Automated storage and retrieval system design with variant lane depths

This paper models a warehouse design problem with 2D automated storage and retrieval system (AS/RS) and 3D AS/RS as options, where 3D racks may have different depths. The design problem is first modeled as a mixed-integer nonlinear program to minimize investment and maximize throughput under various business needs, such as cost structure, responsiveness requirement, demand rates, and inventory levels. The model is then converted to a mixed-integer program based on optimality conditions. A basic Branch-and-Bound algorithm and a modified one are developed to overcome computational challenges. A high throughput expectation leads to a design with shallow storage racks, while high land/equipment costs have opposite impacts. When demand rates are similar across SKUs, heterogeneously distributed inventory levels lead to racks with different depths and assigning SKUs with higher inventory levels to deeper racks. More heterogeneous demand rates also make rack depths more variant and have SKUs with higher demand rates assigned to shallower racks. In other words, the heterogeneities of inventory levels and demand rates have a contradictory effect on the SKU-to-rack assignment and result in racks with more uniform depths when SKUs with high demand also have high inventory levels, which is often the case in practice.