A new iterative fuzzy approach to the multi-objective fractional solid transportation problem with mixed constraints using a bisection algorithm

A multi-objective solid transportation problem that includes source, destination, and mode of transport parameters may have fractional objective functions in real-life applications to maximize the profitability ratio, which could be the profit/cost or profit/time. We refer to such transportation problems as multi-objective fractional solid transportation problems. In addition, although most of the studies in the literature deal with the standard equality-constrained form of the multi-objective fractional solid transportation problem, the mixed-constrained type is addressed in this paper. With these mixed constraints, the multi-objective fractional solid transportation problem offers more flexible modeling of real-world problems that exist in many application areas, but mixed constraints also make the optimization process more challenging. This article presents an iterative fuzzy approach that combines the use of linear programming and the bisection algorithm using linear membership functions to obtain a strongly efficient solution. The algorithm’s ability to convert a nonlinear problem into a set of linear problems is one of its main advantages, and it also decreases the amount of time needed to solve large-scale problems. A numerical example from the literature is adopted to illustrate the solution procedure. Moreover, large-scale instances are generated to further test the presented algorithm, and a comparison between the traditional fuzzy approach and the proposed method is presented.