A Mathematical Model for Rolling Stock Assignment: Network Model and an Application of Column Generation

Abstract

As railway rolling stock is expensive, it is necessary to utilize them as efficiently as possible. Making rolling stock schedule (RSS) is one of processes in the planning phase. RSS is a sequence of daily schedules. A daily schedule is a sequence of train services for a specific train-set. RSS is to make daily schedules and a sequence of them so as to satisfy constraints for daily and monthly inspections which are performed within a certain period of time or a certain mileage, respectively. Each train-set is equally used regarding on cumulative mileage by following the RSS. However, it is often necessary to assign train-set(s) to daily schedules for some reasons irrespective of RSS. Rolling stock assignment (RSA) is to find an assignment of train-sets to daily schedules provided in RSS. In this paper, we represent a problem of rolling stock assignment by a network in which sequences of daily schedule for train-sets correspond to paths and formulate it into a set covering type problem. Furthermore, we propose a solution method based on column generation and rolling schedule.