Double Traversals in Boundary Subaisles: Implications for Two-Block Layouts

TL;DR

This paper proves that in certain warehouse layouts, optimal routes do not require double traversals in boundary subaisles, simplifying route planning and improving efficiency.

Contribution

It extends existing results by showing no double traversals are needed in boundary subaisles of warehouses with multiple aisles, unifying conditions for various layouts.

Findings

No double traversals needed in boundary subaisles of warehouses with at least two aisles.

Exact methods can exclude double-traversal configurations in boundary subaisles.

Simplifies route optimization by reducing admissible edge configurations.

Abstract

The order picking problem seeks the shortest warehouse route that visits all required item locations. Strict conditions are known for single-block rectangular layouts under which optimal routes never require double traversals, while broader results show that double traversals serving cross-aisle connectivity can always be avoided. We strengthen these findings by proving that no double traversals are needed in the boundary subaisles, the uppermost and lowermost subaisle segments, of warehouses with at least two non-empty aisles. This yields a unified strict condition for all single-block layouts and for two-block layouts with more than one aisle. For these widely used layouts, exact methods such as dynamic programming and mathematical programming can therefore exclude the double-traversal configuration from every boundary subaisle, reducing the number of admissible edge configurations without loss of optimality.