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.