Linear fractional transportation problem with varying demand and supply

In this paper, we investigate the transportation problem with fractional objective function when the demand and supply quantities are varying. A set of mathematical programs is obtained to determine the objective value. Due to varying economic policies in the global world, it is hard to specify the supply and demand quantities for transportation problem. A transportation problem with fractional objective function is based on a network structure consisting of a finite number of nodes and arcs attached to them. After the derivation, we obtained the result in range, where the total transportation cost would appear. In addition to allowing for simultaneous changes in supply and demand values, the total cost bounds are calculated directly. This methodology would be very beneficial in the decision making. A numerical example has given in this paper for the support of theory