  In this work, we consider a practical railway dispatching problem: delay and
conflict management on a single-track railway line. We examine the issue of
train dispatching consequences caused by the arrival of an already delayed
train to the segment being considered. This problem is computationally hard and
often needs to be solved timely. Here, we introduce a quadratic unconstrained
binary optimization (QUBO) model of the problem in question, compatible with
the emerging quantum annealing technology. The model's instances can be
executed on present-day quantum annealers. As a proof-of-concept, we solve
selected real-life problems from the Polish railway network using D-Wave
quantum annealers. As a reference, we also provide solutions calculated with
classical methods, including those relevant to the community (linear integer
programming) and a sophisticated algorithm based on tensor networks for solving
QUBO problems.
