David M. Ryan

Railway track allocation: models and methods

Efficiently coordinating the movement of trains on a railway network is a central part of the planning process for a railway company. This paper reviews models and methods that have been proposed in the literature to assist planners in finding train routes. Since the problem of routing trains on a railway network entails allocating the track capacity of the network (or part thereof) over time in a conflict-free manner, all studies that model railway track allocation in some capacity are considered relevant. We hence survey work on the train timetabling, train dispatching, train platforming, and train routing problems, group them by railway network type, and discuss track allocation from a strategic, tactical, and operational level.

Simultaneous disruption recovery of a train timetable and crew roster in real time

This paper describes the development and implementation of an optimization model used to resolve disruptions to an operating schedule in the rail industry. Alterations to the existing train timetable and crewing roster are made simultaneously in real time--previous treatments in the literature have always decoupled these two problems and solved them in series. An integer programming model is developed that constructs a train timetable and crew roster. This model contains two distinct blocks, with separate variables and constraints for the construction of the train timetable and crew roster, respectively. These blocks are coupled by piece of work sequencing constraints and shift length constraints, which involve variables from both blocks. This unique parallel construction process is then used as the basis of a method to deal with the resolution of train disruptions in realtime. Favourable results are presented for both the combined train/driver scheduling model and the real-time disruption recovery model.

An iterative approach to robust and integrated aircraft routing and crew scheduling

In airline scheduling a variety of planning and operational decision problems have to be solved. We consider the problems aircraft routing and crew pairing: aircraft and crew must be allocated to flights in a schedule in a minimal cost way. Although these problems are not independent, they are usually formulated as independent mathematical optimisation models and solved sequentially. This approach might lead to a suboptimal allocation of aircraft and crew, since a solution of one of the problems may restrict the set of feasible solutions of the problem solved later. Also, when minimal cost solutions are used in operations, a short delay of one flight can cause very severe disruptions of the schedule later in the day. We generate solutions that incur small costs and are also robust to typical stochastic variability in airline operations. We solve the two original problems iteratively. Starting from a minimal cost solution, we produce a series of solutions which are increasingly robust. Using data from domestic airline schedules we evaluate the benefits of the approach as well as the trade-off between cost and robustness. We extend our approach considering the aircraft routing problem together with two crew pairing problems, one for technical crew and one for flight attendants.

Flight attendant rostering for short-haul airline operations

The construction of flight attendant (cabin crew) rosters for short-haul (domestic) airline flight services that satisfies rostering constraints and employment contract regulations is a combinatorially complex problem. In this paper the problem is described and an effective optimisation-based solution method is introduced. The rostering problem involves the allocation of days-off and various duties to each crew member over a roster period. The days-off and the duty allocation problems are separated into two distinct subproblems. The days-off allocation solution approach involves complete enumeration of all possible days-off lines for each crew member over the roster period, and then the solution of a set partitioning optimisation to determine a best quality feasible days-off roster. The duty allocation solution approach first involves the generation of many lines-of-work consistent with the days-off solution for each crew member over a subroster period and then the solution of a set partitioning optimisat...

On the integer properties of scheduling set partitioning models

Abstract Many scheduling problems, arising in the transportation industry, can be posed as massive set partitioning zero-one integer programmes. For reasons of computational complexity it is generally unrealistic to attempt to solve the model in this form using conventional integer linear programming. By the imposition of additional structure, derived from the real-world problem but not already implicit in the mathematical model, it is possible to significantly reduce the effects of computational complexity and provide an effective method of obtaining good feasible solutions. In this paper, recent results in graph theory concerning natural integer properties of set partitioning integer programmes are discussed. These results motivate the development of further implicit constraints which simultaneously reduce the dimensionality and increase the proportion of integer basic feasible solutions of the set partitioning linear programme.

