Optimizing logistics warehouse space utilization with minimum total transportation

Abstract

Logistics warehouses are integral to supply chain management, enabling the efficient storage and movement of goods. However, the dynamic operational nature of these facilities, characterized by high product turnover, often results in suboptimal space utilization. This study addresses the inefficiency caused by partially filled pallets and the honeycombing effect, which leads to substantial storage capacity loss. Focusing on a third-party logistics warehouse managing apparel boxes, the uniqueness of each box introduces specific challenges in space optimization. To mitigate these issues, two integer linear programming models were developed. The first model is utilized for emptying and reallocating products from the predetermined low-capacity shelf cells to new locations. The second model simultaneously identifies both the shelf cells to be vacated and the optimal relocation destinations. Both models aim to minimize the total transportation costs. The first model is suited for rapid reallocation and efficient short-term solutions, whereas the second model offers a more holistic approach to long-term space optimization. These models provide a systematic, data-driven solution for enhancing warehouse space management. The problem is also considered bi-objective, with the objectives of maximizing the number of empty shelf cells and minimizing the total transportation costs. The bi-objective mathematical model was scalarized using the epsilon-constraint method and solved for different epsilon values. This process yielded 39 Pareto-optimal solutions. The results indicate that as more cells are emptied, both the total cost and cost per cell increase. Considering the problem in a bi-objective form has also been advantageous for offering the decision-maker not just one solution but a solution set with different numbers of cells to be emptied and different transportation costs.

Keywords

• Logistics warehouse
• Integer programming
• Warehouse space utilization

References

1. [1] M. He, J. Shen, X. Wu and J. Luo, “Logistics space: A literature review from the sustainability perspective,” Sustainability, vol.10, no. 8, pp. 2815, 2018, doi: https://doi.org/10.3390/su10082815.
2. [2] D. Perera, U. Mirando and A. Fernando, “Warehouse space optimization using linear programming model and goal programming model,” Sri Lanka Journal of Economics, Statistics, and Information Management, vol. 1, no. 1, pp. 103-124, 2022.
3. [3] I. H. Mohamud, M. A. Kafi, S.A. Shahron, N. Zainuddin and S. Musa, “The Role of Warehouse Layout and Operations in Warehouse Efficiency: A Literature Review,” Journal Européen des Systèmes Automatisés, vol. 56, no. 1, 2023, doi: https://doi.org/10.18280/jesa.560109.
4. [4] M-K. Lee and E. A. Elsayed, “Optimization of warehouse storage capacity under a dedicated storage policy,” International Journal of Production Research, vol. 43, no. 9, pp. 1785-1805, 2005, doi: https://doi.org/10.1080/13528160412331326496.
5. [5] D. Kansy, G. Tarczynski and P. Hanczar, “Optimization Model for Relocating Items in A Radio-Shuttle Compact Storage System,” International Business Information Management Association (IBIMA), 9780999855141, pp. 2883-2892, 2021, https://wir.ue.wroc.pl/info/article/WUTee8a5e3bb2c74bef92e37729d83538b8/
6. [6] D. Perera, A. Fernando and U. Mirando, “Warehouse Space Optimization Using a Linear Programming Model,” International Conference on Advanced Research in Computing (ICARC-2021), pp. 145-149, 2021, http://repo.lib.sab.ac.lk:8080/xmlui/handle/123456789/1754.
7. [7] M. J. Kang, P. Mobtahej, A. Sedaghat and M. Hamidi, “A Soft Optimization Model to Solve Space Allocation Problems in Breakbulk Terminals”, Computational Research Progress in Applied Science & Engineering (CRPASE), vol. 7, no. 4, 2021, doi: https://doi.org/10.52547/crpase.7.4.2424.
8. [8] F. Georgise, B. Assefa and H. Bekele, “Design of alternative warehouse layout for efficient space utilization: A case of modjo dry port,” Advances In Industrial Engineering and Management (AIEM), vol. 9, no. 1, pp. 6-13, 2020, doi: http://doi.org/10.7508/aiem.01.2020.06.13.

9. [9] S. Derhami, J. S. Smith and K. R. Gue, “Space-efficient layouts for block stacking warehouses,” IISE Transactions, vol. 51, no. 9, pp. 957-971, 2019, doi: https://doi.org/10.1080/24725854.2018.1539280.
10. [10] T. Y. Kim, S. H. Woo and S. W. Wallace, “A recipe for an omnichannel warehouse storage system: Improving the storage efficiency by integrating block stacking and racking,” Computers & Industrial Engineering, vol. 182, pp. 109320, 2023, doi: https://doi.org/10.1016/j.cie.2023.109320.
11. [11] S. Derhami, J. S. Smith and K. R. Gue, “A simulation-based optimization approach to design optimal layouts for block stacking warehouses,” International Journal of Production Economics, vol. 223, pp. 107525, 2020, doi: https://doi.org/10.1016/j.ijpe.2019.107525.
12. [12] L. Zhou, H. Liu, J. Zhao, F. Wang and J. Yang, “Performance Analysis of Picking Routing Strategies in the Leaf Layout Warehouse,” Mathematics, vol.10, no.17, pp. 3149, 2022, doi: https://doi.org/10.3390/math10173149.
13. [13] K. Wang, T. Hu, Z. Wang, Y. Xiang, J. Shao and X. Xiang, “Performance evaluation of a robotic mobile fulfillment system with multiple picking stations under zoning policy,” Computers & Industrial Engineering, vol.169, pp.108229, 2022, doi: https://doi.org/10.1016/j.cie.2022.108229.
14. [14] S. Ahmed, D. Parvathaneni and I. Shareef, “Reorganization of inventory to improve kitting efficiency and maximize space utilization,” Manufacturing Letters, vol. 35, pp. 1366-1377, 2023, doi: https://doi.org/10.1016/j.mfglet.2023.08.128.
15. [15] M. A. Yerlikaya and F. Arıkan, “A novel framework for production planning and class-based storage location assignment: Multi-criteria classification approach,” Heliyon, vol. 10, no. 18, 2024, doi: https://doi.org/10.1016/j.heliyon.2024.e37351.
16. [16] S. Zhang, X. Zheng, F. Xu, S. Wang, Q. Zhang and Y. Cao, “Optimization Management of Storage Location in Stereoscopic Warehouse by Integrating Genetic Algorithm and Particle Swarm Optimization Algorithm,” Journal of Applied Mathematics, vol. 2024, no. 1, pp. 2790066, 2024, doi: https://doi.org/10.1155/2024/2790066.