Analytical models for retrieving items in dense storage systems and optimizing the location of an open square

Abstract

Dense storage systems allow for highly effective use of space; however this comes at a cost: dense storage systems can require the repositioning of stored items to retrieve other more densely desired items. These dense storage systems are found in warehouses and distribution centers, and aboard US Navy ships used for sea-based logistics. This research creates mathematical models to determine the value of an empty space in a specific dense storage environment, the double inverted T configuration. Retrieval distance equations are derived for each item in a layout, which is the distance it takes to move the item from its current position to an exit point. Repositioning distance equations calculate the distance it takes to move an item out of the way and back in order to retrieve an item behind it. Repositioning distance equations are dependent on an item’s block, direction of travel, and repositioning location. The benefit of an empty space is defined by the amount by which the total system’s expected repositioning distance is reduced to reach a target item. This project characterizes open spaces in terms of how many items receive benefit and how much benefit each item receives. An optimization problem is presented to select which location should be left open, which is solved using brute force for a single open square. We find the best locations for an open square occur for squares along the aisle, and close to the vertical walls if h > k, or close to the horizontal wall if h = k. Due to the symmetry in repositioning distances, multiple optimal solutions exist.