Complexity, bounds and dynamic programming algorithms for single track train scheduling

In this work we consider the single track train scheduling problem. The problem consists of scheduling a set of trains from opposite sides along a single track. The track has intermediate stations and the trains are only allowed to pass each other at those stations. Traversal times of the trains on the blocks between the stations only depend on the block lengths but not on the train. This problem is a special case of minimizing the makespan in job shop scheduling with two counter routes and no preemption. We develop a lower bound on the makespan of the train scheduling problem which provides us with an easy solution method in some special cases. Additionally, we prove that for a fixed number of blocks the problem can be solved in pseudo-polynomial time.