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GRASP with Variable Neighborhood Descent for the online order batching problem

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Abstract

The Online Order Batching Problem (OOBP) is a variant of the well-known Order Batching Problem (OBP). As in the OBP, the goal of this problem is to collect all the orders that arrive at a warehouse, following an order batching picking policy, while minimizing a particular objective function. Therefore, orders are grouped in batches, of a maximum predefined capacity, before being collected. Each batch is assigned to a single picker, who collects all the orders within the batch in a single route. Unlike the OBP, this variant presents the peculiarity that the orders considered in each instance are not fully available in the warehouse at the beginning of the day, but they can arrive at the system once the picking process has already begun. Then, batches have to be dynamically updated and, as a consequence, routes must too. In this paper, the maximum turnover time (maximum time that an order remains in the warehouse) and the maximum completion time (total collecting time of all orders received in the warehouse) are minimized. To that aim, we propose an algorithm based in the combination of a Greedy Randomized Adaptive Search Procedure and a Variable Neighborhood Descent. The best variant of our method has been tested over a large set of instances and it has been favorably compared with the best previous approach in the state of the art.

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References

  1. Albareda-Sambola, M., Alonso-Ayuso, A., Molina, E., De Blas, C.S.: Variable neighborhood search for order batching in a warehouse. Asia-Pac. J. Oper. Res. 26(5), 655–683 (2009)

    MATH  Google Scholar 

  2. Chen, F., Wei, Y., Wang, H.: A heuristic based batching and assigning method for online customer orders. Flex. Serv. Manuf. J. 30(4), 640–685 (2018)

    Google Scholar 

  3. Coyle, J.J., Bardi, E.J., Langley, C.J., et al.: The Management of Business Logistics, vol. 6. West Publishing Company Minneapolis, St Paul (1996)

    Google Scholar 

  4. De Koster, M.B.M., Van der Poort, E.S., Wolters, M.: Efficient orderbatching methods in warehouses. Int. J. Prod. Res. 37(7), 1479–1504 (1999)

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  6. De Koster, R., Jan Roodbergen, K., van Voorden, R.: Reduction of walking time in the distribution center of de bijenkorf. In: New trends in distribution logistics, pp. 215–234. Springer, Berlin (1999)

  7. Drury, J., Warehouse Operations Special Interest Group, Order Picking Working Party, Turnbull, B., Institute of Logistics (Great Britain): Towards More Efficient Order Picking. IMM monograph. Institute of Materials Management. ISBN 9781870214063 (1988). https://books.google.es/books?id=LbTKAAAACAAJ

  8. Duarte, A., Pantrigo, J.J., Pardo, E.G., Mladenovic, N.: Multi-objective variable neighborhood search: an application to combinatorial optimization problems. J. Global Optim. 63(3), 515–536 (2015)

    MathSciNet  MATH  Google Scholar 

  9. Duarte, A., Pantrigo, J.J., Pardo, E.G., Sánchez-Oro, J.: Parallel variable neighbourhood search strategies for the cutwidth minimization problem. IMA J. Manag. Math. 27(1), 55–73 (2013)

    MathSciNet  MATH  Google Scholar 

  10. Feo, T.A., Resende, M.: Greedy randomized adaptive search procedures. J. Global Optim. 6, 109–133 (1995)

    MathSciNet  MATH  Google Scholar 

  11. Gademann, A.J.R.M., Van Den Berg, J.P., Van Der Hoff, H.H.: An order batching algorithm for wave picking in a parallel-aisle warehouse. IIE Trans. 33(5), 385–398 (2001)

    Google Scholar 

  12. Gademann, N., Velde, S.: Order batching to minimize total travel time in a parallel-aisle warehouse. IIE Trans. 37(1), 63–75 (2005)

    Google Scholar 

  13. Gibson, D.R., Sharp, G.P.: Order batching procedures. Eur. J. Oper. Res. 58(1), 57–67 (1992)

    Google Scholar 

  14. Gu, J., Goetschalckx, M., McGinnis, L.F.: Research on warehouse design and performance evaluation: a comprehensive review. Eur. J. Oper. Res. 203(3), 539–549 (2010)

    MATH  Google Scholar 

  15. Hall, R.W.: Distance approximations for routing manual pickers in a warehouse. IIE Trans. 25(4), 76–87 (1993)

    Google Scholar 

  16. Hansen, P., Mladenović, N.: Variable neighborhood search: principles and applications. Eur. J. Oper. Res. 130(3), 449–467 (2001)

