Fully interval-valued fuzzy transportation problems: development and prospects

The transportation problem (TP) is one of the most used and tangible applications of linear programming problems that apply to a variety of practical settings. The main objective of this problem is to find an optimal transfer plan with the minimum cost of shipping the goods so that the demands of the destinations are satisfied using the supplies available at the sources. Conventional TPs generally assume that the values of transportation costs and the values of demand and supply are defined by real variables, though these values are unpredictable in TPs due to some uncontrollable factors. The present study formulates a TP when all parameters are interval-valued trapezoidal fuzzy numbers and uses a novel optimization structure to obtain the efficient solution of the resulting problem. The novelty of such optimization process resides in that it requires less computations effort as opposed to the existing methods. The applicability of the proposed approach is illustrated through a numerical example.