Genetic Algorithm-Based Fuzzy Programming Method for Multi-objective Stochastic Transportation Problem Involving Three-Parameter Weibull Distribution

Optimizing problems in the modern era, the single objective optimization problems are insufficient to hold the full data of the problem. Therefore, multi-objective optimization problems come to the rescue. Similarly, in daily life problems, the parameters used in the optimization problem are not always fixed but there may be some uncertainty and it can characterize by fuzzy number. This work underlines the genetic algorithm (GA) based solution of fuzzy transportation problem with more than one objective. With a view to providing the multifaceted choices to decision-maker (DM), the exponential membership function is used with the decision-makers desired number of cases which consisted of shape parameter and aspiration level. Here, we consider the objective functions which are non-commensurable and conflict with each other. To interpret, evaluate and exhibit the usefulness of the proposed method, a numerical example is given.

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Computation of a multi-objective fuzzy stochastic transportation problem

International Journal of Fuzzy Computation and Modelling ◽

10.1504/ijfcm.2014.067129 ◽

2014 ◽

Vol 1 (2) ◽

pp. 212 ◽

Cited By ~ 9

Author(s):

Srikumar Acharya ◽

Narmada Ranarahu ◽

Jayanta Kumar Dash ◽

Mitali Madhumita Acharya

Keyword(s):

Transportation Problem ◽

Multi Objective ◽

Stochastic Transportation Problem

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Multi-Objective Capacitated Solid Transportation Problem with Uncertain Variables

International Journal of Mathematical Engineering and Management Sciences ◽

10.33889/ijmems.2021.6.5.085 ◽

2021 ◽

Vol 6 (5) ◽

pp. 1406-1422

Author(s):

Vandana Y. Kakran ◽

Jayesh M. Dhodiya

Keyword(s):

Transportation Problem ◽

Optimal Solution ◽

Fuzzy Programming ◽

Solid Transportation Problem ◽

Programming Technique ◽

Distance Method ◽

Multi Objective ◽

Uncertain Variables ◽

Value Model ◽

Single Objective

This paper investigates a multi-objective capacitated solid transportation problem (MOCSTP) in an uncertain environment, where all the parameters are taken as zigzag uncertain variables. To deal with the uncertain MOCSTP model, the expected value model (EVM) and optimistic value model (OVM) are developed with the help of two different ranking criteria of uncertainty theory. Using the key fundamentals of uncertainty, these two models are transformed into their relevant deterministic forms which are further converted into a single-objective model using two solution approaches: minimizing distance method and fuzzy programming technique with linear membership function. Thereafter, the Lingo 18.0 optimization tool is used to solve the single-objective problem of both models to achieve the Pareto-optimal solution. Finally, numerical results are presented to demonstrate the application and algorithm of the models. To investigate the variation in the objective function, the sensitivity of the objective functions in the OVM model is also examined with respect to the confidence levels.

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