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For a passenger railway system with a published timetable, train timetable adherence and punctuality are critical performance indicators. Compared with other resource allocation methods, timetable adjustment is a relatively cost-effective approach for improving timetable adherence. The insertion of appropriate time supplement and buffer time into a timetable to reduce delays as well as their propagation can improve punctuality. However, to appropriately distribute available supplement/buffer time is a challenging task, especially for real-world cases. Moreover, a very robust timetable may not necessarily be a good choice, since ideal punctuality might come at the cost of large time slacks. In this study, we propose a simulation-based approach that embeds a linear programming model to effectively adjust the time supplement and buffer time in a given passenger railway timetable to reduce the average delay. The proposed solution approach is empirically applied to instances of various sizes. It is shown that the heuristic can quantify the relationship between timetable efficiency and robustness, which helps railway operators select their ideal balance between these two important yet conflicting issues. Further, numerical studies with a real timetable demonstrate that the timetable can achieve better punctuality with an even lower time supplement after adjustment, and the insights observed in this work have not only academic value but also value for practitioners in their preparation of timetables.

This paper presents a three-phase heuristic to solve for an optimized working plan for a crane to retrieve all the containers from a given yard according to a given order. The optimization goal is to minimize the number of container movements, as well as the crane's working time. After generating an initial feasible movement sequence, the second phase reduces the length of the sequence by repeatedly formulating and generating a binary integer program. With another mixed integer program, phase three reduces the crane's working time by adjusting the movement sequence through iterations. Numerical testing results show that the heuristic is able to solve instances with more than 700 containers, which is within the range of real-world applications. Moreover, the number of movements approaches the lower bound in most cases, and the resulting movement sequence is efficient.

In a railroad system, train pathing is concerned with the assignment of trains to links and tracks, and train timetabling allocates time slots to trains. These important tasks were traditionally done manually, but there is an increasing move toward automated software based on mathematical models and algorithms. Most published models in the literature either focus on train timetabling only, or are too complicated to solve when facing large instances. In this paper, we present an optimization heuristic that includes both train pathing and train timetabling, and has the ability to solve real-sized instances. This heuristic allows the operation time of trains to depend on the assigned track, and also lets the minimum headway between the trains to depend on the trains’ relative status. It generates an initial solution with a simple rule, and then uses a four-step process to derive the solution iteratively. Each iteration starts by altering the order the trains travel between stations, then it assigns the services to the tracks in the stations with a binary integer program, determines the order they pass through the stations with a linear program, and uses another linear program to produce a timetable. After these four steps, the heuristic accepts or rejects the new solution according to a Threshold Accepting rule. By decomposing the original complex problem into four parts, and by attacking each part with simpler neighborhood-search processes or mathematical programs, the heuristic is able to solve realistic instances. When tested with two real-world examples, one from a 159.3 km, 29-station railroad that offers 44 daily services, and another from a 345 km, eight-station high-speed rail with 128 services, the heuristic obtained timetables that are at least as good as real schedules.

In a yard where export containers are piled up, only those on the top are directly accessible to the stacking equipment. As a result, extra rehandles may occur when lifting them up for loading onto ships. One way to improve operational efficiency is to pre-marshal the containers in such an order that it fits the loading sequence. This paper proposes a model to develop a movement plan to improve the layout of containers in a bay. The proposed heuristic consists of a neighborhood search process, an integer programming model, and three minor subroutines. Each of the components plays a different role in the heuristic. Several sets of testing results demonstrate the performance of the heuristic as well as the contributions of the components.

Berths are among the most important resources in a port. In this research we present an optimization-based approach for the berth scheduling problem, which is to determine the berthing time and space for each incoming ship. The neighborhood-search based heuristic treats the quay as a continuous space. In additional to basic physical requirements, this model takes several factors important in practice into consideration, including the first-come-first-served rule, clearance distance between ships, and possibility of ship shifting. Computational experience is provided.

In most container yards around the world, containers are stacked high to utilize yard space more efficiently. In these yards, one major factor that affects their operational efficiency is the need to re-shuffle containers when accessing a container that is buried beneath other containers. One way to achieve higher loading efficiency is to pre-marshal the containers in such a way that it fits the loading sequence. In this research, we present a mathematical model for the container pre-marshalling problem. With respect to a given yard layout and a given sequence that containers are loaded onto a ship, the model yields a plan to re-position the export containers within the yard, so that no extra re-handles will be needed during the loading operation. The optimization goal is to minimize the number of container movements during pre-marshalling. The resulting model is an integer programming model composed of a multi-commodity flow problem and a set of side constraints. Several possible variations of the model as well as a solution heuristic are also discussed. Computation results are provided.

In this paper we propose a model to calculate an optimal vertical alignment of an interchange with a given horizontal layout. The vertical profiles of all ramps in the interchange are solved simultaneously. The problem is formulated as a mixed integer program. A heuristic that can solve the problem very efficiently is also proposed. The model and heuristic were tested by applying the technique to a real life example, a full system interchange with 4 legs and 8 ramps. Comparison of the computational results with the real layout, which was designed by a major consulting firm, indicates that the model produces designs close to those of human experts.