A Combined column generation and heuristics for railway short-term rolling stock planning with regular inspection constraints

The aim of railway rolling stock planning problem is to find an optimal allocation of train-sets for a given set of trips in the train timetable in order to minimize the total cost. We propose a column generation and Lagrangian relaxation heuristics for short-term rolling stock planning problems with regular inspection constraints. The problem is formulated as a subtour traveling salesman problem to find a set of elementary shortest cycles that cover all trips in the timetable. In the proposed method, a tight lower bound is obtained from the continuous relaxation of Dantzig-Wolfe reformulation by column generation. The pricing problem can be formulated as an elementary shortest cycle problem with resource constraints. A labeling algorithm is applied to solve the pricing problem. In order to reduce the computational effort, we apply a general state space augmenting algorithm to solve the pricing problems. Computational results show that the proposed column generation and Lagrangian relaxation heuristics can find good lower and upper bounds for 300 trips within reasonable computing time.