Abstract
A novel part-to-picker warehouse with robotic mobile racks is spreading recently because of its advantages in picking multi-item e-commerce orders. However, warehouse managers may suffer the situation that the new warehouse and an old one coexist in a distribution center. Due to their respective capacities, any warehouse cannot hold all the stock keeping units (SKUs). How to allocate SKUs to the two warehouses is an important decision. It has a significant influence on the cost of combining the SKUs that have to be picked from two warehouses for customer orders. The problem is formulated by using an innovative virtual-warehouse-based idea, the NP-hardness of the problem is proved, and a hybrid algorithm by alternating between the large neighborhood search and local search is developed. Some effective data-driven strategies are proposed to improve the most time-consuming modules of the algorithm. Extensive case studies are conducted and good performances of the algorithm are shown when it is compared with the MIP solver on small-sized cases, and an adapted tabu search and a simulated annealing algorithm on large-sized real-world cases. The sensitivity analyses on key parameters of the problem are made and related managerial insights are obtained.
Similar content being viewed by others
References
Amaldi, E., & Coniglio, S. (2013). A distance-based point-reassignment heuristic for the k-hyperplane clustering problem. European Journal of Operational Research, 227(1), 22–29.
Brimberg, J., Mladenovic, N., Todosijevic, R., & Urosevic, D. (2019). Solving the capacitated clustering problem with variable neighborhood search. Annals of Operations Research, 272(1), 289–321.
Catalán, A., & Fisher, M. (2012). Assortment allocation to distribution centers to minimize split customer orders. Available at SSRN 2166687.
Chen, Y., & Hao, J. K. (2015). Iterated responsive threshold search for the quadratic multiple knapsack problem. Annals of Operations Research, 226(1), 101–131.
Deng, Y., & Bard, J. F. (2011). A reactive GRASP with path relinking for capacitated clustering. Journal of Heuristics, 17(2), 119–152.
Frazelle, E. H. (1990). Stock location assignment and order batching productivity. Georgia Institute of Technology, Atlanta, Georgia.
Gagliardi, J. P., Renaud, J., & Ruiz, A. (2012). On storage assignment policies for unit-load automated storage and retrieval systems. International Journal of Production Research, 50(3), 879–892.
García-Martínez, C., Glover, F., Rodriguez, F. J., Lozano, M., & Martí, R. (2014). Strategic oscillation for the quadratic multiple knapsack problem. Computational Optimization and Applications, 58(1), 161–185.
Khuri, S., Bäck, T., & Heitkötter, J. (1994). The zero/one multiple knapsack problem and genetic algorithms. In Proceedings of the 1994 ACM symposium on Applied computing (pp. 188–193).
Kim, K. H. (1993). A joint determination of storage locations and space requirements for correlated items in a miniload automated storage-retrieval system. The International Journal of Production Research, 31(11), 2649–2659.
Kulturel, S., Ozdemirel, N. E., Sepil, C., & Bozkurt, Z. (1999). Experimental investigation of shared storage assignment policies in automated storage/retrieval systems. IIE Transactions, 31(8), 739–749.
Laalaoui, Y. (2013). Improved swap heuristic for the multiple knapsack problem. International work-conference on artificial neural networks (pp. 547–555). Springer.
Lai, X., & Hao, J. K. (2016). Iterated variable neighborhood search for the capacitated clustering problem. Engineering Applications of Artificial Intelligence, 56, 102–120.
Li, J., Moghaddam, M., & Nof, S. Y. (2016). Dynamic storage assignment with product affinity and ABC classification—a case study. The International Journal of Advanced Manufacturing Technology, 84(9–12), 2179–2194.
Martello, S., & Toth, P. (1990). Knapsack problems: Algorithms and computer implementations. John Wiley & Sons.
Martínez-Gavara, A., Campos, V., Gallego, M., Laguna, M., & Martí, R. (2015). Tabu search and GRASP for the capacitated clustering problem. Computational Optimization and Applications, 62(2), 589–607.
Meller, R. D., & Pazour, J. A. (2008). A heuristic for SKU assignment and allocation in an a-frame system. In IIE Annual Conference. Proceedings (p. 770). Institute of Industrial and Systems Engineers (IISE).
Morán-Mirabal, L. F., González-Velarde, J. L., Resende, M. G., & Silva, R. M. (2013). Randomized heuristics for handover minimization in mobility networks. Journal of Heuristics, 19(6), 845–880.
Mulvey, J. M., & Beck, M. P. (1984). Solving capacitated clustering problems. European Journal of Operational Research, 18(3), 339–348.
MWPVL International Inc. (2020). A supply chain consultant evaluation of Kiva systems (Amazon robotics). https://mwpvl.com/html/kiva_systems.html
Pisinger, D. (1999). An exact algorithm for large multiple knapsack problems. European Journal of Operational Research, 114(3), 528–541.
Pisinger, D., & Ropke, S. (2010). Large neighborhood search. Handbook of metaheuristics (pp. 399–419). Springer.
Sosland, S. (2020). King Arthur adapts to pandemic with change in business model. https://www.bakingbusiness.com/articles/50800-king-arthur-adapts-to-pandemic-with-change-in-business-model
Tobe, F. (2018). Warehousing, fulfillment and DC transformation trends. https://www.therobotreport.com/warehousing-fulfillment-and-dc-transformation-trends/
Xiao, J., & Zheng, L. (2010). A correlated storage location assignment problem in a single-block-multi-aisles warehouse considering BOM information. International Journal of Production Research, 48(5), 1321–1338.
Yan, B., Yan, C., Long, F., & Tan, X. C. (2018). Multi-objective optimization of electronic product goods location assignment in stereoscopic warehouse based on adaptive genetic algorithm. Journal of Intelligent Manufacturing, 29(6), 1273–1285.
Zhang, Y., Lin, W. H., Huang, M., & Hu, X. (2021). Multi-warehouse package consolidation for split orders in online retailing. European Journal of Operational Research, 289(3), 1040–1055.
Zhou, Q., Benlic, U., Wu, Q., & Hao, J. K. (2019). Heuristic search to the capacitated clustering problem. European Journal of Operational Research, 273(2), 464–487.
Acknowledgements
The authors would like to thank the editors and anonymous reviewers for their constructive comments and invaluable contributions to enhance the presentation of this paper. This research is supported by the National Natural Science Foundation of China (No. 71971036, 71931009, 71871035), the Major Program of Key Disciplines in Dalian (No. 2019J11CY002), the Key R&D project of Liaoning Provincial Department of Science and Technology (No. 2020JH2/10100042), and the MOE Layout Foundation of Humanities and Social Sciences (No. 19YJA630084).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Wang, Z., Xu, W., Hu, X. et al. Inventory allocation to robotic mobile-rack and picker-to-part warehouses at minimum order-splitting and replenishment costs. Ann Oper Res 316, 467–491 (2022). https://doi.org/10.1007/s10479-021-04190-1
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-021-04190-1