Earthworks planning for road construction projects: a case study

In this paper we construct earthwork allocation plans for a linear infrastructure road project. Fuel consumption metrics and an innovative block partitioning and modelling approach are applied to reduce costs. 2D and 3D variants of the problem were compared to see what effect, if any, occurs on solution quality. 3D variants were also considered to see what additional complexities and difficulties occur. The numerical investigation shows a significant improvement and a reduction in fuel consumption as theorised. The proposed solutions differ considerably from plans that were constructed for a distance based metric as commonly used in other approaches. Under certain conditions, 3D problem instances can be solved optimally as 2D problems

Modelling single line train operations

Scheduling of trains on a single line involves using train priorities for the resolution of conflicts. The mathematical programming model described in the first part of this paper schedules trains over a single line track when the priority of each train in a conflict depends on an estimate of the remaining crossing and overtaking delay. This priority is used in a branch and bound procedure to allow the determination of optimal solutions quickly. This is demonstrated with the use of an example. Rail operations over a single line track require the existence of a set of sidings at which trains can cross and/ or overtake each other. Investment decisions on upgrading the number and location of these sidings can have a significant impact on both customer service and rail profitability. Sidings located at insufficient positions may lead to high operating costs and congestion. The second part of this paper puts forward a model to determine the optimal position of a set of sidings on a single track rail corridor. The sidings are positioned to minimise the total delay and train operating costs of a given cyclic train schedule. The key feature of the model is the allowance of non-constant train velocities and non-uniform departure times

A new approach to spatial data interpolation using higher-order statistics

Interpolation techniques for spatial data have been applied frequently in various fields of geosciences. Although most conventional interpolation methods assume that it is sufficient to use first- and second-order statistics to characterize random fields, researchers have now realized that these methods cannot always provide reliable interpolation results, since geological and environmental phenomena tend to be very complex, presenting non-Gaussian distribution and/or non-linear inter-variable relationship. This paper proposes a new approach to the interpolation of spatial data, which can be applied with great flexibility. Suitable cross-variable higher-order spatial statistics are developed to measure the spatial relationship between the random variable at an unsampled location and those in its neighbourhood. Given the computed cross-variable higher-order spatial statistics, the conditional probability density function is approximated via polynomial expansions, which is then utilized to determine the interpolated value at the unsampled location as an expectation. In addition, the uncertainty associated with the interpolation is quantified by constructing prediction intervals of interpolated values. The proposed method is applied to a mineral deposit dataset, and the results demonstrate that it outperforms kriging methods in uncertainty quantification. The introduction of the cross-variable higher-order spatial statistics noticeably improves the quality of the interpolation since it enriches the information that can be extracted from the observed data, and this benefit is substantial when working with data that are sparse or have non-trivial dependence structures

Absolute Capacity Determination and Timetabling in Railways

To determine with certainty the capacity of a railway line or network a train timetabling problem should be solved. However due to the size and complexity of this timetabling problem, simpler approximations and simulations are more often used in practice. Absolute capacity on the other hand may be more simply obtained by ignoring the possibility of collision conflicts which are manifested as interference delays and occur as a result of insufficient passing facilities. This is achieved by allowing trains to pass through one another on non-critical sections in the timetable. Under this assumption, the full timetabling problem may be considerably reduced. In this paper details of a timetabling approach are presented and the calculation of important parameters required in the approach. Mathematical models for solving both the full and reduced timetabling problem are then developed. Alternative heuristics however are also proposed and extended because the reduced problem is still of considerable size and complexity

Techniques for inserting additional trains into existing timetables

In this paper techniques for scheduling additional train services (SATS) are considered as is train scheduling involving general time window constraints, fixed operations, maintenance activities and periods of section unavailability. The SATS problem is important because additional services must often be given access to the railway and subsequently integrated into current timetables. The SATS problem therefore considers the competition for railway infrastructure between new services and existing services belonging to the same or different operators. The SATS problem is characterised as a hybrid job shop scheduling problem with time window constraints. To solve this problem constructive algorithm and metaheuristic scheduling techniques that operate upon a disjunctive graph model of train operations are utilised. From numerical investigations the proposed framework and associated techniques are tested and shown to be effective