Exact algorithms for the order picking problem

TL;DR

This paper introduces two exact algorithms for the warehouse order picking problem, aiming to minimize time and labor, and compares their performance with a TSP solver.

Contribution

It presents a strengthened mixed-integer programming formulation and a generalized dynamic programming algorithm for the order picking problem.

Findings

The algorithms are effective and outperform TSP solver Concorde in experiments.

Preprocessing and valid inequalities improve the mixed-integer programming approach.

The dynamic programming approach generalizes existing algorithms for multiple cross-aisles.

Abstract

Order picking is the problem of collecting a set of products in a warehouse in a minimum amount of time. It is currently a major bottleneck in supply-chain because of its cost in time and labor force. This article presents two exact and effective algorithms for this problem. Firstly, a sparse formulation in mixed-integer programming is strengthened by preprocessing and valid inequalities. Secondly, a dynamic programming approach generalizing known algorithms for two or three cross-aisles is proposed and evaluated experimentally. Performances of these algorithms are reported and compared with the Traveling Salesman Problem (TSP) solver Concorde.