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A Mixed Approach for Pallet Building Problem with Practical Constraints

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Enterprise Information Systems (ICEIS 2020)

Abstract

We study a pallet building problem that originates from a case study in a company that produces robotized systems for freight transportation and logistics. We generalize the problem by including the concept of family of items, which allows us to consider specific constraints such as visibility and contiguity. We solve the problem with an algorithm based on a two-step strategy: an Extreme Points heuristic is used to group items into horizontal layers and an exact method is invoked to stack layers one over the other to form pallets. The performance of the algorithm is assessed through extensive computational tests on real-world instances. The results show that the exact model considerably increases the solution quality, creating very compact packings with a limited computational effort.

Supported by University of Parma, and by University of Modena and Reggio Emilia under grant FAR 2018.

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References

  1. Alonso, M.T., Alvarez-Valdes, R., Iori, M., Parreño, F.: Mathematical models for multi container loading problems with practical constraints. Comput. Ind. Eng. 127, 722–733 (2019)

    Article  Google Scholar 

  2. Alonso, M.T., Alvarez-Valdes, R., Iori, M., Parreño, F., Tamarit, J.M.: Mathematical models for multi container loading problems. OMEGA 66, 106–117 (2017)

    Article  Google Scholar 

  3. Alonso, M.T., Alvarez-Valdes, R., Parreño, F., Tamarit, J.M.: Algorithms for pallet building and truck loading in an interdepot transportation problem. Math. Probl. Eng. 2016, 1–11 (2016)

    Article  Google Scholar 

  4. Alvarez-Valdes, R., Parreño, F., Tamarit, J.M.: A branch-and-cut algorithm for the pallet loading problem. Comput. Oper. Res. 32, 3007–3029 (2005)

    Article  MathSciNet  Google Scholar 

  5. Alvarez-Valdes, R., Parreño, F., Tamarit, J.M.: Reactive GRASP for the strip-packing problem. Comput. Oper. Res. 35, 1065–1083 (2008)

    Article  Google Scholar 

  6. Bischoff, E.E., Ratcliff, M.S.W.: Issues in the development of approaches to container loading. Omega 23, 377–390 (1995)

    Article  Google Scholar 

  7. Bortfeldt, A., Gehring, H.: A hybrid genetic algorithm for the container loading problem. Eur. J. Oper. Res. 131, 143–161 (2001)

    Article  Google Scholar 

  8. Bortfeldt, A., Wäscher, G.: Constraints in container loading - a state-of-the-art review. Eur. J. Oper. Res. 229, 1–20 (2013)

    Article  MathSciNet  Google Scholar 

  9. Burke, E.K., Kendall, G., Whitwell, G.: A new placement heuristic for the orthogonal stock-cutting problem. Oper. Res. 52, 655–671 (2004)

    Article  Google Scholar 

  10. Chazelle, B.: The bottomn-left bin-packing heuristic: an efficient implementation. IEEE Trans. Comput. C-32, 697–707 (1983)

    Google Scholar 

  11. Crainic, T.G., Perboli, G., Tadei, R.: Extreme point-based heuristics for three-dimensional bin packing. INFORMS J. Comput. 20, 368–384 (2008)

    Article  MathSciNet  Google Scholar 

  12. Crainic, T.G., Perboli, G., Tadei, R.: Recent advances in multi-dimensional packing problems. In: New Technologies, chap. 5. IntechOpen (2012)

    Google Scholar 

  13. Côté, J.F., Dell’Amico, M., Iori, M.: Combinatorial benders’ cuts for the strip packing problem. Oper. Res. 62, 643–661 (2014)

    Article  MathSciNet  Google Scholar 

  14. da Silva, E.F., Leão, A.A.S., Toledo, F.M.B., Wauters, T.: A matheuristic framework for the three-dimensional single large object placement problem with practical constraints. Comput. Oper. Res. 124, 105058 (2020)

    Google Scholar 

  15. de Queiroz, T.A., Miyazawa, F.K.: Two-dimensional strip packing problem with load balancing, load bearing and multi-drop constraints. Int. J. Prod. Econ. 145, 511–530 (2013)

