Maintenance Location Routing for Rolling Stock Under Line and Fleet Planning Uncertainty

Abstract

Rolling stock needs regular maintenance in a maintenance facility. Rolling stock from different fleets are routed to maintenance facilities by interchanging the destinations of trains at common stations and by using empty drives. We consider the problem of locating maintenance facilities in a railway network under uncertain or changing line planning, fleet planning and other uncertain factors. These uncertainties and changes are modeled by a discrete set of scenarios. We show that this new problem is NP-hard and provide a two-stage stochastic programming and a two-stage robust optimization formulation. The second-stage decision is a maintenance routing problem with similarity to a minimum cost-flow problem. We prove that the facility location decisions remain unchanged under a simplified routing problem and this gives rise to an efficient mixed integer programming (MIP) formulation. This result also allows us to find an efficient decomposition algorithm for the robust formulation based on scenario addition (SA). Computational work shows that our improved MIP formulation can efficiently solve instances of industrial size. SA improves the computational time for the robust formulation even further and can handle larger instances due to more efficient memory usage. Finally, we apply our algorithms on practical instances of the Netherlands Railways and give managerial insights.

Economies of scale in recoverable robust maintenance location routing for rolling stock

“…The maximum difference between the WS and the RRMLP for the ten instances is 1.9% and the 526 average difference is 0.8%. This difference is smaller than the 3.2% found in Tönissen et al (2018) , we expect that one of the 527 reasons for this is the allowed recovery. In this section we answer the question, "What influence has the annual unplanned maintenance frequency on the num-559 ber of opened facilities and the optimal worst-case cost?".…”

“…515 Furthermore, we can observe that the NS instances require more iterations (approximately 4 vs 2) and that solving the MIP 516 (with a subset of the scenarios) goes quickly for the computational instances, while it takes a long time to close the gap for 517 the NS instances. From the RMLRP and SMLRP, we know that the computational instances are not easy, as they are more dif-518 ficult than the NS instances in Tönissen et al (2018) . Consequently, the large difference in solution time is caused by some 519 characteristics specific to the RRMLRP.…”

The stochastic maintenance location routing allocation problem for rolling stock

“…Maintenance routing for rolling stock is studied by Anderegg et al (2003), Kroon (2005, 2007) and for aviation by Gopalan and Talluri (1998), Sarac et al (2006), Liang et al (2015) and many others. The combination of maintenance routing and facility location for aviation is studied by Feo and Bard (1989) and Gopalan (2014), for locomotives by Xie et al (2016), and for rolling stock by Tönissen et al (2019) and Tönissen and Arts (2018). The paper of Tönissen et al (2019), includes the maintenance routing for rolling stock in an aggregate way into a facility location model.…”

“…The maintenance location routing problem for rolling stock was introduced by Tönissen et al (2019), and extended by Tönissen and Arts (2018). Tönissen and Arts (2018) show that the best strategy is to reduce transportation cost by locating many small facilities instead of opening a few large facilities to profit from economies of scale.…”

A branch-and-price approach for trip sequence planning of high-speed train units

“…Four heuristic algorithms, based on column generation, were proposed and compared. Tönissen et al [30] proposed a two-stage stochastic programming model and a two-stage robust optimization model to integrate maintenance facility location problem and train unit scheduling problem under uncertain conditions. In the first stage, they considered the maintenance facility location problem, and in the second stage, they considered train unit scheduling problem.…”