Fixed charge transportation problem with type-2 fuzzy variables

•Formulation of two fixed charge transportation problems with type-2 fuzzy parameters.•Transportation Costs, supplies, demands, conveyance capacities are taken as type-2 fuzzy variables.•CV-based reduction methods and centroid method are applied for defuzzification.•Chance-constrained programming model is formulated using generalized credibility measure for the second problem.•Sensitivity analysis is done for different generalized credibility levels.

This paper considers two fixed charge transportation problems with type-2 fuzzy parameters. Unit transportation costs, fixed costs in the first problem and unit transportation costs, fixed costs, supplies and demands in the second problem are type-2 fuzzy variables. For the first problem, to get corresponding defuzzified values of the type-2 fuzzy cost parameters, first critical value (CV)-based reduction methods are applied to reduce type-2 fuzzy variables into type-1 fuzzy variables and then centroid method is used for complete defuzzification. Besides this, we also apply geometric defuzzification method to the type-2 fuzzy cost parameters in the first problem to provide a comparison of the results. Coming to the second problem, a chance-constrained programming model is formulated using generalized credibility measure for the objective function as well as the constraints with the CV-based reductions of corresponding type-2 fuzzy parameters. Next, the reduced model is turned into equivalent parametric programming problem. The deterministic problems so obtained are then solved by using the standard optimization solver – LINGO. We have provided numerical examples illustrating the proposed models and techniques. Some sensitivity analyzes for the second model are also presented.