Applied Soft Computing ( IF 5.472 ) Pub Date : 2020-07-29 , DOI: 10.1016/j.asoc.2020.106589 Sharmistha Halder Jana; Biswapati Jana
In this paper, two types of hybrid random type-2 uncertain variables such as random type-2 triangular and random type-2 Gaussian fuzzy variables are used to express the uncertain parameters in a four-dimensional transportation problem. Here selling price, purchasing costs, transportation costs, fixed charges, sources, demands, capacities of conveyances are considered as hybrid random type-2 uncertain parameters. The objective function of the proposed model is de-randomized using the expected value method and the constraints of the model are de-randomized using the probability chance constraint programming method. After that, the proposed model is de-fuzzified by CV based reduction technique. These two reduced crisp problems are solved by Generalized Reduced Gradient (GRG) technique using LINGO 14.0 software. The models are numerically illustrated. Some sensitivity analyses are also presented. Conventional solid (3D) and general (2D) transportation problems are derived as particular cases.