Fractional transportation problem with non-linear discount cost

The generalization of linear programming is a fractional programming where the objective function is a proportion of two linear functions. Likewise, in fractional transportation problem the aim is to optimize or improve the ratio of two cost functions or damage functions or demand functions. Since the ratio of two functions is considered, the fractional programming models become more appropriate for dealing with real life problems. The fractional transportation problem (FTP) plays a very important role in supply management for reducing cost and amending service. In real life, the parameters in the models are rarely known exactly and have to be evaluated. This paper investigates the fractional transportation problem (FTP) with some discount cost that avails during the shipment time. The transportation problem, which is one of integer programming problems, deals with distributing any commodity from any group of 'sources' to any group of destinations or 'sinks' in the most effective way with a given 'supply' and 'demand' constraints. The volume of goods to be transported from one place to another incurs some discount cost that could effectively reduce the shipment cost which is directly related to the profit associated with the shipment. This paper is aimed at studying the optimal solution for the problem has been achieved by using Karush-Kuhn-Tucker (KKT) optimality algorithm. Finally, a numerical example is illustrated to support the algorithm.