Freight Transportation Network Design Problem for Maximizing throughput under Uncertainty

Abstract

A mathematical programming formulation is developed to determine the throughput of a freight transportation network. The impact of demand and capacity uncertainty on the throughput is systematically studied. Mathematical proofs are provided to show that accounting for capacity uncertainty by using a single-point expected value can lead to systematic overestimation of network throughput. This result is also valid for other measures, such as system capacity. Two sampling-based methodologies–independent random number and common random number–are provided to determine network design decisions in the presence of demand uncertainty. The sampling-based solution methods provide an approximate estimate of optimal solution and provide probabilistic bounds on the optimality gap. The presented methodologies are generic and can be applied even if different functional forms (nonlinear, nonconvex) are used to model various aspects of the freight transportation network. The numerical tests demonstrate that not accounting for capacity uncertainty can result in overestimation of system throughput of up to 40%. A common random number-based sampling strategy was found to significantly outperform the independent random number strategy for all the scenarios tested.