Determining Cost vs. Time Pareto-Optimal Frontiers in Multi-Modal Transportation Problems

This paper provides a framework for choosing modes of transportation (rail, highway, air, etc.) by taking into account the conflicting objectives of minimizing total transportation costs and average shipment times. An efficient algorithm using the operator theory of parametric programming is presented for determining the Pareto-optimal or efficient curve denoting the minimum attainable value for the second objective for differing values of the first objective. The algorithm also provides the optimal routes, modes of transportation, and the corresponding shipping amounts for every efficient point.