Exact results for the order picking time distribution under return routing

TL;DR

This paper provides exact mathematical expressions for the distribution of order picking times in warehouses using return routing, considering various storage policies and warehouse layouts, with numerical comparisons of their performance.

Contribution

It derives exact Laplace-Stieltjes transforms for order picking time distributions in warehouses with return routing, covering multiple storage policies and layouts.

Findings

Exact transforms for order picking time distributions

Comparison of storage policies and layouts

Numerical inversion results

Abstract

This paper derives exact expressions for the Laplace-Stieltjes transform of the order picking time in single- and 2-block warehouses. We consider manual warehouses that deploy return routing and assume that order sizes follow a Poisson distribution. The results in this paper apply to a wide range of storage policies, including but not restricted to class-based and random storage. Furthermore, we compare the performance of the storage policies and warehouse lay-outs by using numerical inversion of the Laplace-Stieltjes transforms.