Extended abstract for “ Approximate column generation for some ship scheduling problems ”

We present a Dantzig-Wolfe procedure for the ship scheduling problem with flexible cargo sizes. This problem is similar to the well-known pickup and delivery problem with time windows, but the cargo sizes are defined to be within intervals instead of having fixed values. We show that the introduction of flexible cargo sizes to the column generation framework is not straightforward, and we handle the flexible cargo sizes heuristically when solving the subproblems. This leads to convergence issues in the branch-and-price search tree, and an optimal solution cannot be guaranteed. Hence we have introduced a method that generates an upper bound on the optimal maximization objective. We have compared our method with an a priori column generation approach, and our computational experiments on real world cases show that the Dantzig-Wolfe approach is faster than the a priori generation of columns, and we are able to deal with larger or more loosely constrained instances. By using the techniques introduced here, a more extensive set of real world cases can be solved either to optimality or within a small deviation from optimality.