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International Conference on Optimization and Learning

OLA 2021: Optimization and Learning pp 216–226Cite as

Formulation of a Layout-Agnostic Order Batching Problem

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1443))

Abstract

To date, research on warehouse order-batching has been limited by reliance on rigid assumptions regarding rack layouts. Although efficient optimization algorithms have been provided for conventional warehouse layouts with Manhattan style blocks of racks, they are limited in that they fail to generalize to unconventional layouts. This paper builds on a generalized procedure for digitization of warehouses where racks and other obstacles are defined using two-dimensional polygons. We extend on this digitization procedure to introduce a layout-agnostic minisum formulation for the Order Batching Problem (OBP), together with a sub-problem for the OBP for a single vehicle, the single batch OBP. An algorithm which optimizes the single batch OBP iteratively until an approximate solution to the OBP can be obtained, is discussed. The formulations will serve as the fundament for further work on layout-agnostic OBP optimization and generation of benchmark datasets. Experimental results for the digitization process involving various settings are presented.

This work was partially supported by the Wallenberg AI, Autonomous Systems and Software Program (WASP) funded by the Knut and Alice Wallenberg Foundation.

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References

  1. de Koster, R., 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). https://doi.org/10.1016/j.ejor.2006.07.009

    Article  MATH  Google Scholar 

  2. Jiang, X., Zhou, Y., Zhang, Y., Sun, L., Hu, X.: Order batching and sequencing problem under the pick-and-sort strategy in online supermarkets. Proc. Comput. Sci. 126, 1985–1993 (2018). https://doi.org/10.1016/j.procs.2018.07.254

    Article  Google Scholar 

  3. Sharp, G.P., Gibson, D.R.: Order batching procedures. Eur. J. Oper. Res. 58, 57–67 (1992)

    Article  Google Scholar 

  4. Gademann, N., van de Velde, S.: Order batching to minimize total travel time in a parallel-aisle warehouse. IIE Trans. 37(1), 63–75 (2005). https://doi.org/10.1080/07408170590516917

    Article  Google Scholar 

  5. Valle, C.A., Beasley, B.A.: Order batching using an approximation for the distance travelled by pickers. Eur. J. Oper. Res. 284(2), 460–484 (2019)

    Article  MathSciNet  Google Scholar 

  6. Ratliff, H., Rosenthal, A.: Order-picking in a rectangular warehouse: a solvable case of the traveling salesman problem. Oper. Res. 31, 507–521 (1983)

    Article  Google Scholar 

  7. Cordeau, J.-F., Laporte, G., Savelsbergh, M., Vigo, D.: Vehicle routing. In: Transportation, Handbooks in Operations Research and Management Science, vol. 14, pp. 195–224 (2007)

    Google Scholar 

  8. Bozer, Y.A., Kile, J.W.: Order batching in walk-and-pick order picking systems. Int. J. Prod. Res. 46(7), 1887–1909 (2008). https://doi.org/10.1080/00207540600920850

    Article  MATH  Google Scholar 

  9. Briant, O., Cambazard, H., Cattaruzza, D., Catusse, N., Ladier, A.-L., Ogier, M.: An efficient and general approach for the joint order batching and picker routing problem. Eur. J. Oper. Res. 285(2), 497–512 (2020). https://doi.org/10.1016/j.ejor.2020.01.059

    Article  MathSciNet  MATH  Google Scholar 

  10. Kulak, O., Sahin, Y., Taner, M.E.: Joint order batching and picker routing in single and multiple-cross-aisle warehouses using cluster-based tabu search algorithms. Flex. Serv. Manuf. J. 24(1), 52–80 (2012). https://doi.org/10.1007/s10696-011-9101-8

    Article  Google Scholar 

  11. Masae, M., Glock, C.H., Grosse, E.H.: Order picker routing in warehouses: a systematic literature review. Int. J. Prod. Econ. 224, 107564 (2020). https://doi.org/10.1016/j.ijpe.2019.107564

    Article  Google Scholar 

  12. Chang, P.-Y., Damodaran, P., Melouk, S.: Minimizing makespan on parallel batch processing machines. Int. J. Prod. Res. 42(19), 4211–4220 (2004). https://doi.org/10.1080/00207540410001711863

    Article  Google Scholar 

  13. van Rensburg, L.J.: Artificial intelligence for warehouse picking optimization - an NP-hard problem. M.Sc., Uppsala University (2019)

    Google Scholar 

  14. Valle, C.A., 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). https://doi.org/10.1016/j.ejor.2017.03.069

    Article  MathSciNet  MATH  Google Scholar 

  15. Li, J., Huang, R., Dai, J.B.: Joint optimisation of order batching and picker routing in the online retailer’s warehouse in China. Int. J. Prod. Res. 55(2), 447–461 (2017). https://doi.org/10.1080/00207543.2016.1187313

    Article  Google Scholar 

  16. Psaraftis, H., Wen, M., Kontovas, C.: Dynamic vehicle routing problems: three decades and counting. Networks 67, 3–31 (2015). https://doi.org/10.1002/net.21628

