Abstract
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.
Highlights
The competitive environment of the business market
We have considered two cases in constraints of the proposed model: (1) when demand and supply are in interval type multi-choice, and (2) when demand and supply are random variables follows some types of probability distributions
Other than we have suggested some proposal in work like Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) approach to obtain the best fit for probability distributions
Summary
The competitive environment of the business market. Every business is so struggling to discover some lucrative transport strategies to deliver the products to customers. Kamal et al (2018) considered a MOTP and developed a new technique called the distance-based method for solving it. Inspired by such type of work have been done in multi-criteria decision-making TPs. It is challenging for DMs to make a reasonable assumption about profit and minimize the total TC if information about the parameters of the real-world problem is precisely not known.
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