A Solid Transportation Problem with Additional Constraints Using Gaussian Type-2 Fuzzy Environments

This paper deals with nonlinear transportation problem where one part of unit transportation cost varies with distance from some origin, and the problems consist one more impurity restriction. Moreover, the fixed unit transportation costs are imprecise ones. In model I, some parameters (i.e. production cost, transport cost, supply, demand and unit of impurity at demand point) are considered as Gaussian type-2 fuzzy variable, while model II considered only the supply and demand which are deterministic. The type-2 fuzzy variables are transformed into type-I fuzzy variables with the help of CV-based reduction method. Genetic algorithm (GA) has been applied to solve the proposed models. Finally, an illustration is presented numerically to demonstrate the experimental results.