In this paper, we have developed an algorithm to determine the trade-off solution pairs in a special type of transportation problem considering two objectives,viz., cost and time. It is assumed that the time of transportation from an origin to a destination depends on the quantity transported. This results in a time objective, which is a piecewise constant increasing function. The cost objective function is taken to be linear. A potential physical situation of this model is given and a numerical example is worked out to illustrate the algorithm.