Integrated Simulation, Heuristic and Optimisation Approaches to Staff Scheduling

This paper details a new simulation and optimisation based system for personnel scheduling (rostering) of customs staff at the Auckland International Airport, New Zealand. An integrated approach using simulation, heuristic descent, and integer programming techniques has been developed to determine near-optimal staffing levels. The system begins by using a new simulation system embedded within a heuristic search to determine minimum staffing levels for arrival and departure work areas. These staffing r equirements are then used as the input to an integer programming model, which optimally allocates full- and part-time staff to each period of the working day. These shifts are then assigned to daily work schedules having a six-day-on, three-day-off structure. The application of these techniques has resulted in significantly lower staffing levels, while at the same time creating both high-quality rosters and ensuring that all passenger processing targets are met. This paper charts the development of this system, outlines failures where they have occurred, and summarises the ongoing impacts of this work on the organisation.

Inexact Cuts in Benders Decomposition

Benders decomposition is a well-known technique for solving large linear programs with a special structure. In particular, it is a popular technique for solving multistage stochastic linear programming problems. Early termination in the subproblems generated during Benders decomposition (assuming dual feasibility) produces valid cuts that are inexact in the sense that they are not as constraining as cuts derived from an exact solution. We describe an inexact cut algorithm, prove its convergence under easily verifiable assumptions, and discuss a corresponding Dantzig--Wolfe decomposition algorithm. The paper is concluded with some computational results from applying the algorithm to a class of stochastic programming problems that arise in hydroelectric scheduling.

The train driver recovery problem-A set partitioning based model and solution method

The need to recover a train driver schedule occurs during major disruptions in the daily railway operations. Based on data from the Danish passenger railway operator DSB S-tog A/S, a solution method to the train driver recovery problem (TDRP) is developed. The TDRP is formulated as a set partitioning problem. We define a disruption neighbourhood by identifying a small set of drivers and train tasks directly affected by the disruption. Based on the disruption neighbourhood, the TDRP model is formed and solved. If the TDRP solution provides a feasible recovery for the drivers within the disruption neighbourhood, we consider that the problem is solved. However, if a feasible solution is not found, the disruption neighbourhood is expanded by adding further drivers or increasing the recovery time period. Fractional solutions to the LP relaxation of the TDRP are resolved with a constraint branching strategy using the depth-first search of the Branch & Bound tree. The LP relaxation of the TDRP possesses strong integer properties. We present test scenarios generated from the historical real-life operations data of DSB S-tog A/S. The numerical results show that all but one tested instances produce integer solutions to the LP relaxation of the TDRP and solutions are found within a few seconds.

Towards a General Managerial Framework for Performance Measurement: A Comprehensive Highway Maintenance Application

This paper describes the application of Data Envelopment Analysis (DEA) to a highway maintenance setting, using measures of inputs, outputs and outcomes reported by New Zealand local authorities. A general framework of performance measurement is developed and illustrated through application to the highway setting. The framework encompasses a performance pyramid embodying multiple-perspectives of the organisation with a structure of measures linking critical success factors to process drivers, methods of data analysis and influencing factors such as professional culture. Distinctions between measures of outcome, output and input enable finer partitioning of analyses into managerial notions of efficiency, effectiveness and economy. The impact of environmental factors on efficiency is explored through two approaches suggested in the literature.

A set packing inspired method for real-time junction train routing

Efficiently coordinating the often large number of interdependent, timetabled train movements on a railway junction, while satisfying a number of operational requirements, is one of the most important problems faced by a railway company. The most critical variant of the problem arises on a daily basis at major railway junctions where disruptions to rail traffic make the planned schedule/routing infeasible and rolling stock planners are forced to re-schedule/re-route trains in order to recover feasibility. The dynamic nature of the problem means that good solutions must be obtained quickly. In this paper we describe a set packing inspired formulation of this problem and develop a branch-and-price based solution approach. A real life test instance arising in Germany and supplied by the major German railway company, Deutsche Bahn, indicates the efficiency of the proposed approach by confirming that practical problems can be solved to within a few percent of optimality in reasonable time.