Optimal placement of warehouse cross-aisles in a picker-to-part warehouse with class-based storage

Given a picker-to-part warehouse having a simple rectilinear aisle arrangement with north-south storage aisles and east-west travel aisles (or cross-aisles), this article investigates the optimal placement of the cross-aisles as a consequence of the probability mass function of the order pick points, as determined by the storage policy. That is, what placement of the cross-aisles will result in a minimal expected path length for the picker? An analytical solution procedure is developed for the optimal placement of a single middle cross-aisle for a given storage policy. A simplifying assumption is made as regards picker routing, but arbitrary non-random storage policies are considered. The solution procedure is generalized to a method for multiple cross-aisles. Some example problems are solved and a simulation study is used to measure the impact of the assumptions made to generate the method.