Multi-Objective Transportation Problem Under Type-2 Trapezoidal Fuzzy Numbers With Parameters Estimation and Goodness of Fit

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.

A Proposed Method for Finding Initial Solutions to Transportation Problems

“…The TM is an Optimization tool for minimizing the shipping cost for transporting units from m sources to various n destinations to provide cost-effective distributing patterns for Logistics and Supply Chain Organizations (LSCO), etc. According to the paper of Kamal et al (2021), the TM is considered as a logistic (or network) problem to control the delivery of items at minimum costs. This cost minimization is indispensable in maintaining profitability of industries in production and distribution of items.…”

“…is linearly proportional to the amount of units sent along it. The LP formulation of TMs (according to Kamal et al (2021), Prasad and Singh (2020) and Saleh and Shiker (2022)) requires a set of decision variables, an objective function and model constraints.…”

A 2-Phase Method for Solving Transportation Problems with Prohibited Routes

“…Khamami & Saputra (2019) used a modified version of the Floyd's method to develop a Shortest Path Determination Application (SPDA) to control transport routes in a city and the application yielded good results with accuracy, following a comparative analysis with results from the traditional Floyd's method. Kamal et al (2021) presented a Multi-Objective TP with type-2 trapezoidal fuzzy objective functions. A two-phase technique was applied in transforming the trapezoidal objective function into an equivalent form and a Fuzzy Goal Programming (FGP) technique was employed to solve the problem for optimal decisions.…”

Application of Time Series Analysis to Supplier Selection Problem: A Problem of Multi-Objective Decision Making

“…The fuzziness in the parameters ( problem was eliminated by employing interval trapezoidal type 2 fuzzy numbers (IT2TpFN) based on a type-2 fuzzy set. Definition 1[Kamal et al (2021)]: For IT2TpFN, the UMF and LMF can be defined as:…”