EMU circulation planning for Silesian Railways: case study and a quantum approach

We study daily rolling stock circulation planning for electric multiple units (EMUs) on a regional passenger network, focusing on services where identical EMUs may be coupled in pairs on selected routes. Motivated by the operational needs of the regional operator Silesian Railways in Poland, we formulate an acyclic mixed-integer linear program on a one-day horizon that incorporates depot balance constraints, demand-driven seat and bicycle capacity limits (which is a new aspect requested by the regional operator and the local passenger community), and simple crew availability constraints. Using a graph-hypergraph representation of trips and single or coupled EMU movements, we first solve the problem with a classical ILP solver. We then derive a Quadratic Unconstrained Binary Optimization (QUBO) reformulation, which is frequently used as input for quantum optimization, and evaluate its solutions using quantum annealing on D-Wave Advantage systems and the classical quantum-inspired VeloxQ solver. Computational experiments on real-world instances from the Silesian network, with up to 404 train trips and 11 EMU types, show that the ILP approach can obtain high-quality daily circulation plans within at most about 40 minutes. In contrast, current quantum and quantum-inspired solvers are restricted to substantially smaller subinstances (up to 51 and 78 train trips, respectively) due to the large number of terms in the QUBO and, in the case of quantum hardware, embedding limitations. These results quantify the current frontier of QUBO-based methods for rolling stock circulation and point toward hybrid decision-support architectures in which quantum or quantum-inspired optimizers address only local subproblems within a broader classical planning framework.