A bilevel rescheduling framework for optimal inter-area train coordination

Railway dispatchers reschedule trains in real-time in order to limit the propagation of disturbances and to regulate traffic in their respective dispatching areas by minimizing the deviation from the off-line timetable. However, the decisions taken in one area may influence the quality and even the feasibility of train schedules in the other areas. Regional control centers coordinate the dispatchers\u27 work for multiple areas in order to regulate traffic at the global level and to avoid situations of global infeasibility. Differently from the dispatcher problem, the coordination activity of regional control centers is still underinvestigated, even if this activity is a key factor for effective traffic management. This paper studies the problem of coordinating several dispatchers with the objective of driving their behavior towards globally optimal solutions. With our model, a coordinator may impose constraints at the border of each dispatching area. Each dispatcher must then schedule trains in its area by producing a locally feasible solution compliant with the border constraints imposed by the coordinator. The problem faced by the coordinator is therefore a bilevel programming problem in which the variables controlled by the coordinator are the border constraints. We demonstrate that the coordinator problem can be solved to optimality with a branch and bound procedure. The coordination algorithm has been tested on a large real railway network in the Netherlands with busy traffic conditions. Our experimental results show that a proven optimal solution is frequently found for various network divisions within computation times compatible with real-time operations

Susceptibility of optimal train schedules to stochastic disturbances of process times

This work focuses on the stochastic evaluation of train schedules computed by a microscopic scheduler of railway operations based on deterministic information. The research question is to assess the degree of sensitivity of various rescheduling algorithms to variations in process times (running and dwell times). In fact, the objective of railway traffic management is to reduce delay propagation and to increase disturbance robustness of train schedules at a network scale. We present a quantitative study of traffic disturbances and their effects on the schedules computed by simple and advanced rescheduling algorithms. Computational results are based on a complex and densely occupied Dutch railway area; train delays are computed based on accepted statistical distributions, and dwell and running times of trains are subject to additional stochastic variations. From the results obtained on a real case study, an advanced branch and bound algorithm, on average, outperforms a First In First Out scheduling rule both in deterministic and stochastic traffic scenarios. However, the characteristic of the stochastic processes and the way a stochastic instance is handled turn out to have a serious impact on the scheduler performance

Production Scheduling in a Steelmaking-Continuous Casting Plant

In this paper we describe an optimization procedure for planning the production of steel ingots in a steelmaking-continuous casting plant. The strict requirements of the production process defeated most of the earlier approaches to steelmaking-continuous casting production scheduling, mainly due to the lack of information in the optimization models. Our formulation of the problem is based on the alternative graph, which is a generalization of the disjunctive graph of Roy and Sussman. The alternative graph formulation allow us to describe in detail all the constraints that are relevant for the scheduling problem. We then solve the problem by using a beam search procedure, and compare our results with a lower bound of the optimal solutions and with the actual performance obtained in the plant. Computational experience shows the effectiveness of this approach

Assessment of flexible timetables in real-time traffic management of a railway bottleneck

A standard practice to improve punctuality of railway services is the addition of time reserves in the timetable to recover perturbations occurring in operations. However, time reserves reduce line capacity, and the amount of time reserves that can be inserted in congested areas is, therefore, limited. In this paper, we investigate the new concept of flexible timetable as an effective policy to improve punctuality without decreasing the capacity usage of the lines. The principle of a flexible timetable is to plan less in the timetable and to solve more inter-train conflicts during operations. The larger degree of freedom left to real-time management offers better chance to recover disturbances. We illustrate a detailed model for conflict resolution, based on the alternative graph formulation, and analyze different algorithms for resolving conflicts, based on simple local rules or global optimization. We compare the solutions obtained for different levels of flexibility and buffer time inserted in the timetable. An extensive computational study, based on a bottleneck area of the Dutch railway network, confirms that flexibility is a promising concept to improve train punctuality and to increase the throughput of a railway network

A branch and bound algorithm for scheduling trains in a rail network

The paper studies a train scheduling problem faced by railway infrastructure managers during real-time traffic control. When train operations are perturbed, a new conflict-free timetable of feasible arrival and departure times needs to be re-computed, such that the deviation from the original one is minimized. The problem can be viewed as a huge job shop scheduling problem with no-store constraints. We make use of a careful estimation of time separation among trains, and model the scheduling problem with an alternative graph formulation. We develop a branch and bound algorithm which includes implication rules enabling to speed up the computation. An experimental study, based on a bottleneck area of the Dutch rail network, shows that a truncated version of the algorithm provides proven optimal or near optimal solutions within short time limits

Flexible timetables for real-time train rescheduling

A common strategy for railway traffic management consists in the off-line development of a detailed timetable, and operating in real time with strict adherence to it. In real time, unforeseen events may require to partially modify the planned timetable. A recent trend in railway companies is for managing congested areas by planning less in the off-line phase, and solving train conflicts in real time. In this paper we investigate the concept of flexible timetable, and the relations between flexibility and delay minimization. We use a detailed model for conflict resolution, based on the alternative graph formulation, and a branch and bound algorithm for solving the problem at optimality. We compare optimal solutions computed when varying timetable flexibility. An extensive computational study on a small and complicated rail network has been carried out, based on a bottleneck area of the Dutch railway network

A new class of greedy heuristics for job shop scheduling problems

In this paper we introduce a new class of greedy heuristics for general job shop scheduling problems. In particular we deal with the classical job shop, i.e. with unlimited capacity buffer, and job shop problems with blocking and no-wait. The proposed algorithm family is a simple randomized greedy family based on a general formulation of the job shop problem. We report on an extensive study of the proposed algorithms, and comparisons with other greedy algorithms are presented