Optimal Re-Slotting with Minimum Exchanges in Uniform-Storage Warehouses

This paper generalizes the Greedy Exchange Method for Warehouse Slotting (GEMWS) to distribution centers with uniform storage locations and independent, interchangeable storage classes. Starting from an existing warehouse allocation, GEMWS iteratively exchanges the highest-velocity rear-pick assignment with the lowest-velocity forward-pick assignment within each class. The method achieves globally optimal forward-pick velocity over the class-constrained feasible allocation space while requiring the minimum possible number of pairwise exchanges. Designed for practical implementation, GEMWS operates using warehouse management system data and a lightweight Python implementation, without requiring commercial optimization software or mathematical programming solvers. Its heap-based implementation has O(n log n) worst-case computational complexity. Synthetic experiments verify the minimum-exchange guarantee across 3,000 instances and demonstrate computational scalability to 100,000 assignments. An optional minimum-gain threshold reduces exchange counts by approximately 57% while retaining 99.8% of attainable forward-pick velocity in the reported experiments. This work extends the original GEMWS framework (Saiq, 2026), available at https://doi.org/10.5281/zenodo.23096290.