The Stochastic Container Relocation Problem

TL;DR

This paper introduces a stochastic model for the container relocation problem, proposing new algorithms, bounds, and heuristics, with extensive computational testing demonstrating improved performance and conjecturing optimality of a heuristic in specific cases.

Contribution

It presents a novel multi-stage stochastic model, optimal and approximate algorithms, new heuristics, and theoretical bounds for the stochastic container relocation problem.

Findings

The PBFS algorithm is optimal for the stochastic model.

The PBFS-Approximate algorithm provides bounded error solutions.

New heuristics outperform existing methods in computational tests.

Abstract

The Container Relocation Problem (CRP) is concerned with finding a sequence of moves of containers that minimizes the number of relocations needed to retrieve all containers, while respecting a given order of retrieval. However, the assumption of knowing the full retrieval order of containers is particularly unrealistic in real operations. This paper studies the stochastic CRP (SCRP), which relaxes this assumption. A new multi-stage stochastic model, called the batch model, is introduced, motivated, and compared with an existing model (the online model). The two main contributions are an optimal algorithm called Pruning-Best-First-Search (PBFS) and a randomized approximate algorithm called PBFS-Approximate with a bounded average error. Both algorithms, applicable in the batch and online models, are based on a new family of lower bounds for which we show some theoretical properties. Moreover, we introduce two new heuristics outperforming the best existing heuristics. Algorithms, bounds and heuristics are tested in an extensive computational section. Finally, based on strong computational evidence, we conjecture the optimality of the "Leveling" heuristic in a special "no information" case, where at any retrieval stage, any of the remaining containers is equally likely to be retrieved next.