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 (o r class) of locomotive. This is typical of problems arising in many passeng er train networks and an exact solution method exists for the general form of this problem (Forbes et al(1)) This paper describes the analysis of a pa rticular 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 c an be solved in two separate stages. The first stage (an integer programmin g model) determines the type of locomotive that will hall each trip. The se cond 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 p roblem size, resulting in greatly reduced computation time (4 seconds as op posed to a number of hours).