Code: A Fast Exact Pricing Algorithm for the Railway Crew Scheduling Problem

The railway crew scheduling problem consists of selecting a least cost set of duties that cover all tasks. Large-scale crew scheduling problems are typically solved with column generation, where in each iteration a pricing problem needs to be solved. When the duty constraints consist in a maximum duty length, a meal break constraint, and the requirement to start and end at the same crew depot, the fastest known exact pricing algorithm has O(|N|3) complexity, |N| being the number of tasks.

In this work we propose an O(|N|2) exact pricing algorithm. We compare the two algorithms on randomly generated instances and show that a reduction in computation time of 95% is attained on instances of size |N|=1,250.