yusufi Irfan Ali
author_sort	Murshid Kamal
title	Multi-objective transportation problem under type-2 trapezoidal fuzzy numbers with parameters estimation and goodness of fit
title_short	Multi-objective transportation problem under type-2 trapezoidal fuzzy numbers with parameters estimation and goodness of fit
title_full	Multi-objective transportation problem under type-2 trapezoidal fuzzy numbers with parameters estimation and goodness of fit
title_fullStr	Multi-objective transportation problem under type-2 trapezoidal fuzzy numbers with parameters estimation and goodness of fit
title_full_unstemmed	Multi-objective transportation problem under type-2 trapezoidal fuzzy numbers with parameters estimation and goodness of fit
title_sort	multi-objective transportation problem under type-2 trapezoidal fuzzy numbers with parameters estimation and goodness of fit
publisher	Vilnius Gediminas Technical University
publishDate	2021
url	https://doaj.org/article/cde807110ff646b2ba8ad7fbae381d9b
work_keys_str_mv	AT murshidkamal multiobjectivetransportationproblemundertype2trapezoidalfuzzynumberswithparametersestimationandgoodnessoffit AT alialarjani multiobjectivetransportationproblemundertype2trapezoidalfuzzynumberswithparametersestimationandgoodnessoffit AT ahteshamulhaq multiobjectivetransportationproblemundertype2trapezoidalfuzzynumberswithparametersestimationandgoodnessoffit AT faiznoorkhanyusufi multiobjectivetransportationproblemundertype2trapezoidalfuzzynumberswithparametersestimationandgoodnessoffit AT irfanali multiobjectivetransportationproblemundertype2trapezoidalfuzzynumberswithparametersestimationandgoodnessoffit
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Multi-objective transportation problem under type-2 trapezoidal fuzzy numbers with parameters estimation and goodness of fit

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