The stochastic maintenance location routing allocation problem for rolling stock

We study a problem where – given a railway network and different fleets – we have to locate maintenance locations and allocate the fleets to these locations. The allocation of fleets to the maintenance locations complicates the maintenance location routing problem. For each candidate location different facility sizes can be chosen and for each size there is an associated annual facility cost that captures the economies of scale in facility size. Because of the strategic nature of facility location, these facilities should be able to handle changes such as adjustments to the line plan and the introduction of new rolling stock types. We capture these changes by discrete scenarios and we formulate this two-stage stochastic problem as a mixed integer problem. Furthermore, we perform a case study with the Netherlands Railways that provides novel managerial insights by showing that the number of opened maintenance facilities highly depends on the allocation restrictions.