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 × 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. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Warehouse sizing to minimize inventory and storage costs

This paper considers a warehouse sizing problem whose objective is to minimize the total cost of ordering, holding, and warehousing of inventory. Unlike typical economic lot sizing models, the warehousing cost structure examined here is not the simple unit rate type, but rather a more realistic step function of the warehouse space to be acquired. In the cases when only one type of stock‐keeping unit (SKU) is warehoused, or when multiple SKUs are warehoused, but, with separable inventory costs, closed form solutions are obtained for the optimal warehouse size. For the case of multi‐SKUs with joint inventory replenishment cost, a heuristic with a provable performance bound of 94% is provided. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 299–312, 2001     

See the light: Optimization of put-to-light order picking systems

Put-to-light order picking systems invert the basic logic of conventional picker-to-parts systems. Instead of successively visiting the storage positions of the stock keeping units (SKUs) when collecting picking orders, an order picker accompanies successive bins each containing multiple items of a specific SKU along a lane of subsequent orders. Whenever the picker passes an order requiring the current SKU, which is indicated by a light signal, she puts the requested number of items into the bin associated with the order. Such an order picking system is well-suited if the assortment is not overly large and all orders demand similar SKUs, so that it is mainly applied in distribution centers of brick-and-mortar retail chains. This paper evaluates four different setups of put-to-light systems, which, during operations, require the solution of different storage assignment and SKU sequencing problems. We formulate these problems, prove computational complexity, and suggest suited solution algorithms. By applying these algorithms in a comprehensive computational study, we benchmark the impact of the four different setups on picking performance. In this way, warehouse managers receive decision support on how to set up their put-to-light systems.