Optimum cost- time trade off in a capacitated fixed charge transportation problem with bounds on rim conditions

In this paper, an algorithm is presented to find the optimum time cost trade off in a capacitated fixed charge transportation problem giving the same priority to both time and cost. Sometimes, there is a condition that we can send an amount more than or less than a certain specified amount which gives rise to capacitated time minimizing transportation problem. Moreover, sometimes a fixed cost (like set up cost for machines, landing fees at an airport, cost of renting a vehicle) is also associated with every origin that gives rise to fixed charge problems. From the practical point of view, the cost minimizing transportation problem and the time minimizing transportation problem can not be viewed as two independent problems. In this paper, an algorithm is presented that gives efficient time cost trade off pairs which minimizes cost and time simultaneously in a capacitated fixed charge transportation problem. A numerical example is given to illustrate the developed algorithm.