SL-LDA: LDA-Based Storage Location Assignment for Automated Warehouses Under MAPD Constraints

Storage location assignment in automated warehouses strongly affects order-processing efficiency. Existing co-occurrence-based approaches often rely on pointwise mutual information (PMI) statistics or direct frequency co-occurrence. This paper compares two deliberately chosen representation families for storage assignment in automated warehouses operated under Multi-Agent Pickup and Delivery (MAPD) constraints: Pointwise Positive PMI (PPPMI), representing direct pairwise co-occurrence, and Latent Dirichlet Allocation (LDA), representing latent-topic smoothing. The purpose is not to benchmark every possible representation space, but to make the pairwise-versus-latent contrast interpretable under a fixed execution pipeline consisting of task construction, visit-order selection, path planning, and collision avoidance. The broader research setting is motivated by real warehouse order data in which SKU co-occurrence structure is present, but such logs mix latent-topic effects, explicit family-based co-occurrence, noise, and demand variation. We therefore use two controlled abstractions of order structure: one generator with latent-topic mixtures and one generator with more direct family co-occurrence. We embed the proposed LDA representation and the PPPMI baseline in constrained-clustering and simulated-annealing placement methods and evaluate them against frequency-based, load-balancing, and random baselines. Evaluation is conducted in a fixed extended MAPD simulator that explicitly models orientation-aware motion, turning costs, service times, dynamic task release, and collision avoidance. In the latent-topic regime, LDA-based methods tended to form the leading group in average finite-horizon makespan, computed over completed combinations of random seeds and operating conditions. In the supplementary direct-co-occurrence condition, PPPMI was competitive in the plain representation comparison, while LDA-driven local search on top of a frequency-based initial layout remained strong. These results do not imply that LDA is universally superior; rather, they indicate that the relative suitability of PPPMI and LDA depends on the order structure and on how the representation interacts with the placement optimizer. The controlled generators are useful for isolating those effects, but they do not replace external validation on real warehouse logs.