Puzzle-based storage systems

We introduce and develop models for a physical goods storage system based on the 15-puzzle, a classic children’s game in which 15 numbered tiles slide within a 4 x 4 grid. The objective of the game is to arrange the tiles in numerical sequence, starting from a random arrangement. For our purposes, the tiles represent totes, pallets, or even containers that must be stored very densely, and the objective is to maneuver items to an input–output point for retrieval or processing. We develop analytical results for storage configurations having a single empty location (as in the game) and experimental results for configurations with multiple empty locations. Designs with many empty locations can be made to form aisles, allowing us to compare puzzle-based designs with traditional aisle-based designs found in warehousing systems.