Buffers are prevalent in many production systems, where they are often manually man- aged by human operators who make decisions about item placement, retrieval sequences, and space allocation based on experience and intuition. However, current labor shortages highlight the urgent need to automate these tasks. This paper addresses the Buffer Reshuffling and Retrieval (BRR) problem, which aims to optimize the reshuffling and retrieval of unit loads within a buffer zone. The buffer zone is assumed to be a designated area on the floor where items are stored without the use of shelves or other intermediary structures. We extend the static BRR model, which assumes a fixed set of items, to address the complexities of modern, dynamic production logistics. Specifically, we introduce two extensions: (1) a dynamic variant that accounts for new items requiring storage in the buffer, and (2) a dynamic multi-AMR variant that utilizes multiple Autonomous Mobile Robots (AMRs). Our contribution lies in the development of a compre- hensive Integer Programming (IP) framework encompassing all three variants: static, dy- namic, and dynamic with multiple AMRs. The computational complexity of these IP models hinders their direct application in real-time, large-scale production settings. However, by introducing and solving illustrative instances, this IP framework provides a foundation for future research into heuristic and learning based algorithms.

inputs contains the Instance descriptions as json files. results contains the found solutions as json files.

The inputs and results jsons can be