    Article  Google Scholar 

  16. Delorme, M., Iori, M., Martello, S.: Bin packing and cutting stock problems: mathematical models and exact algorithms. Eur. J. Oper. Res. 255, 1–20 (2016)

    Article  MathSciNet  Google Scholar 

  17. Delorme, M., Iori, M., Martello, S.: Logic based benders decomposition for orthogonal stock cutting problems. Comput. Oper. Res. 78, 290–298 (2017)

    Article  MathSciNet  Google Scholar 

  18. Egeblad, J., Garavelli, C., Lisi, S., Pisinger, D.: Heuristics for container loading of furniture.Eur. J. Oper. Res. 200, 881–892 (2010)

    Article  Google Scholar 

  19. Elhedhli, S., Gzara, F., Yildiz, B.: Three-dimensional bin packing and mixed-case palletization. INFORMS J. Optim. 1(4), 323–352 (2019)

    Article  MathSciNet  Google Scholar 

  20. Gilmore, P.C., Gomory, R.E.: Multistage cutting stock problems of two or more dimensions. Oper. Res. 13, 94–120 (1965)

    Article  Google Scholar 

  21. Gzara, F., Elhedhli, S., Yildiz, B.C.: The pallet loading problem: three-dimensional bin packing with practical constraints. Eur. J. Oper. Res. 287(3), 1062–1074 (2020)

    Article  MathSciNet  Google Scholar 

  22. Haessler, R.W., Talbot, F.B.: Load planning for shipments of low density products. Eur. J. Oper. Res. 44, 289–299 (1990)

    Article  Google Scholar 

  23. Hopper, E., Turton, B.: Application of genetic algorithms to packing problems - a review. In: Soft Computing in Engineering Design and Manufacturing, pp. 279–288 (1998)

    Google Scholar 

  24. Imahori, S., Yagiura, M.: The best-fit heuristic for the rectangular strip packing problem: an efficient implementation and the worst-case approximation ratio. Comput. Oper. Res. 37, 325–333 (2010)

    Article  Google Scholar 

  25. Iori, M., de Lima, V.L., Martello, S., Miyazawa, F.K., Monaci, M.: Two-dimensional cutting and packing: Problems and solution techniques. Eur. J. Oper. Res. (2020). (forthcoming)

    Google Scholar 

  26. Iori, M., Locatelli, M., Moreira, M.C.O., Silveira, T.: Solution of a practical pallet building problem with visibility and contiguity constraints. In: International Conference on Enterprise Information Systems, vol. 1, pp. 327–338. SciTePress (2020)

    Google Scholar 

  27. Iori, M., Martello, S.: Routing problems with loading constraints. TOP 18, 4–27 (2010)

    Article  MathSciNet  Google Scholar 

  28. Iori, M., Martello, S.: An annotated bibliography of combined routing and loading problems. Yugoslav J. Oper. Res. 23, 311–326 (2013)

    Article  MathSciNet  Google Scholar 

  29. Jovanovic, R., Tuba, M., Voß, S.: Fixed set search applied to the traveling salesman problem, pp. 63–77. International Workshop on Hybrid Metaheuristics (2019)

    Google Scholar 

  30. Jovanovic, R., Voß, S.: Fixed set search applied to the minimum weighted vertex cover problem. In: Kotsireas, I., Pardalos, P., Parsopoulos, K.E., Souravlias, D., Tsokas, A. (eds.) SEA 2019. LNCS, vol. 11544, pp. 490–504. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-34029-2_31

    Chapter  Google Scholar 

  31. Jovanovic, R., Voß, S.: The fixed set search applied to the power dominating set problem. Expert Systems, p. e12559 (2020)

    Google Scholar 

  32. Józefowska, J., Pawlak, G., Pesch, E., Morze, M., Kowalski, D.: Fast truck-packing of 3D boxes. Eng. Manage. Prod. Serv. 10, 29–40 (2018)

