Distribution Planning for Rail and Truck Freight Transportation Systems
Rail and truck freight transportation systems provide vital logistics services today. Rail systems are generally used to transport heavy and bulky commodities over long distances, while trucks tend to provide fast and flexible service for small and high-value products. In this dissertation, we study two different distribution planning problems that arise in rail and truck transportation systems.
In the railroad industry, shipments are often grouped together to form a block to reduce the impact of reclassification at train yards. We consider the time and capacity constrained routing (TCCR) problem, which assigns shipments to blocks and train-runs to minimize overall transportation costs, while considering the train capacities and shipment due dates. Two mathematical formulations are developed, including an arc-based formulation and a path-based formulation. To solve the problem efficiently, two solution approaches are proposed. The sequential algorithm assigns shipments in order of priority while considering the remaining train capacities and due dates. The bump-shipment algorithm initially schedules shipments simultaneously and then reschedules the shipments that exceed the train capacity. The algorithms are evaluated using a data set from a major U.S. railroad with approximately 500,000 shipments. Industry-sized problems are solved within a few minutes of computational time by both the sequential and bump-shipment algorithms, and transportation costs are reduced by 6% compared to the currently used trip plans.
For truck transportation systems, trailer fleet planning (TFP) is an important issue to improve services and reduce costs. In this problem, we consider the quantities and types of trailers to purchase, rent, or relocate among depots to meet time varying demands. Mixed-integer programming models are developed for both homogeneous and heterogeneous TFP problems. The objective is to minimize the total fleet investment costs and the distribution costs across multiple depots and multiple time periods.
For homogeneous TFP problem, a two-phase solution approach is proposed. Phase I concentrates on distribution costs and determines the suggested fleet size. A sweep-based routing heuristic is applied to generate candidate routes of good quality. Then a reduced mathematical model selects routes for meeting customer demands and determines the preferred fleet size. Phase II provides trailer purchase, relocation, and rental decisions based on the results of Phase I and relevant cost information. This decomposition approach removes the interactions between depots and periods, which greatly reduces the complexity of the integrated optimization model.
For the heterogeneous TFP problem, trailers with different capacities, costs, and features are considered. The two-phase approach, developed for the homogeneous TFP, is modified. A rolling horizon scheme is applied in Phase I to consider the trailer allocations in previous periods when determining the fleet composition for the current period. Additionally, the sweep-based routing heuristic is also extended to capture the characteristics of continuous delivery practice where trailers are allowed to refill products at satellite facilities. This heuristic generates routes for each trailer type so that the customer-trailer restrictions are accommodated. The numerical studies, conducted using a data set with three depots and more than 400 customers, demonstrate the effectiveness of the two-phase approaches. Compared to the integrated optimization models, the two-phase approaches obtain quality solutions within a reasonable computational time and demonstrate robust performance as the problem sizes increase. Based on these results, a leading industrial gas provider is currently integrating the proposed solution approaches as part of their worldwide distribution planning software.