Integrated inbound train split and load planning in an intermodal railway terminal

Highlights

• This paper addresses a novel practical problem faced by a major North American railway.

• The problem involves decisions such as how inbound trains are split, on which tracks the railcars are parked for loading and off-loading operations, and how the railcars are assigned to outbound blocks.

• We propose a 2-step approach that considers all the decisions that must be made by terminal operators.

• Tests based on realistic benchmark instances indicate that our approach is able to generate good quality solutions for all instances.

Abstract

In the last decades the intermodal transportation of containers has become a key component of the entire international trade system, as it allows safe and efficient intercontinental door-to-door movement of freight by combining land and sea transportation services. Intermodal railway terminals are special components of these systems that allow container traffic to be consolidated from different sources and to be transported by train over long distances. This paper addresses a practical problem faced by a major North American railway. On a daily basis, terminal operators must make several decisions such as how inbound trains are split into sequences of railcars, on which tracks these railcars are parked for loading and off-loading operations, and how the railcars are assigned to outbound blocks so as to fulfill the demand of each block. We introduce an approach that incorporates all these decisions to obtain improved solutions. In a first step, a mixed integer linear programming (MILP) model is used to create a set of patterns that specify how each inbound train is split and how the railcars are assigned to the blocks. Then, in a second step, another MILP formulation decides which patterns to use and where to park the railcars. Tests on generated benchmark instances based on realistic data from the railway indicate that our approach is able to generate good quality solutions for all instances and can be used by the company to assist decision makers in generating less costly and more efficient plans.

Introduction

Intermodal freight transportation may be considered as one of the cornerstones of globalization, as it allows for the efficient intercontinental door-to-door movement of goods through multiple modes of land and sea transportation services that often involve several different carriers. In a classical example of an intermodal chain, loaded containers leave the initial shipper location by truck and are directed either to a port or to an intermodal railway terminal, from where a train will transport them to a port. A ship then moves the containers to another port, from where they are transported to the destination by one or a combination of several means of transportation (Crainic and Kim 2007).

These intermodal terminals are special transshipment nodes that are responsible for consolidating traffic and dispatching containers on trains destined to other nodes of the network, so that these containers can eventually reach their final destination. For a comprehensive survey of the literature on intermodal transportation we refer the reader to the surveys of Crainic and Kim (2007) and of SteadieSeifi et al. (2014).

Most of the intermodal traffic is containerized, which ensures a safer, cheaper and more reliable means of transportation without handling the cargo. Indeed, the North American market of intermodal transportation has performed remarkably well in the last decade or so, with annual growth rates of about 15% (SteadieSeifi et al. 2014). While the international market mainly follows the ISO standard and uses 20-, 40- and 45-ft containers, in North America there are also 48- and 53-ft containers, which are used for domestic traffic. Another feature of this market is that trains are usually double stacked and there are many types of railcars with different characteristics, e.g., number of platforms, platform length (40, 45, 48 or 53 feet long) and weight loading limit. This great variety of containers and railcar types has a significant impact on the difficulty of the load planning, which concerns the assignment of containers to railcar slots (see, e.g., Mantovani et al. 2018). Performing a proper matching between railcars and containers in the load planning is important to ensure the best usage of the available capacity of railcars but also the fuel efficiency of the train, because loading influences aerodynamics aspects.

In practice, the set of railcars that is made available to load containers is the result of decisions that derive from a block plan. The block planning is a tactical problem which is critical for the design of an efficient and profitable rail transportation system (Bodin et al., 1980). A block is defined as a group of railcars, with possibly different origins and destinations, that are moved as a single unit between terminals. The railcars of the same block do not need to be handled individually at intermediate terminals, which reduces handling costs.

In this paper we focus on an operational problem faced by a North American railway in the context of rail transportation of intermodal containers. In particular, we consider (1) how inbound trains are split (cut) into sequences of railcars after entering the intermodal terminal, (2) on which tracks those railcars are parked for loading and off-loading operations or even for temporary storage, and (3) the assignment of railcars to outbound blocks so as to fulfill the demand of each block. Fig. 1 illustrates how these decisions are related and how inbound trains are processed and outbound trains assembled. Because we focus on operational decisions, we assume that the block plan is given. However, the choice of the individual cars that compose each block is optimized based on the available resources.

Our main contributions are to introduce a novel practical problem in intermodal transportation, and to propose an approach that incorporates all the aforementioned decisions to obtain better solutions than when a sequential decision process is used. This approach proceeds in two steps. The first one creates a set of patterns (called configurations) that specify how each inbound train is split and how railcars are assigned to the blocks. Therefore, this step deals with decisions (1) and (2) of Fig. 1, which are heavily interconnected. Decision (3) is then handled in a second step, where we decide which configurations to use and where to park the railcars, making sure that it is possible to bring the railcars to their assigned track and to pull them out when they have to depart. To perform the first step we introduce a mixed integer linear programming (MILP) formulation that uses an efficient way to represent groups of consecutive railcars that are destined to the same block. The second step is solved by means of another MILP formulation which ensures that the railcars can be parked onto the tracks and that the outbound trains can be properly assembled. In order to test our algorithms we generated a set of realistic instances based on real data provided by the railway. Our experiments show that, although the problem is very complex, our solution approach is able to generate good quality solutions for all benchmark instances. These results also indicate that aspects such as the composition of the inbound trains and the amount of traffic in the terminal play a larger role than the variations in the demand of blocks, in determining how difficult it is to find feasible solutions for a given instance.

The remainder of the paper is organized as follows. Section 2 presents a brief discussion of the related literature. Section 3 describes the problem and the notation used throughout the paper. Section 4 presents the solution approach, whereas Section 5 reports the results of the computational experiments. Finally, Section 6 provides some conclusions.