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

TL;DR

The paper introduces the unit-load pre-marshalling problem (UPMP) for block stacking storage, aiming to minimize relocation moves to eliminate blockages so unit loads can be retrieved by priority groups. It presents two solution pipelines: (i) a CPMP-inspired A* approach for UPMP with a single access direction, and (ii) a novel two-stage method for up to four access directions that fixes access directions via a network-flow model and then applies a tree search on virtual lanes with a MIP-based lower bound. Computational experiments on a public benchmark show that enabling multiple access directions dramatically reduces both the total number of moves and the required runtime, increasing the set of solvable instances, especially at high fill levels. The work highlights significant practical benefits for dense block-stacking warehouses, with implications for layout design, traffic management, and future research directions including scalability to multi-bay systems and enhanced heuristics.

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.

Figures (18)

• Figure 1: Example of a single storage bay in a block stacking storage system with a robotic forklift.
• Figure 2: Example storage bays with eight unit loads in the CPMP via crane in a) as well as side access in the UPMP via one direction in b) and three directions in c). The directly accessible unit loads are dark-gray.
• Figure 3: State representation of the UPMP.
• Figure 4: Example configuration and solution of the UPMP
• Figure 5: Example of the tree search procedure (simple lower bound as blocking items in dark gray) similar to the illustration in tierneySolvingPremarshallingProblem2017