Modelling and Solving the Joint Order Batching and Picker Routing Problem in Inventories

  • Cristiano Arbex Valle
  • John E. Beasley
  • Alexandre Salles da Cunha
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9849)


In this work we investigate the problem of order batching and picker routing in inventories. These are labour and capital intensive problems, often responsible for a substantial share of warehouse operating costs. In particular, we consider the case of online grocery shopping in which orders may be composed of dozens of items. To the best of our knowledge, no exact algorithms have been proposed for this problem. We therefore introduce three integer programming formulations for the joint problem of batching and routing, one of them involving exponentially many constraints to enforce connectivity requirements and two compact formulations based on network flows. For the former we implement a branch-and-cut algorithm which separates connectivity constraints. We built a test instance generator, partially based on publicly-available real world data, in order to compare empirically the three formulations.


Order batching Picker routing Inventory management Integer programming 


  1. 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. (APJOR) 26(05), 655–683 (2009)CrossRefzbMATHGoogle Scholar
  2. 2.
    Azadnia, A.H., Taheri, S., Ghadimi, P., Saman, M.Z.M., Wong, K.Y.: Order batching in warehouses by minimizing total tardiness: a hybrid approach of weighted association rule mining and genetic algorithms. Sci. World J. 2013(1), 1–13 (2013)CrossRefGoogle Scholar
  3. 3.
    Chen, M.C., Wu, H.P.: An association-based clustering approach to order batching considering customer demand patterns. Omega 33(4), 333–343 (2004)CrossRefGoogle Scholar
  4. 4.
    Cornuéjols, G., Fonlupt, J., Naddef, D.: The travelling salesman problem on a graph and some related integer polyhedra. Math. Program. 33(1), 1–27 (1985)CrossRefzbMATHGoogle Scholar
  5. 5.
    CPLEX Optimizer: IBM (2016). Accessed 8 Feb 2016
  6. 6.
    Dekker, R., de Koster, M.B.M., Roodbergen, K.J., van Kalleveen, H.: Improving order-picking response time at Ankor’s warehouse. Interfaces 34(4), 303–313 (2004)CrossRefGoogle Scholar
  7. 7.
    Fleischmann, B.: A cutting-plane procedure for the traveling salesman problem on a road network. Eur. J. Oper. Res. 21(3), 307–317 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Gibson, D.R., Sharp, G.P.: Order batching procedures. Eur. J. Oper. Res. 58(1), 57–67 (1992)CrossRefGoogle Scholar
  9. 9.
    Goldberg, A.V., Tarjan, R.E.: A new approach to the maximum flow problem. J. ACM 35(4), 921–940 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Hart, P., Nilsson, N., Raphael, B.: A formal basis for the heuristic determination of minimum cost paths. IEEE Trans. Syst. Sci. Cybern. 4(2), 100–107 (1968)CrossRefGoogle Scholar
  11. 11.
    Henn, S., Koch, S., Wäscher, G.: Order batching in order picking warehouses: a survery of solution approaches. In: Manzini, R. (ed.) Warehousing in the Global Supply Chain, pp. 105–137. Springer, London (2012). Chap. 6CrossRefGoogle Scholar
  12. 12.
    Henn, S., Schmid, V.: Metaheuristics for order batching and sequencing in manual order picking systems. Comput. Ind. Eng. 66(2), 338–351 (2013)CrossRefGoogle Scholar
  13. 13.
    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)CrossRefzbMATHGoogle Scholar
  14. 14.
    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 (2004)CrossRefGoogle Scholar
  15. 15.
    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)CrossRefzbMATHGoogle Scholar
  16. 16.
    de Koster, R., van der Poort, E.S., Wolters, M.: Efficient orderbatching methods in warehouses. Int. J. Prod. Res. 37(7), 1479–1504 (1999)CrossRefzbMATHGoogle Scholar
  17. 17.
    Lam, C.H., Choy, K., Ho, G., Lee, C.: An order-picking operations system for managing the batching activities in a warehouse. Int. J. Syst. Sci. 45(6), 1283–1295 (2014)CrossRefzbMATHGoogle Scholar
  18. 18.
    Letchford, A.N., Nasiri, S.D., Theis, D.O.: Compact formulations of the Steiner traveling salesman problem and related problems. Eur. J. Oper. Res. 228(1), 83–92 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Letchford, A.N., Oukil, A.: Exploiting sparsity in pricing routines for the capacitated arc routing problem. Comput. Oper. Res. 36(7), 2320–2327 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Lin, S., Kernighan, B.W.: An effective heuristic algorithm for the traveling-salesman problem. Oper. Res. 21(2), 498–516 (1973)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Lucena, A.: Steiner problem in graphs: Lagrangean relaxation and cutting planes. COAL Bull. 21(1), 2–8 (1992)Google Scholar
  22. 22.
    Matusiak, M., de Koster, R., Kroon, L., Saarinen, J.: A fast simulated annealing method for batching precedence-constrained customer orders in a warehouse. Eur. J. Oper. Res. 236(3), 968–977 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    MySQL Foodmart Database (2008). Accessed 31 Jan 2016
  24. 24.
    Orloff, C.S.: A fundamental problem in vehicle routing. Networks 4(1), 35–64 (1974)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Padberg, M., Rinaldi, G.: A branch-and-cut algorithm for resolution of large scale of symmetric traveling salesman problem. SIAM Rev. 33(1), 60–100 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Petersen II, C.G.: An evaluation of order picking routing policies. Int. J. Oper. Prod. Manage. 17(11), 1098–1111 (1997)CrossRefGoogle Scholar
  27. 27.
    Roodbergen, K.J., de Koster, R.: Routing methods for warehouses with multiple cross aisles. Int. J. Prod. Res. 39(9), 1865–1883 (2001)CrossRefzbMATHGoogle Scholar
  28. 28.
    Roodbergen, K.J., de Koster, R.: Routing order pickers in a warehouse with a middle aisle. Eur. J. Oper. Res. 133(1), 32–43 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Theys, C., Bräysy, O., Dullaert, W., Raa, B.: Using a TSP heuristic for routing order pickers in warehouses. Eur. J. Oper. Res. 200(3), 755–763 (2010)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Cristiano Arbex Valle
    • 1
  • John E. Beasley
    • 2
  • Alexandre Salles da Cunha
    • 1
  1. 1.Departamento de Ciência da ComputaçãoUniversidade Federal de Minas GeraisBelo HorizonteBrazil
  2. 2.Mathematical SciencesBrunel UniversityUxbridgeUK

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