On The Expectation Of The Largest Gap In A Warehouse

The expectation of the largest gap between two consecutive picks in an aisle is a basic building block in modelling the pick travel distance for the largest gap routing policy in a warehouse. Researchers have predominantly used either simulation or recursive algorithms for its estimation. This paper develops analytical expressions for this statistic in, both, continuous and discrete aisles using the statistical theory of ordered uniform spacings. We further demonstrate how these results can apply to the entire multi-aisle warehouse. Our results show that these expressions are accurate and extremely fast to evaluate as compared to the existing approaches.