Improved formulations of the joint order batching and picker routing problem

TL;DR

This paper introduces improved mathematical formulations for the integrated order batching and picker routing problem, enhancing computational efficiency and solution quality in warehouse order picking operations.

Contribution

The paper develops new formulations based on connectivity constraints and cutting planes, and explores problem properties and auxiliary graphs for better optimization.

Findings

Significant computational improvements over previous models

Effective formulations for both single-block and multiple-block warehouses

Enhanced understanding of problem structure and properties

Abstract

Order picking is the process of retrieving ordered products from storage locations in warehouses. In picker-to-parts order picking systems, two or more customer orders may be grouped and assigned to a single picker. Then routing decision regarding the visiting sequence of items during a picking tour must be made. (J.Won and S.Olafsson 2005) found that solving the integrated problem of batching and routing enables warehouse managers to organize order picking operations more efficiently compared with solving the two problems separately and sequentially. We therefore investigate the mathematical programming formulation of this integrated problem. We present several improved formulations for the problem based on the findings of (Valle, Beasley, and da Cunha 2017), that can significantly improve computational results. More specifically, we reconstruct the connectivity constraints and generate new cutting planes in our branch-and-cut framework. We also discuss some problem properties by studying the structure of the graphical representation, and we present two types of additional constraints. We also consider the no-reversal case of this problem. We present efficient formulations by building different auxiliary graphs. Finally, we present computational results for publicly available test problems for single-block and multiple-block warehouse configurations