Fixed charge 4D-TP for a breakable item under hybrid random type-2 uncertain environments

Abstract

The concept of hybrid random type-2 uncertainty is yet to be used in decision-making problems. Here, under this category, random type-2 triangular fuzzy, random type-2 Gaussian fuzzy and random type-2 zigzag uncertain variables are presented. For illustration, a fixed charge four dimension transportation problem (FC4D-TP) for a breakable item is formulated with its selling prices, purchasing costs, transportation costs, fixed charges, availability, demands and conveyances’ capacities as hybrid random type-2 uncertain parameters. The model is de-randomized using probability chance constraint. The reduced type-2 triangular and Gaussian fuzzy models are de-fuzzified by CV based reduction technique and the type-2 zigzag uncertain model is transformed to deterministic one by expected value-based reduction method. In addition to these, the model with type-2 triangular fuzzy parameters is also de-fuzzified by two other methods such as CV-centroid based defuzzification and nearest interval approximation methods. All these reduced deterministic problems along with some particular models are solved by Generalized Reduced Gradient method using LINGO 18.0 and numerically illustrated. Some sensitivity analyses are presented. Expressions of a previous model are deduced. Importance of FC4D-TP formulation is pointed out. Effects of hybrid uncertainties are also discussed. The proposed nature of parameters’ uncertainty is illustrated.