An optimization model for the design of rack storage systems

The paper deals with the design of rack storage systems in multiple product situations. Given the production/delivery patterns of the different products and shared storage policies, the aim is to identify the amount of storage area that should be devoted to single deep selective racks and the amount for non-selective racks. The non-selective rack storage systems under analysis are accessed in a LIFO (last-in first-out) manner (e.g., "drive-in" racks). In particular, the racks under analysis consist of lane levels of different heights. This makes the problem challenging when also the unit loads may have different heights (e.g., because of product load restrictions). In such a situation, small unit loads can be put in high lanes, not vice versa. Moreover, the volumetric utilization and the storage efficiency of the warehouse become key performance indicators, so that the optimal mix of racks of different heights should be investigated. Thus, the paper presents a mathematical programming model able to address the considerations outlined above, along with floor space constraints. The objective is identify the number of single deep selective racks, the mix and number of non-selective racks and the lane depths so that the volumetric storage efficiency is maximized.