Skip to main content
SpringerLink
Log in

Optimization of the Storage Location Assignment Problem Using Nested Annealing

  • Conference paper
  • First Online:
Operations Research and Enterprise Systems (ICORES 2022, ICORES 2023)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1985))

  • 98 Accesses

Abstract

The Storage Location Assignment Problem (SLAP) has a significant impact on the efficiency of warehouse operations. We propose a multi-phase optimizer for the SLAP, where the quality of an assignment is based on distance estimates of future-forecasted order-picking. Candidate assignments are first sampled using a Markov Chain accept/reject method. Order-picking Traveling Salesman Problems (TSPs) are then modified according to the assignments and solved. The model is graph-based and generalizes to any obstacle layout in two dimensions. We investigate whether optimization speed-ups are possible using methods such as cost approximation, rejection of samples with low approximate cost and restarts from local minima. Results demonstrate that these methods improve performance, with total travel-cost reductions of up to 30% within 8 h of CPU-time. We share a public repository with SLAP instances and corresponding benchmark results on the generalizable TSPLIB format.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 59.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 79.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    https://math.uwaterloo.ca/tsp/concorde/downloads/downloads.htm, collected 27-05-2022.

  2. 2.

    https://developers.google.com/optimization/routing/tsp, collected 12-06-2022.

  3. 3.

    https://github.com/johanoxenstierna/OBP/instances, collected 19-10-2022.

  4. 4.

    https://github.com/johanoxenstierna/L40_266, collected 14-11-2022.

References

  1. Applegate, D., Cook, W., Dash, S., Rohe, A.: Solution of a min-max vehicle routing problem. INFORMS J. Comput. 14, 132–143 (2002)

    Article  MathSciNet  Google Scholar 

  2. Azadeh, K., De Koster, R., Roy, D.: Robotized and automated warehouse systems: review and recent developments. Transp. Sci. 53, 917–945 (2019)

    Article  Google Scholar 

  3. Boysen, N., Stephan, K.: The deterministic product location problem under a pick-by-order policy. Discret. Appl. Math. 161(18), 2862–2875 (2013)

    Article  MathSciNet  Google Scholar 

  4. Cardona, L.F., Rivera, L., Martínez, H.J.: Analytical study of the fishbone warehouse layout. Int. J. Log. Res. Appl. 15(6), 365–388 (2012)

    Article  Google Scholar 

  5. Charris, E., et al.: The storage location assignment problem: a literature review. Int. J. Ind. Eng. Comput. 10, 199–224 (2018)

    Google Scholar 

  6. Christen, J.A., Fox, C.: Markov Chain Monte Carlo using an approximation. J. Comput. Graph. Stat. 14(4), 795–810 (2005). https://www.jstor.org/stable/27594150

  7. Ene, S., Öztürk, N.: Storage location assignment and order picking optimization in the automotive industry. Int. J. Adv. Manuf. Technol. 60, 1–11 (2011). https://doi.org/10.1007/s00170-011-3593-y

    Article  Google Scholar 

  8. Fontana, M.E., Nepomuceno, V.S.: Multi-criteria approach for products classification and their storage location assignment. Int. J. Adv. Manuf. Technol. 88(9), 3205–3216 (2017)

    Article  Google Scholar 

  9. Garfinkel, M.: Minimizing multi-zone orders in the correlated storage assingment problem. PhD Thesis, School of Industrial and Systems Engineering, Georgia Institute of Technology (2005)

    Google Scholar 

  10. Gidas, B.: Nonstationary Markov chains and convergence of the annealing algorithm. J. Stat. Phys. 39(1), 73–131 (1985). https://doi.org/10.1007/BF01007975

    Article  MathSciNet  Google Scholar 

  11. Hahsler, M., Kurt, H.: TSP - infrastructure for the traveling salesperson problem. J. Stat. Softw. 2, 1–21 (2007)

    Google Scholar 

  12. Henn, S., Wäscher, G.: Tabu search heuristics for the order batching problem in manual order picking systems. Eur. J. Oper. Res. 222(3), 484–494 (2012)

