Multi-item solid transportation problem with type-2 fuzzy parameters

• Formulation of a multi-item solid transportation problem with type-2 fuzzy parameters.
• Nearest interval approximation of continuous type-2 fuzzy variable with CV-based reduction method.
• Chance constraint programming with generalized credibility.
• Type-2 triangular fuzzy variables are used for illustration.
• Transformed deterministic problems are solved using GRG technique (using LINGO solver) and Genetic Algorithm.

In this paper, a multi-item solid transportation problem with parameters, e.g., transportation costs, supplies and demands as type-2 triangular fuzzy variables is formulated. In this problem there are restrictions on some items and conveyances so that some specific items cannot be transported through some particular conveyances. With the critical value (CV)-based reductions of type-2 fuzzy variables, a chance-constrained programming model is formulated for the problem and then this model is converted to an equivalent deterministic form. Here, we propose a method to find nearest interval approximations for continuous type-2 fuzzy variables. A deterministic form for the problem is also obtained by applying interval analysis using the interval approximations of continuous type-2 fuzzy variables. The reduced deterministic problems are solved using a gradient based optimization – Generalized Reduced Gradient (GRG) technique (using LINGO solver) and Genetic Algorithm. Numerical example is provided to illustrate the problem and methods.

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