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

TL;DR

This work addresses the container pre-marshalling problem under uncertainty in ship arrivals by modeling arrival orders with a multivariate distribution and optimizing the $CV@R$ of misplaced containers. It introduces a mixed-integer linear program to minimize tail risk and develops an exact cutting-plane algorithm to solve large-scale instances, showing improved layout quality over robust optimization and scalable computation. The approach leverages scenario-based uncertainty, CV@R representations (lifting and cutting-plane), and a structured MILP with detailed constraints for counting misplaced containers. Empirical results on synthetic Bay layouts demonstrate the method’s effectiveness and computational advantages, highlighting its practical relevance for terminals facing uncertain ship schedules.

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.

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