Abstract
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.
Highlights
The classical transportation problem (TP) was mostly utilized while taking the best decision in business and management and according to Verma et al (1997), its structure is same as a linear programming problem (LPP)
We provided the number of solutions under different estimation using genetic algorithm (GA) based approach with different shape parameter and various ranges of aspiration level
Corresponding to each α and each above six cases contain the combination of shape parameter and aspiration level, the Table 3, Table 4 and Table 5 represents the values of the objective function, corresponding membership value, degree of satisfaction and the final product operator value
Summary
The classical transportation problem (TP) was mostly utilized while taking the best decision in business and management and according to Verma et al (1997), its structure is same as a linear programming problem (LPP). Lee and Moore (1973) study and obtained the solution of multi-objective transportation problem (MOTP) with a goal programming approach. In the study of multi-objective solid transportation problem (MOSTP) and its solution with fuzzy programming approach. Almost proposed method uses a balance type fuzzy programming model and fail for the unbalance model The solution of such an unbalanced model can be acquired with the GA based hybrid approach. We provided the number of solutions under different estimation using GA based approach with different shape parameter and various ranges of aspiration level This method provides an effective solution of fuzzy type TP, handles the situations of the problem effectively and give a higher degree of satisfaction to the objective functions. It took for each objective function to determine the value of exponential membership function
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