3D Box Packing with Heuristics and Metric Analytics
Article Sidebar
Heuristic Algorithms,
Genetic Algorithm Optimization,
Logistics and Space Utilization,
Packing Efficiency and Stability
Main Article Content
Mashal Kasem Alqudah
Dhidhi Pambudi
Mohd Zaki Zakaria
Abstract
Background of Study: The 3D Bin Packing Problem (3D-BPP) is an NP-hard problem crucial for logistics and supply chain optimization, aiming to efficiently pack boxes into containers while maximizing space and maintaining stability. Traditional heuristics like First Fit and Best Fit are fast but lack optimality and adaptability in dynamic environments. Metaheuristic approaches, such as Genetic Algorithms (GA), offer better solutions but with higher computational costs.
Aims and Scope of Paper: This study presents a comparative analysis of First Fit, Best Fit, and a custom Genetic Algorithm as packing strategies for 3D-BPP. It evaluates these methods against multiple performance metrics to understand their trade-offs and proposes future research directions.
Methods: The study uses a dataset of 5,000 cargo records from an Indonesian logistics company, including item dimensions and weights, preprocessed for normalization and filtering. A 3D simulation environment built with PyBullet visualizes the packing process. Performance metrics include space utilization, total packed weight, packing time, access efficiency, stability score, and placement success rate. A Wall-Building heuristic acts as a fallback for unplaced items.
Result: First Fit provides fast, lightweight solutions suitable for real-time applications. Best Fit shows marginally better space utilization but lacks robustness. The Genetic Algorithm outperforms both heuristics in packing quality, accessibility, and load stability, though with significantly higher computation time. No single algorithm dominates across all metrics.
Conclusion: The choice of packing method should align with specific operational constraints: speed, compactness, or quality. A hybrid model combining heuristic initialization with GA refinement is a promising direction for future research to develop more intelligent, context-aware packing systems.
Article Details
Copyright (c) 2025 Mashal Kasem Alqudah, Dhidhi Pambudi, Mohd Zaki Zakaria
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
References
Ahmed, S., Parvathaneni, D., & Shareef, I. (2023). Reorganization of inventory to improve kitting efficiency and maximize space utilization. Manufacturing Letters, 35, 1366–1377. https://doi.org/10.1016/j.mfglet.2023.08.128
Alam, T., Qamar, S., Dixit, A., & Benaida, M. (2021). Genetic algorithm: Reviews, implementations and applications. International Journal of Engineering Pedagogy, 10(6), 57–77. https://doi.org/10.3991/IJEP.V10I6.14567
Albers, S., Khan, A., & Ladewig, L. (2021). Best Fit Bin Packing with Random Order Revisited. Algorithmica, 83(9), 2833–2858. https://doi.org/10.1007/s00453-021-00844-5
Ananno, A. A., & Ribeiro, L. (2024). A Multi-Heuristic Algorithm for Multi-Container 3-D Bin Packing Problem Optimization Using Real World Constraints. IEEE Access, 12(March), 42105–42130. https://doi.org/10.1109/ACCESS.2024.3378063
Calzavara, G., Iori, M., Locatelli, M., Moreira, M. C. O., & Silveira, T. (2021). Mathematical models and heuristic algorithms for pallet building problems with practical constraints. Annals of Operations Research. https://doi.org/10.1007/s10479-021-04349-w
El-hajj, M. (2025). Enhancing Communication Networks in the New Era with Artificial Intelligence : Techniques , Applications , and Future Directions. Network, 5(1), 1–45. https://doi.org/10.3390/network5010001
Erbayrak, S., Özkır, V., & Mahir Yıldırım, U. (2021). Multi-objective 3D bin packing problem with load balance and product family concerns. Computers and Industrial Engineering, 159(May). https://doi.org/10.1016/j.cie.2021.107518
Hashali, S. D., Yang, S., & Xiang, X. (2024). Route Planning Algorithms for Unmanned Surface Vehicles (USVs): A Comprehensive Analysis. Journal of Marine Science and Engineering, 12(3), 2–33. https://doi.org/10.3390/jmse12030382
Jiwapatria, S., Setio, H. D., Sidi, I. D., & Kusumaningrum, P. (2024). Multi-objective optimization of active control system using population guidance and modified reference-point-based NSGA-II. Results in Control and Optimization, 16(July), 100453. https://doi.org/10.1016/j.rico.2024.100453
Kaboudvand, S., & Montreuil, B. (2024). Simulation-Based Assessment of Hyperconnected Megacity Parcel Logistics. Logistics, 8(3), 2–32. https://doi.org/10.3390/logistics8030066
Kaleta, M., & Śliwiński, T. (2025). Neural-Driven Constructive Heuristic for 2D Robotic Bin Packing Problem. Electronics (Switzerland), 14(10). https://doi.org/10.3390/electronics14101956
Lee, M. (2023). Recent Advances in Deep Learning for Protein-Protein Interaction Analysis: A Comprehensive Review. Molecules, 28(13). https://doi.org/10.3390/molecules28135169
Munien, C., & Ezugwu, A. E. (2021). Metaheuristic algorithms for one-dimensional bin-packing problems: A survey of recent advances and applications. Journal of Intelligent Systems, 30(1), 636–663. https://doi.org/10.1515/jisys-2020-0117
Murdivien, S. A., & Um, J. (2023). BoxStacker: Deep Reinforcement Learning for 3D Bin Packing Problem in Virtual Environment of Logistics Systems. Sensors, 23(15), 1–15. https://doi.org/10.3390/s23156928
Nemat, B., Razzaghi, M., Bolton, K., & Rousta, K. (2022). Design affordance of plastic food packaging for consumer sorting behavior. Resources, Conservation and Recycling, 177, 105949. https://doi.org/10.1016/j.resconrec.2021.105949
Popescu, D. A. (2025). An Enhanced Genetic Algorithm for Optimized Educational Assessment Test Generation Through Population Variation. Big Data and Cognitive Computing, 9(4). https://doi.org/10.3390/bdcc9040098
Sawicki, P., Sawicka, H., Karkula, M., & Zajda, K. (2025). Combined Rough Sets and Rule-Based Expert System to Support Environmentally Oriented Sandwich Pallet Loading Problem. Energies, 18(2), 2–48. https://doi.org/10.3390/en18020268
V. Romero, S., Osaba, E., Villar-Rodriguez, E., Oregi, I., & Ban, Y. (2023). Hybrid approach for solving real-world bin packing problem instances using quantum annealers. Scientific Reports, 13(1), 1–11. https://doi.org/10.1038/s41598-023-39013-9
Viu-Roig, M., & Alvarez-Palau, E. J. (2020). The impact of E-Commerce-related last-mile logistics on cities: A systematic literature review. Sustainability (Switzerland), 12(16), 2–19. https://doi.org/10.3390/su12166492
Zhang, R., Wang, J., Liu, C., Su, K., Ishibuchi, H., & Jin, Y. (2025). Synergistic integration of metaheuristics and machine learning: latest advances and emerging trends. Artificial Intelligence Review, 58(9). https://doi.org/10.1007/s10462-025-11266-y
Zhao, H., She, Q., Zhu, C., Yang, Y., & Xu, K. (2021). Online 3D Bin Packing with Constrained Deep Reinforcement Learning. 35th AAAI Conference on Artificial Intelligence, AAAI 2021, 1, 741–749. https://doi.org/10.1609/aaai.v35i1.16155