    MathSciNet  MATH  Google Scholar 

  17. Hansen, P., Mladenović, N., Moreno-Pérez, J.A.: Variable neighbourhood search: methods and applications. Ann. Oper. Res. 175(1), 367–407 (2010)

    MathSciNet  MATH  Google Scholar 

  18. Henn, S.: Algorithms for on-line order batching in an order picking warehouse. Comput. Oper. Res. 39(11), 2549–2563 (2012)

    MATH  Google Scholar 

  19. Henn, S., Koch, S., Doerner, K., Strauss, C., Wäscher, G.: Metaheuristics for the order batching problem in manual order picking systems. BuR Bus. Res. J. 3(1), 82–105 (2010)

    Google Scholar 

  20. Henn, S., Schmid, V.: Metaheuristics for order batching and sequencing in manual order picking systems. Comput. Ind. Eng. 66(2), 338–351 (2013)

    Google Scholar 

  21. 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)

    MATH  Google Scholar 

  22. Ho, Y.-C., Tseng, Y.-Y.: A study on order-batching methods of order-picking in a distribution centre with two cross-aisles. Int. J. Prod. Res. 44(17), 3391–3417 (2006)

    MATH  Google Scholar 

  23. Hsu, C.-M., Chen, K.-Y., Chen, M.-C.: Batching orders in warehouses by minimizing travel distance with genetic algorithms. Comput. Ind. 56(2), 169–178 (2005)

    MathSciNet  Google Scholar 

  24. Koch, S., Wäscher, G.: A grouping genetic algorithm for the Order Batching Problem in distribution warehouses. J. Bus. Econ. 86(1–2), 131–153 (2016)

    Google Scholar 

  25. Menéndez, B., Bustillo, M., Pardo, E.G., Duarte, A.: General variable neighborhood search for the order batching and sequencing problem. Eur. J. Oper. Res. 263(1), 82–93 (2017)

    MathSciNet  MATH  Google Scholar 

  26. Menéndez, B., Pardo, E.G., Alonso-Ayuso, A., Molina, E., Duarte, A.: Variable neighborhood search strategies for the order batching problem. Comput. Oper. Res. 78, 500–512 (2017)

    MathSciNet  MATH  Google Scholar 

  27. Menéndez, B., Pardo, E.G., Duarte, A., Alonso-Ayuso, A., Molina, E.: General variable neighborhood search applied to the picking process in a warehouse. Electron. Notes Discrete Math. 47, 77–84 (2015)

    MathSciNet  MATH  Google Scholar 

  28. Menéndez, B., Pardo, E.G., Sánchez-Oro, J., Duarte, A.: Parallel variable neighborhood search for the min–max order batching problem. Int. Trans. Oper. Res, 24(3), 635–662 (2017)

    MathSciNet  MATH  Google Scholar 

  29. Mladenović, N., Hansen, P.: Variable neighborhood search. Comput. Oper. Res. 24(11), 1097–1100 (1997)

    MathSciNet  MATH  Google Scholar 

  30. Öncan, T.: MILP formulations and an iterated local search algorithm with Tabu thresholding for the order batching problem. J. Oper. Res. 243, 142–155 (2015)

    MathSciNet  MATH  Google Scholar 

  31. Öncan, T., Cağırıcı, M.: MILP formulations for the order batching problem in low-level picker-to-part warehouse systems. IFAC Proc. Vol. 46(9), 471–476 (2013)

    Google Scholar 

  32. Pan, C.-H., Liu, S.-Y.: A comparative study of order batching algorithms. Omega 23(6), 691–700 (1995)

    Google Scholar 

  33. Pardo, E.G., Mladenović, N., Pantrigo, J.J., Duarte, A.: Variable formulation search for the cutwidth minimization problem. Appl. Soft Comput. 13(5), 2242–2252 (2013)

    MATH  Google Scholar 

  34. Pérez-Rodríguez, R., Hernández-Aguirre, A., Jöns, S.: A continuous estimation of distribution algorithm for the online order-batching problem. Int. J. Adv. Manuf. Technol. 79(1), 569–588 (2015)

    Google Scholar 

  35. Petersen, C.G.: An evaluation of order picking routeing policies. Int. J. Oper. Prod. Manag. 17(11), 1098–1111 (1997)

    Google Scholar 

  36. Petersen, C.G.: Routeing and storage policy interaction in order picking operations. Decis. Sci. Inst. Proc. 31(3), 1614–1616 (1995)

