  This paper is concerned with the container pre-marshalling problem, which
involves relocating containers in the storage area so that they can be
efficiently loaded onto ships without reshuffles. In reality, however, ship
arrival times are affected by various external factors, which can cause the
order of container retrieval to be different from the initial plan. To
represent such uncertainty, we generate multiple scenarios from a multivariate
probability distribution of ship arrival times. We derive a mixed-integer
linear optimization model to find an optimal container layout such that the
conditional value-at-risk is minimized for the number of misplaced containers
responsible for reshuffles. Moreover, we devise an exact algorithm based on the
cutting-plane method to handle large-scale problems. Numerical experiments
using synthetic datasets demonstrate that our method can produce high-quality
container layouts compared with the conventional robust optimization model.
Additionally, our algorithm can speed up the computation of solving large-scale
problems.
