Mixed integer programming for minimizing the period of a cyclic railway timetable for a single track with two train types

Abstract

In this paper we extend the work of Bergmann (1975) to investigate the capacity of a single track, unidirectional rail line that adheres to a cyclic timetable. A set of intermediate stations lies between an origin and destination with one siding at each station. Two types of trains—express and local—are dispatched from the origin in alternating fashion. The local stops at every intermediate station and the express stops at no intermediate stations. A mixed integer linear program is developed in order to minimize the length of the dispatching cycle and minimize the total stopping (dwell) time of the local train at all stations combined. Constraints include a minimum dwell time for the local train at each station, a maximum total dwell time for the local train, and headway considerations on the main line and in stations. Hundreds of randomly generated problem instances with up to 70 stations are considered and solved to optimality in a reasonable amount of time using IBM ILOG CPLEX.