Modified Dynamic Programming Algorithms for Order Picking in Single-Block and Two-Block Rectangular Warehouses

TL;DR

This paper introduces modified dynamic programming algorithms for warehouse order picking that leverage deterministic travel patterns, significantly improving computational efficiency while maintaining optimality.

Contribution

It proposes structural modifications to existing algorithms based on recent insights, achieving linear-time complexity and reducing computational effort in warehouse layout optimization.

Findings

Computational effort reduced by factors up to 1.81

Modifications preserve linear-time complexity in number of aisles

Numerical experiments confirm efficiency improvements

Abstract

Recent research has shown that optimal picker tours in rectangular warehouses exhibit deterministic travel patterns within each aisle, and that certain previously considered traversals are unnecessary. Using these insights, this paper proposes modifications to dynamic programming algorithms that improve computational efficiency without affecting optimality. For layouts with and without a central cross-aisle, the modifications preserve linear-time complexity in the number of aisles while reducing the number of state-action evaluations per stage. The proposed modifications reduce computational effort by factors up to 1.81, confirmed by numerical experiments. These findings are encouraging and highlight how structural refinements can yield significant improvements in practical performance of algorithms.