We introduce the Block Rearrangement Problem (BRaP), a challenging component of large warehouse management which involves rearranging storage blocks within dense grids to achieve a goal state. We formally define the BRaP as a graph search problem. Building on intuitions from sliding puzzle problems, we propose five search-based solution algorithms, leveraging joint configuration space search, classical planning, multi-agent pathfinding, and expert heuristics. We evaluate the five approaches empirically for plan quality and scalability. Despite the exponential relation between search space size and block number, our methods demonstrate efficiency in creating rearrangement plans for deeply buried blocks in up to 80x80 grids.

In Amazon robotic warehouses, the destination-to-chute mapping problem is crucial for efficient package sorting. Often, however, this problem is complicated by uncertain and dynamic package induction rates, which can lead to increased package recirculation. To tackle this challenge, we introduce a Distributionally Robust Multi-Agent Reinforcement Learning (DRMARL) framework that learns a destination-to-chute mapping policy that is resilient to adversarial variations in induction rates. Specifically, DRMARL relies on group distributionally robust optimization (DRO) to learn a policy that performs well not only on average but also on each individual subpopulation of induction rates within the group that capture, for example, different seasonality or operation modes of the system. This approach is then combined with a novel contextual bandit-based estimator of the worst-case induction distribution for each state-action pair, significantly reducing the cost of exploration and thereby increasing the learning efficiency and scalability of our framework. Extensive simulations demonstrate that DRMARL achieves robust chute mapping in the presence of varying induction distributions, reducing package recirculation by an average of 80% in the simulation scenario.