    Article  Google Scholar 

  13. Kallina, C., Lynn, J.: Application of the cube-per-order index rule for stock location in a distribution warehouse. Interfaces 7(1), 37–46 (1976). https://www.jstor.org/stable/25059400

  14. Kofler, M., Beham, A., Wagner, S., Affenzeller, M.: Affinity based slotting in warehouses with dynamic order patterns. In: Klempous, R., Nikodem, J., Jacak, W., Chaczko, Z. (eds.) Advanced Methods and Applications in Computational Intelligence. Topics in Intelligent Engineering and Informatics, vol. 6, pp. 123–143. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  15. Koster, R.D., Le-Duc, T., Roodbergen, K.J.: Design and control of warehouse order picking: a literature review. Eur. J. Oper. Res. 182(2), 481–501 (2007)

    Article  Google Scholar 

  16. Kruk, S.: Practical Python AI Projects: Mathematical Models of Optimization Problems with Google OR-Tools. Apress, New York (2018)

    Book  Google Scholar 

  17. Kübler, P., Glock, C., Bauernhansl, T.: A new iterative method for solving the joint dynamic storage location assignment, order batching and picker routing problem in manual picker-to-parts warehouses. Comput. Ind. Eng. 147, 106645 (2020)

    Article  Google Scholar 

  18. Larco, J.A., Koster, R.D., Roodbergen, K.J., Dul, J.: Managing warehouse efficiency and worker discomfort through enhanced storage assignment decisions. Int. J. Prod. Res. 55(21), 6407–6422 (2017). https://doi.org/10.1080/00207543.2016.1165880

    Article  Google Scholar 

  19. Lee, I.G., Chung, S.H., Yoon, S.W.: Two-stage storage assignment to minimize travel time and congestion for warehouse order picking operations. Comput. Ind. Eng. 139, 106129 (2020) https://doi.org/10.1016/j.cie.2019.106129, https://www.sciencedirect.com/science/article/pii/S0360835219305984

  20. Li, J., Moghaddam, M., Nof, S.Y.: Dynamic storage assignment with product affinity and ABC classification-a case study. Int. J. Adv. Manuf. Technol. 84(9), 2179–2194 (2016). https://doi.org/10.1007/s00170-015-7806-7

    Article  Google Scholar 

  21. Liu, C.M.: Clustering techniques for stock location and order-picking in a distribution center. Comput. Oper. Res. 26(10), 989–1002 (1999). https://doi.org/10.1016/S0305-0548(99)00026-X, https://www.sciencedirect.com/science/article/pii/S030505489900026X

  22. Mackay, D.J.C.: Introduction to Monte Carlo methods. In: Jordan, M.I. (ed.) Learning in Graphical Models. NATO ASI Series, vol. 89, pp. 175–204. Springer, Dordrecht (1998). https://doi.org/10.1007/978-94-011-5014-9_7

    Chapter  Google Scholar 

  23. Mantel, R., et al.: Order oriented slotting: a new assignment strategy for warehouses. Eur. J. Ind. Eng. 1, 301–316 (2007)

    Article  Google Scholar 

  24. Maruyama, K., Yamazaki, T.: Improved efficiency of warehouse picking by co-optimization of order batching and storage location assignment. J. Adv. Mech. Des. Syst. Manuf. 16(5), JAMDSM0052-JAMDSM0052 (2022). https://doi.org/10.1299/jamdsm.2022jamdsm0052

  25. Ming-Huang Chiang, D., Lin, C.P., Chen, M.C.: Data mining based storage assignment heuristics for travel distance reduction. Expert Syst. 31(1), 81–90 (2014)

    Article  Google Scholar 

  26. Oxenstierna, J., Krueger, V., Malec, J.: New benchmarks and optimization model for the storage location assignment problem. In: 3rd International Conference on Innovative Intelligent Industrial Production and Logistics, IN4PL 2022. SciTePress (2022)

