We propose modifications to the travel-time models for non-traditional warehouse layouts, Flying-V Fishbone, by incorporating a vertical travel dimension. The Flying-V model determines a cross aisle intersection for every picking aisle, while the Fishbone model determines a single point where the inserted cross aisle intersects the side of the warehouse. The shape and angle of the cross aisle is unrestricted for the Flying-V layout, while the angle is unrestricted for the Fishbone layout. The resulting non-linear optimization models incorporate Chebychev travel within the picking aisles. We compare both the shape of the aisle and the percent improvement over a traditional warehouse with the results found in previous research that ignores vertical travel. We show that the percent improvement diminishes as the height of the rack increases, with Fishbone maintaining a higher percent improvement over Flying-V. We also show that while the shape of Flying-V can be considerably altered by considering vertical travel, the Fishbone layout often maintains its recommended shape regardless of the height of the rack. We also altered the travel rules for the Flying-V model in order to find simpler designs and obtained near-optimal results. We conclude with recommendations for effective implementation of these two designs
