Solving the unit-load pre-marshalling problem in block stacking storage systems with multiple access directions

TL;DR

This paper introduces new methods for efficiently pre-marshalling block stacking storage systems with multiple access directions, reducing sorting effort and access time through innovative algorithms and models.

Contribution

It develops a novel two-step solution approach for multiple access directions using network flow and A* algorithms, extending existing methods for single access direction.

Findings

Multiple access directions significantly decrease total access time.

The proposed algorithms effectively minimize unit-load moves.

Computational experiments demonstrate improved performance over traditional methods.

Abstract

Block stacking storage systems are highly adaptable warehouse systems with low investment costs. With multiple, deep lanes they can achieve high storage densities, but accessing some unit loads can be time-consuming. The unit-load pre-marshalling problem sorts the unit loads in a block stacking storage system in off-peak time periods to prepare for upcoming orders. The goal is to find a minimum number of unit-load moves needed to sequence a storage bay in ascending order based on the retrieval priority group of each unit load. In this paper, we present two solution approaches for determining the minimum number of unit-load moves. We show that for storage bays with one access direction, it is possible to adapt existing, optimal tree search procedures and lower bound heuristics from the container pre-marshalling problem. For multiple access directions, we develop a novel, two-step solution approach based on a network flow model and an A* algorithm with an adapted lower bound that is applicable in all scenarios. We further analyze the performance of the presented solutions in computational experiments for randomly generated problem instances and show that multiple access directions greatly reduce both the total access time of unit loads and the required sorting effort.