Scheduling and Platforming Trains at Busy Complex Stations

We consider the problem of train planning or scheduling for large, busy, complex train stations, which are common in Europe and elsewhere, though not in North America. We develop the constraints and objectives for this problem, but these are too computationally complex to solve by standard combinatorial search or integer programming methods. Also, the problem is somewhat political in nature, that is, it does not have a clear objective function because it involves multiple train operators with conflicting interests. We therefore develop scheduling heuristics analogous to those successfully adopted by train planners using ''manual'' methods. We tested the model and algorithms by applying to a typical large station that exhibits most of the complexities found in practice. The results compare well with those found by traditional methods, and take account of cost and preference trade-offs not handled by those methods. With successive refinements, the algorithm eventually took only a few seconds to run, the time depending on the version of the algorithm and the scheduling problem. The scheduling models and algorithms developed and tested here can be used on their own, or as key components for a more general system for train scheduling for a rail line or network.Train scheduling for a busy station includes ensuring that there are no conflicts between several hundred trains per day going in and out of the station on intersecting paths from multiple in-lines and out-lines to multiple platforms, while ensuring that each train is allowed at least its minimum required headways, dwell time, turnaround time and trip time. This has to be done while minimizing (costs of) deviations from desired times, platforms or lines, allowing for conflicts due to through-platforms, dead-end platforms, multiple sub-platforms, and possible constraints due to infrastructure, safety or business policy.

The general and specific effects of educational programmes aimed at promoting awareness of and respect for diversity among young children

This article reports the findings of a mixed-method evaluation of a pilot educational programme undertaken with 6-7 year olds in a sample of primary schools in England with the aim of increasing their awareness of and respect for diversity through theatre, workshops and related teacher-led classroom activities. The qualitative feedback from the teachers involved was extremely positive and encouraging and an analysis of the actual impact of the pilot programme on the children’s attitudes and awareness, using an experimental design, demonstrated some positive effects. In particular, the programme was found to increase the children’s general awareness of diversity and their ability to recognise instances of exclusion. While not a planned objective of the pilot programme, the evaluation also examined whether it had any effects on the children’s attitudes to specific differences, in this particular case racial differences. Interestingly, however, no evidence was found of any change in the children’s racial attitudes. With this in mind the article suggests that there is a need to distinguish between the general and specific effects of such educational programmes. The article considers the implications of this for future work in the area and also stresses the need to undertake more thorough and rigorous evaluations of such initiatives.