Maintenance scheduling in a railway corricdor

TL;DR

This paper studies a complex railway maintenance scheduling problem, identifying its computational difficulty and providing efficient solutions for specific simplified cases involving train path conflicts and traffic directions.

Contribution

It introduces a novel scheduling problem in railway maintenance, proves NP-completeness in general, and offers polynomial-time algorithms for special cases with limited train path interference.

Findings

NP-complete in general case

Polynomial-time solution for single train path impact case

Efficient $O(n^4)$ algorithm for unidirectional traffic case

Abstract

We investigate a novel scheduling problem which is motivated by an application in the Australian railway industry. Given a set of maintenance jobs and a set of train paths over a railway corridor with bidirectional traffic, we seek a schedule of jobs such that a minimum number of train paths are cancelled due to conflict with the job schedule. We show that the problem is NP-complete in general. In a special case of the problem when every job under any schedule just affects one train path, and the speed of trains is bounded from above and below, we show that the problem can be solved in polynomial time. Moreover, in another special case of the problem where the traffic is unidirectional, we show that the problem can be solved in time $O(n^4)$.