# The Multi-AMR Buffer Storage, Retrieval, and Reshuffling Problem: Exact and Heuristic Approaches

arXiv: https://arxiv.org/abs/2603.26542 · HTML: https://mlsanity.com/paper/2603.26542/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 28 references that are in the map.
- First posted on arXiv 27 Mar 2026.

## Builds on (most cited first, 4 of 4)

- [Solving the unit-load pre-marshalling problem in block stacking storage systems with multiple access directions](https://mlsanity.com/paper/2207.09118/) (2022)
- [Sorting multibay block stacking storage systems](https://mlsanity.com/paper/2405.04847/) (2024)
- [Symbolic Planning and Multi-Agent Path Finding in Extremely Dense Environments with Unassigned Agents](https://mlsanity.com/paper/2509.01022/) (2025)
- [Robust Out-of-Order Retrieval for Grid-Based Storage at Maximum Capacity](https://mlsanity.com/paper/2601.19144/) (2026)

## Abstract (arXiv)

Buffer zones are essential in production systems to decouple sequential processes. In dense floor storage environments, such as space-constrained brownfield facilities, manual operation is increasingly challenged by severe labor shortages and rising operational costs. Automating these zones requires solving the Buffer Storage, Retrieval, and Reshuffling Problem (BSRRP). While previous work has addressed scenarios where the focus is limited to reshuffling and retrieving a fixed set of items, real-world manufacturing necessitates an adaptive approach that also incorporates arriving unit loads. This paper introduces the Multi-AMR BSRRP, coordinating a robot fleet to manage concurrent reshuffling, alongside time-windowed storage and retrieval tasks, within a shared floor area. We formulate a Binary Integer Programming (IP) model to obtain exact solutions for benchmarking purposes. As the problem is NP-hard, rendering exact methods computationally intractable for industrial scales, we propose a hierarchical heuristic. This approach decomposes the problem into an A* search for task-level sequence planning of unit load placements, and a Constraint Programming (CP) approach for multi-robot coordination and scheduling. Experiments demonstrate orders-of-magnitude computation time reductions compared to the exact formulation. These results confirm the heuristic's viability as responsive control logic for high-density production environments.