    Google Scholar 

  33. Kurpel, D.V., Scarpin, C.T., Pécora Junior, J.E., Schenekemberg, C.M., Coelho, L.C.: The exact solutions of several types of container loading problems. Eur. J. Oper. Res. 284, 87–107 (2020)

    Article  MathSciNet  Google Scholar 

  34. Leung, S.C.H., Zhang, D., Sim, K.M.: A two-stage intelligent search algorithm for the two-dimensional strip packing problem. Eur. J. Oper. Res. 215, 57–69 (2011)

    Article  Google Scholar 

  35. Lodi, A., Martello, S., Monaci, M., Vigo, D.: Two-Dimensional Bin Packing Problems, pp. 107–129. John Wiley & Sons, Ltd (2014)

    Google Scholar 

  36. Martins, G.H.A., Dell, R.F.: Solving the pallet loading problem. Eur. J. Oper. Res. 184, 429–440 (2008)

    Article  MathSciNet  Google Scholar 

  37. Neli\(\beta \)en, J.: How to use structural constraints to compute an upper bound for the pallet loading problem. Eur. J. Oper. Res. 84, 662–680 (1995)

    Google Scholar 

  38. Ranck Júnior, R., Yanasse, H.H., Morabito, R., Junqueira, L.: A hybrid approach for a multi-compartment container loading problem. Expert Syst. Appl. 137, 471–492 (2019)

    Article  Google Scholar 

  39. Ribeiro, G.M., Lorena, L.A.N.: Lagrangean relaxation with clusters and column generation for the manufacturers pallet loading problem. Comput. Oper. Res. 34, 2695–2708 (2007)

    Article  Google Scholar 

  40. Scheithauer, G.: Introduction to Cutting and Packing Optimization. Springer International Publishing (2018)

    Google Scholar 

  41. Schmid, V., Doerner, K.F., Laporte, G.: Rich routing problems arising in supply chain management. Eur. J. Oper. Res. 224, 435–448 (2013)

    Article  MathSciNet  Google Scholar 

  42. Silva, E., Oliveira, J.F., Wäscher, G.: The pallet loading problem: a review of solution methods and computational experiments. Int. Trans. Oper. Res. 23, 147–172 (2016)

    Article  MathSciNet  Google Scholar 

  43. Terno, J.J., Scheithauer, G., Sommerwei\(\beta \), U., Riehme, J.: An efficient approach for the multi-pallet loading problem. J. Eur. J. Oper. Res. 123, 372–381 (2000)

    Google Scholar 

  44. Tsai, D.: Modeling and analysis of three-dimensional robotic palletizing systems for mixed carton sizes. Ph.D. thesis, Iowa State University (1987)

    Google Scholar 

  45. Vidal, T., Crainic, T.G., Gendreau, M., Prins, C.: Heuristics for multi-attribute vehicle routing problems: a survey and synthesis. Eur. J. Oper. Res. 231, 1–21 (2013)

    Article  MathSciNet  Google Scholar 

  46. Wäscher, G., Hau\(\beta \)ner, H., Schumann, H.: An improved typology of cutting and packing problems. Eur. J. Oper. Res. 183, 1109–1130 (2007)

    Google Scholar 

  47. Wu, K.C., Ting, C.J.: A two-phase algorithm for the manufacturer’s pallet loading problem. In: IEEE International Conference on Industrial Engineering and Engineering Management, pp. 1574–1578 (2007)

    Google Scholar 

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Correspondence to Tiago Silveira .

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Iori, M., Locatelli, M., Moreira, M.C.O., Silveira, T. (2021). A Mixed Approach for Pallet Building Problem with Practical Constraints. In: Filipe, J., Śmiałek, M., Brodsky, A., Hammoudi, S. (eds) Enterprise Information Systems. ICEIS 2020. Lecture Notes in Business Information Processing, vol 417. Springer, Cham. https://doi.org/10.1007/978-3-030-75418-1_7

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  • DOI: https://doi.org/10.1007/978-3-030-75418-1_7

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