4-dimensional transportation problem for substitute and complementary items under rough environment

Abstract

In this paper, an innovative 4-dimensional multifarious breakable items transportation problem (4DMBITP) has been proposed. Here, per unit selling expenses, per unit purchasing prices, per unit transportation expenditures, fixed charge, availability of the sources, demands of the destination, conveyances capacities and total available budget are expressed by rough intervals. The transported items are substitutable and complementary in nature. The demand of the items at the destination are directly related to the substitutability and complementary nature of the products and own selling price. The suggested model is converted into a deterministic one using lower and upper approximation intervals following Hamzehee et al. [1] as well as Expected Value Technique. The converted model is optimized through Generalized Reduced Gradient (GRG) techniques using LINGO 14 software. Finally, numerical examples are presented to illustrate the preciseness of the proposed model.