Optimising locomotive requirements for a pre-planned train schedule

2 Abstract Every rail operator wishes to minimise the size of their locomotive fleet in order to reduce costs. This minimum fleet size problem requires a rail operator to allocate locomotives to the trains in a predefined train schedule so that the total number of locomotives required is minimised. The key to this is deciding how and when to transfer locomotives to where they can be better utilised. The rail operator for this hypothetical problem runs approximately 7,200 trains per week involving movements between 780 locations. An integer programming formulation was developed based on the work (2002) 1 and a solver applied this formulation to a train schedule to find the optimal solution. As the solution process was highly computationally intensive, the largest partial train schedule that was able to be solved by the integer programming solver was 21% of the size of the full train schedule, taking 2½ hours to converge on the optimal solution. An alternative algorithm, called the work unit levels algorithm, was developed. This algorithm schedules locomotives by identifying all valid ways to transfer locomotives between trains, then allocating the train schedule in an order dependent on the possible interconnections between trains. When this algorithm was applied to the largest partial train schedule that could be solved by the integer programming solver, it arrived at a similar solution in 6 seconds. The algorithm took 13 minutes to solve the full problem. Acknowledgements 3 Acknowledgements I remember myself as a primary school boy with a profound curiosity as to what made things move on the computer screen. I fiddled unsuccessfully for countless hours with Microsoft's QuickBasic programming language trying to teach myself programming. When I finally created my first program – a colourful, ever-changing abstract drawing that looked like a screensaver – I felt like I was flying to the moon. Since then, my enthusiasm, excitement and passion for software development has grown unstoppably. I owe a special thanks to Dr Lynette Hardie-Wills from the Regional Education of Lincoln University, who took the risk of admitting me to her regional studies program years before I would sit the exams for the University Entrance qualification. I would also like to thank Arjan van Hasselt, Jade Software Corporation, who recruited me to be a Jade Kid in the year 2000. This started my journey into their programming language, JADE, which has shaped a large part of my life so …