    Article  MathSciNet  Google Scholar 

  17. Bué, M., Cattaruzza, D., Ogier, M., Semet, F.: A two-phase approach for an integrated order batching and picker routing problem. In: Dell’Amico, M., Gaudioso, M., Stecca, G. (eds.) A View of Operations Research Applications in Italy. ASS, vol. 2, pp. 3–18. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-25842-9_1

    Chapter  Google Scholar 

  18. Bortolini, M., Faccio, M., Ferrari, E., Gamberi, M., Pilati, F.: Design of diagonal cross-aisle warehouses with class-based storage assignment strategy. Int. J. Adv. Manuf. Technol. 100(9), 2521–2536 (2019). https://doi.org/10.1007/s00170-018-2833-9

    Article  Google Scholar 

  19. Fumi, A., Scarabotti, L., Schiraldi, M.: The effect of slot-code optimization in warehouse order picking. Int. J. Bus. Manag. 5, 5–20 (2013). https://doi.org/10.5772/56803

    Article  Google Scholar 

  20. Gue, K.R., Meller, R.D.: Aisle configurations for unit-load warehouses. IIE Trans. 41(3), 171–182 (2009). https://doi.org/10.1080/07408170802112726

    Article  Google Scholar 

  21. Henn, S.: Algorithms for on-line order batching in an order picking warehouse. Comput. Oper. Res. 39(11), 2549–2563 (2012). https://doi.org/10.1016/j.cor.2011.12.019

    Article  MATH  Google Scholar 

  22. Chen, M.-C., Wu, H.-P.: An association-based clustering approach to order batching considering customer demand patterns. Omega 33(4), 333–343 (2005). https://doi.org/10.1016/j.omega.2004.05.003

    Article  MathSciNet  Google Scholar 

  23. 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). https://doi.org/10.1016/j.ejor.2012.05.049

    Article  MATH  Google Scholar 

  24. Cergibozan, Ç., Tasan, A.: Genetic algorithm based approaches to solve the order batching problem and a case study in a distribution center. J. Intell. Manuf. 1–13 (2020). https://doi.org/10.1007/s10845-020-01653-3

  25. Braekers, K., Ramaekers, K., Nieuwenhuyse, I.V.: The vehicle routing problem: state of the art classification and review. Comput. Ind. Eng. 99, 300–313 (2016). https://doi.org/10.1016/j.cie.2015.12.007

    Article  Google Scholar 

  26. Pillac, V., Gendreau, M., Guéret, C., Medaglia, A.L.: A review of dynamic vehicle routing problems. Eur. J. Oper. Res. 225(1), 1–11 (2013). https://doi.org/10.1016/j.ejor.2012.08.015

    Article  MathSciNet  MATH  Google Scholar 

  27. Mansouri, M., Lagriffoul, F., Pecora, F.: Multi vehicle routing with nonholonomic constraints and dense dynamic obstacles (2017). https://doi.org/10.1109/IROS.2017.8206195

  28. Bochtis, D.D., Sørensen, C.G.: The vehicle routing problem in field logistics part I. Biosyst. Eng. 104(4), 447–457 (2009). https://doi.org/10.1016/j.biosystemseng.2009.09.003

    Article  Google Scholar 

  29. Santis, R.D., Montanari, R., Vignali, G., Bottani, E.: An adapted ant colony optimization algorithm for the minimization of the travel distance of pickers in manual warehouses. Eur. J. Oper. Res. 267(1), 120–137 (2018). https://doi.org/10.1016/j.ejor.2017.11.017

    Article  MathSciNet  MATH  Google Scholar 

  30. Furini, F., Ljubić, I., Sinnl, M.: An effective dynamic programming algorithm for the minimum-cost maximal knapsack packing problem. Eur. J. Oper. Res. 262(2), 438–448 (2017). https://doi.org/10.1016/j.ejor.2017.03.061

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

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

    Johan Oxenstierna, Jacek Malec & Volker Krueger

  2. Kairos Logic AB, Lund, Sweden

    Johan Oxenstierna

  3. Thompson Institute, University of the Sunshine Coast, Sunshine Coast, QLD, Australia

    Louis Janse van Rensburg

Authors
  1. Johan Oxenstierna
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  2. Louis Janse van Rensburg
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  3. Jacek Malec
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  4. Volker Krueger
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Corresponding author

Correspondence to Johan Oxenstierna .

Editor information

Editors and Affiliations

  1. University of Cádiz, Cádiz, Spain

    Bernabé Dorronsoro

  2. University of Technology of Troyes, Troyes, France

    Lionel Amodeo

  3. University of Catania, Catania, Italy

    Mario Pavone

  4. University of Cádiz, Cádiz, Spain

    Patricia Ruiz

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Oxenstierna, J., van Rensburg, L.J., Malec, J., Krueger, V. (2021). Formulation of a Layout-Agnostic Order Batching Problem. In: Dorronsoro, B., Amodeo, L., Pavone, M., Ruiz, P. (eds) Optimization and Learning. OLA 2021. Communications in Computer and Information Science, vol 1443. Springer, Cham. https://doi.org/10.1007/978-3-030-85672-4_16

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  • DOI: https://doi.org/10.1007/978-3-030-85672-4_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-85671-7

  • Online ISBN: 978-3-030-85672-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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