Assignment of Freight Traffic in a Large-scale Intermodal Network under Uncertainty

Abstract

This paper presents a methodology for freight traffic assignment in a large-scale road-rail intermodal network under uncertainty. Network uncertainties caused by natural disasters have dramatically increased in recent years. Several of these disasters (e.g., Hurricane Sandy, Mississippi River Flooding, and Hurricane Harvey) severely disrupted the U.S. freight transportation network, and consequently, the supply chain. To account for these network uncertainties, a stochastic freight traffic assignment model is formulated. An algorithmic framework, involving the sample average approximation and gradient projection algorithm, is proposed to solve this challenging problem. The developed methodology is tested on the U.S. intermodal network with freight flow data from the Freight Analysis Framework. The experiments consider three types of natural disasters that have different risks and impacts on transportation networks: earthquakes, hurricanes, and floods. It is found that for all disaster scenarios, freight ton-miles are higher compared to the base case without uncertainty. The increase in freight ton-miles is the highest under the flooding scenario; this is because there are more states in the flood-risk areas, and they are scattered throughout the U.S.

Solving a Multimodal Routing Problem with Pickup and Delivery Time Windows under LR Triangular Fuzzy Capacity Constraints

“…Therefore, given a confidence level δ ∈ [0.5, 1], the crisp reformulation of Cr ∼ g ≥ τ ≥ δ can be realized by Equation (24).…”

“…Huang [22] assumes that the capacities of water and rail transportation obeys the normal distribution and designs a two-stage stochastic programming model for the multimodal routing problem in the stochastic environment. Uddin et al [23,24] utilize the scenario-based approach to model the uncertain capacities of rail transportation and terminals and build stochastic programming models for the MRP. Contrary to stochastic programming, based on the fuzzy set theory [25], Sun et al [8], Li et al [13], and Lu et al [26] use triangular fuzzy numbers to model capacity uncertainty and establish the fuzzy chance-constrained programming (FCCP) models to deal with their MRPs.…”

“…All these papers cited above state the significant influence of capacity uncertainty on the optimization of the MRP and promote the research progress on MRP under capacity uncertainty. However, the stochastic models taken by References [22][23][24] need to use large numbers of data to fit the probability distribution of the uncertain capacity, while there are not enough data in most cases [28]. The scenario-based approach to model the uncertain capacity as large numbers of scenarios challenges the computational efficiency of problem-solving [11].…”