Use statistical analysis to approximate integrated order batching problem

Abstract

This paper highlights the tight relationship between the picking and packing processes in warehouse management and the need to consider them as an integrated problem. The study describes and models this integrated problem as a mixed-integer programming model, to optimise overall labour costs by determining the assignment of the subsets of orders, i.e. batches, for picking and packing. To address the issue of model complexity, the paper presents a statistical-based framework for generating approximate models and selecting the optimal one through examination. Based on the examination results, a pair-swapping heuristic is additionally proposed to be combined as a hybrid algorithm. Numerical experiments based on a real-world case demonstrate the effectiveness of the framework-proposed and selected hybrid algorithm by comparison with other framework-proposed approximate models, a solver, and existing heuristics. Our findings indicate that the combined usage of integrated picking and packing processes planning and the hybrid algorithm proposed and selected within the statistical-based framework can effectively reduce the cost of warehouse management.

Keywords:

• Logistics
• warehouse
• order batching
• mixed integer linear programming
• Monte Carlo method
• statistical methods

Data availability statement

The data that support the findings of this study are available from the corresponding author Chuanhou Gao, upon reasonable request.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was funded by the National Nature Science Foundation of China [grant numbers 12071428, 62111530247 and 12320101001], and the Zhejiang Provincial Natural Science Foundation of China [grant number LZ20A010002].

Notes on contributors

Sen Xue

Sen Xue received the B.S. degree in Information and Computing Science from Zhejiang University, Hangzhou, China in 2020. He is currently working toward the Ph.D. degree in Operations Research in the School of Mathematical Sciences, Zhejiang University, Hangzhou, China. His research interests include Integer Programming, machine learning and logistics.

Chuanhou Gao

Chuanhou Gao received the B.Sc. degrees in Chemical Engineering from Zhejiang University of Technology, China, in 1998, and the Ph.D. degrees in Operational Research and Cybernetics from Zhejiang University, China, in 2004. From June 2004 until May 2006, he was a Postdoctor in the Department of Control Science and Engineering at Zhejiang University. Since June 2006, he has joined the Department of Mathematics at Zhejiang University, where he is currently a Full Professor. He was a visiting scholar at Carnegie Mellon University from Oct. 2011 to Oct. 2012. His research interests are in the areas of optimisation, chemical reaction network theory, machine learning, and thermodynamic process control. He is an associate editor of IEEE Transactions on Automatic Control and of International Journal of Adaptive Control and Signal Processing.