Container pre-marshalling problem minimizing CV@R under uncertainty of ship arrival times

TL;DR

This paper addresses the container pre-marshalling problem under uncertain ship arrival times by developing a mixed-integer linear model that minimizes CVaR, and introduces an exact algorithm to efficiently solve large-scale instances.

Contribution

It presents a novel optimization model minimizing CVaR for container layouts considering arrival time uncertainty, along with an efficient exact solution algorithm.

Findings

The proposed method outperforms conventional robust optimization in layout quality.

The algorithm significantly speeds up large-scale problem solving.

Numerical results demonstrate high-quality container arrangements under uncertainty.

Abstract

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.