Production of locomotive rosters for a multi-class single-locomotive problem

A multi-class single locomotive (MCSL) problem is defined in this paper as one involving the allocation of a single locomotive to each of a number of pre-timetabled trains, some of which can be pulled by more than one type (or class) of locomotive. This is typical of problems arising in many passenger train networks and an exact solution method exists for the general form of this problem. This paper describes the analysis of a particular type of MCSL problem, as faced by the Public Transport Corporation (PTC) in the Australian State of Victoria, where all journeys either start or end at one location (Melbourne). Because of this feature, the problem can be solved in two separate stages. The first stage (an integer programming model) determines the type of locomotive that will haul each trip. The second stage, which can either be solved by the LP assignment algorithm or by computerised inspection, determines the locomotive rosters (the sequence of round trips that each locomotive hauls). Splitting the problem into two stages achieves a significant reduction in problem size, resulting in greatly reduced computation time (4 seconds as opposed to a number of hours).