Fixed Charged Solid Transportation Problem With Budget Constraints in Type-2 Fuzzy Variables

Abstract

A multi-objective fixed charged solid transportation model with criterion e.g. transportation penalty, amounts, demands, carriages and budget constraints as type-2 triangular fuzzy variables with condition on few components and carriages is proposed here. With the critical value based reductions of corresponding type-2 fuzzy variables, a nearest interval approximation model and a chance constrained programming model applying generalized credibility measure for the constraints is proposed for this particular problem. The credibility measure is also applied to the objective functions of the chance constrained programming model. The model is then transformed into the corresponding crisp deterministic form by these two methods. A numerical example is provided to explain the model with hypothetical data and is then worked out by applying a gradient based optimization - Generalized Reduced Gradient technique (applying LINGO 16). The corresponding objective function values are compared numerically by two approaches after transforming it to crisp form by these two methods.