    Google Scholar 

  27. Oxenstierna, J., Malec, J., Krueger, V.: Analysis of computational efficiency in iterative order batching optimization. In: Proceedings of the 11th International Conference on Operations Research and Enterprise Systems - ICORES, pp. 345–353. SciTePress (2022). https://doi.org/10.5220/0010837700003117

  28. Oxenstierna, J., Rensburg, L.V., Stuckey, P., Krueger, V.: Storage assignment using nested annealing and hamming distances. In: Proceedings of the 12th International Conference on Operations Research and Enterprise Systems - ICORES, pp. 94–105. SciTePress (2023). https://doi.org/10.5220/0011785100003396. backup Publisher: INSTICC ISSN: 2184-4372

  29. Rajasekaran, S., Reif, J.H.: Nested annealing: a provable improvement to simulated annealing. Theoret. Comput. Sci. 99(1), 157–176 (1992)

    Article  MathSciNet  Google Scholar 

  30. Rathod, A.B., Gulhane, S.M., Padalwar, S.R.: A comparative study on distance measuring approches for permutation representations. In: 2016 IEEE International Conference on Advances in Electronics, Communication and Computer Technology (ICAECCT), pp. 251–255. IEEE (2016)

    Google Scholar 

  31. Janse van Rensburg, L.J.V.: Artificial intelligence for warehouse picking optimization - an NP-hard problem. Master’s thesis, Uppsala University (2019)

    Google Scholar 

  32. Roodbergen, K.J., Koster, R.: Routing methods for warehouses with multiple cross aisles. Int. J. Prod. Res. 39(9), 1865–1883 (2001)

    Article  Google Scholar 

  33. Schapire, R.: Using Output Codes to Boost Multiclass Learning Problems (2001)

    Google Scholar 

  34. Tak, H., Meng, X.L., Dyk, D.A.V.: A repelling-attracting metropolis algorithm for multimodality. J. Comput. Graph. Stat. 27(3), 479–490 (2018). https://doi.org/10.1080/10618600.2017.1415911

    Article  MathSciNet  Google Scholar 

  35. Trindade, M.A.M., Sousa, P., Moreira, M.: Ramping up a heuristic procedure for storage location assignment problem with precedence constraints. Flex. Serv. Manuf. J. 34, 646–669 (2022). https://doi.org/10.1007/s10696-021-09423-w

    Article  Google Scholar 

  36. Valle, C., Beasley, J.E., da Cunha, A.S.: Optimally solving the joint order batching and picker routing problem. Eur. J. Oper. Res. 262(3), 817–834 (2017)

    Article  MathSciNet  Google Scholar 

  37. Wales, D.J., Doye, J.P.K.: Global optimization by basin-hopping and the lowest energy structures of Lennard-jones clusters containing up to 110 atoms. J. Phys. Chem. A 101, 5111–5116 (1997)

    Article  Google Scholar 

  38. Wu, J., Qin, T., Chen, J., Si, H., Lin, K.: Slotting optimization algorithm of the stereo warehouse. In: Proceedings of the 2012 2nd International Conference on Computer and Information Application (ICCIA 2012), pp. 128–132. Atlantis Press (2014). https://doi.org/10.2991/iccia.2012.31

  39. Wutthisirisart, P., Noble, J.S., Chang, C.A.: A two-phased heuristic for relation-based item location. Comput. Ind. Eng. 82, 94–102 (2015) https://doi.org/10.1016/j.cie.2015.01.020, https://www.sciencedirect.com/science/article/pii/S036083521500039X

  40. Xiang, X., Liu, C., Miao, L.: Storage assignment and order batching problem in Kiva mobile fulfilment system. Eng. Optim. 50(11), 1941–1962 (2018). https://doi.org/10.1080/0305215X.2017.1419346

    Article  MathSciNet  Google Scholar 

  41. Yu, M., Koster, R.B.M.D.: The impact of order batching and picking area zoning on order picking system performance. Eur. J. Oper. Res. 198(2), 480–490 (2009)

