  We address the applicability of hybrid quantum-classical heuristics for
practical railway rescheduling management problems. We build an integer linear
model for the given problem and solve it with D-Wave's quantum-classical hybrid
solver as well as with CPLEX for comparison. The proposed approach is
demonstrated on a real-life heterogeneous urban network in Poland, including
both single- and multi-track segments and covers all the requirements posed by
the operator of the network. The computational results demonstrate the
readiness for application and benefits of quantum-classical hybrid solvers in
the realistic railway scenario: they yield acceptable solutions on time, which
is a critical requirement in a rescheduling situation. At the same time, the
solutions that were obtained were feasible. Moreover, though they are
probabilistic (heuristics) they offer a valid alternative by returning a range
of possible solutions the dispatcher can choose from. And, most importantly,
they outperform classical solvers in some cases.