    Google Scholar 

  37. Ratliff, H.D., Rosenthal, A.S.: Order-picking in a rectangular warehouse: a solvable case of the traveling salesman problem. Oper. Res. 31(3), 507–521 (1983)

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  39. Roodbergen, K.J., Petersen, C.G.: How to improve order picking efficiency with routing and storage policies. In: G.R. Forger et al. (eds.), Progress in Material Handling Practice. Material Handling Institute, Charlotte, North Carolina, pp. 107–124 (1999)

  40. Rosenwein, M.B.: A comparison of heuristics for the problem of batching orders for warehouse selection. Int. J. Prod. Res. 34(3), 657–664 (1996)

    MATH  Google Scholar 

  41. Rubrico, J.I.U., Higashi, T., Tamura, H., Ota, J.: Online rescheduling of multiple picking agents for warehouse management. Robot. Comput. Integr. Manuf. 27(1), 62–71 (2011)

    Google Scholar 

  42. Scholz, A., Schubert, D., Wäscher, G.: Order picking with multiple pickers and due dates—simultaneous solution of order batching, batch assignment and sequencing, and picker routing problems. Eur. J. Oper. Res. 263(2), 461–478 (2017)

    MathSciNet  MATH  Google Scholar 

  43. Scholz, A., Wäscher, G.: Order Batching and Picker Routing in manual order picking systems: the benefits of integrated routing. CEJOR 25(2), 491–520 (2017)

    MathSciNet  MATH  Google Scholar 

  44. Tang, L.C., Chew, E.P.: Order picking systems: batching and storage assignment strategies. Comput. Ind. Eng. 33(3), 817–820 (1997). Selected Papers from the Proceedings of 1996 ICC&IC

    Google Scholar 

  45. Van Nieuwenhuyse, I., Colpaert, J.: Order batching in multi-server pick-and-sort warehouses. DTEW-KBI 0731, 1–29 (2007)

    Google Scholar 

  46. Zhang, J., Wang, X., Chan, F.T.S., Ruan, J.: On-line order batching and sequencing problem with multiple pickers: a hybrid rule-based algorithm. Appl. Math. Model. 45, 271–284 (2017)

    MathSciNet  MATH  Google Scholar 

  47. Zhang, J., Wang, X., Huang, K.: Integrated on-line scheduling of order batching and delivery under b2c e-commerce. Comput. Ind. Eng. 94, 280–289 (2016)

    Google Scholar 

  48. Zhang, J., Wang, X., Huang, K.: On-line scheduling of order picking and delivery with multiple zones and limited vehicle capacity. Omega 79, 104–115 (2018)

    Google Scholar 

  49. Žulj, I., Kramer, S., Schneider, M.: A hybrid of adaptive large neighborhood search and tabu search for the order-batching problem. Eur. J. Oper. Res. 264(2), 653–664 (2018)

    MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Universidad Politécnica de Madrid, C/Alan Turing s/n (Ctra. de Valencia, Km. 7), 28031, Madrid, Spain

    Sergio Gil-Borrás

  2. Universidad Rey Juan Carlos, C/Tulipán s/n, 28933, Móstoles, Madrid, Spain

    Eduardo G. Pardo, Antonio Alonso-Ayuso & Abraham Duarte

Authors
  1. Sergio Gil-Borrás
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  2. Eduardo G. Pardo
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  3. Antonio Alonso-Ayuso
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  4. Abraham Duarte
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Corresponding author

Correspondence to Eduardo G. Pardo.

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This research was partially funded by the projects: MTM2015-63710-P, RTI2018-094269-B-I00, TIN2015-65460-C2-2-P and PGC2018-095322-B-C22 from Ministerio de Ciencia, Innovación y Universidades (Spain); by Comunidad de Madrid and European Regional Development Fund, Grant Ref. P2018/TCS-4566; and by Programa Propio de I+D+i de la Universidad Politécnica de Madrid (Programa 466A).

Appendices

Appendix A: Results per instance (instance set Albareda [1])

Table 13 Results per instance for the dataset introduced in [1] over the two considered objective functions
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Appendix B: Results per instance (instance set Henn [18])

Table 14 Results per instance for the dataset introduced in [18] over the two considered objective functions
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Gil-Borrás, S., Pardo, E.G., Alonso-Ayuso, A. et al. GRASP with Variable Neighborhood Descent for the online order batching problem. J Glob Optim 78, 295–325 (2020). https://doi.org/10.1007/s10898-020-00910-2

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