    Article  Google Scholar 

  42. Yu, V.F., Winarno, Maulidin, A., Redi, A.A.N.P., Lin, S.W., Yang, C.L.: Simulated Annealing with Restart Strategy for the Path Cover Problem with Time Windows. Mathematics 9(14) (2021). https://doi.org/10.3390/math9141625, https://www.mdpi.com/2227-7390/9/14/1625

  43. Zhang, R.Q., et al.: New model of the storage location assignment problem considering demand correlation pattern. Comput. Ind. Eng. 129, 210–219 (2019). https://doi.org/10.1016/j.cie.2019.01.027, https://www.sciencedirect.com/science/article/pii/S0360835219300294

  44. Žulj, I., Glock, C.H., Grosse, E.H., Schneider, M.: Picker routing and storage-assignment strategies for precedence-constrained order picking. Comput. Ind. Eng. 123, 338–347 (2018). https://doi.org/10.1016/j.cie.2018.06.015, https://www.sciencedirect.com/science/article/pii/S0360835218302869

Download references

Acknowledgements

This work was partially supported by the Wallenberg AI, Autonomous Systems and Software Program (WASP) funded by the Knut and Alice Wallenberg Foundation. We also convey thanks to Kairos Logic AB for software.

Author information

Authors and Affiliations

  1. Department of Computer Science, Lund University, Lund, Sweden

    Johan Oxenstierna & Volker Krueger

  2. Faculty of Information Technology, Monash University, Melbourne, Australia

    Peter J. Stuckey

  3. Flux Robotics, Caltowie, Australia

    Louis Janse van Rensburg

  4. Kairos Logic AB, Lund, Sweden

    Johan Oxenstierna

Authors
  1. Johan Oxenstierna
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Louis Janse van Rensburg
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Peter J. Stuckey
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Volker Krueger
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Johan Oxenstierna .

Editor information

Editors and Affiliations

  1. Cardiff University, Cardiff, UK

    Federico Liberatore

  2. Department of National Defence, Ottawa, ON, Canada

    Slawo Wesolkowski

  3. RMIT University, Melbourne, VIC, Australia

    Marc Demange

  4. GH Parlier Consulting, Catonsville, MD, USA

    Greg H. Parlier

Appendix

Appendix

Examples of pick-rounds before and after 100 iterations of SLAP optimization (left and right respectively). The SLAP can be challenging even when there are only six pick-rounds in the picking-log. While it is relatively easy to spot suitable swaps of locations for pick-rounds involving few products, it is more difficult when pick-rounds are long. One of the products is picked in all of the pick-rounds, and as that product is moved, it affects total distance in an unforseeable manner.

Fig. 8.
figure 8

Pictures of optimally solved pick-rounds (TSP’s) before (left) and after SLAP optimization (right). The product which is picked in all pick-rounds is the lower-rightmost one in the upper two pictures (before and after it was moved).

Full size image
Table 1. Aggregate averages of results from 5279885 generated samples for optimization runs on the 266 publicly shared instances. The results are aggregated based on ranges of number of products (the first column).
Full size table
Table 2. Aggregate averages of results on dataset 3, where the two cost approximators are compared. The CPU-times are here for predictions of single TSPs.
Full size table

Rights and permissions

Reprints and permissions

Copyright information

© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Oxenstierna, J., van Rensburg, L.J., Stuckey, P.J., Krueger, V. (2024). Optimization of the Storage Location Assignment Problem Using Nested Annealing. In: Liberatore, F., Wesolkowski, S., Demange, M., Parlier, G.H. (eds) Operations Research and Enterprise Systems. ICORES ICORES 2022 2023. Communications in Computer and Information Science, vol 1985. Springer, Cham. https://doi.org/10.1007/978-3-031-49662-2_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-49662-2_12

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-49661-5

  • Online ISBN: 978-3-031-49662-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation