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
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)
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)
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)
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)
Alvarez-Valdes, R., Parreño, F., Tamarit, J.M.: Reactive GRASP for the strip-packing problem. Comput. Oper. Res. 35, 1065–1083 (2008)
Bischoff, E.E., Ratcliff, M.S.W.: Issues in the development of approaches to container loading. Omega 23, 377–390 (1995)
Bortfeldt, A., Gehring, H.: A hybrid genetic algorithm for the container loading problem. Eur. J. Oper. Res. 131, 143–161 (2001)
Bortfeldt, A., Wäscher, G.: Constraints in container loading - a state-of-the-art review. Eur. J. Oper. Res. 229, 1–20 (2013)
Burke, E.K., Kendall, G., Whitwell, G.: A new placement heuristic for the orthogonal stock-cutting problem. Oper. Res. 52, 655–671 (2004)
Chazelle, B.: The bottomn-left bin-packing heuristic: an efficient implementation. IEEE Trans. Comput. C-32, 697–707 (1983)
Crainic, T.G., Perboli, G., Tadei, R.: Extreme point-based heuristics for three-dimensional bin packing. INFORMS J. Comput. 20, 368–384 (2008)
Crainic, T.G., Perboli, G., Tadei, R.: Recent advances in multi-dimensional packing problems. In: New Technologies, chap. 5. IntechOpen (2012)
Côté, J.F., Dell’Amico, M., Iori, M.: Combinatorial benders’ cuts for the strip packing problem. Oper. Res. 62, 643–661 (2014)
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)
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)
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)
Delorme, M., Iori, M., Martello, S.: Logic based benders decomposition for orthogonal stock cutting problems. Comput. Oper. Res. 78, 290–298 (2017)
Egeblad, J., Garavelli, C., Lisi, S., Pisinger, D.: Heuristics for container loading of furniture.Eur. J. Oper. Res. 200, 881–892 (2010)
Elhedhli, S., Gzara, F., Yildiz, B.: Three-dimensional bin packing and mixed-case palletization. INFORMS J. Optim. 1(4), 323–352 (2019)
Gilmore, P.C., Gomory, R.E.: Multistage cutting stock problems of two or more dimensions. Oper. Res. 13, 94–120 (1965)
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)
Haessler, R.W., Talbot, F.B.: Load planning for shipments of low density products. Eur. J. Oper. Res. 44, 289–299 (1990)
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)
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)
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)
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)
Iori, M., Martello, S.: Routing problems with loading constraints. TOP 18, 4–27 (2010)
Iori, M., Martello, S.: An annotated bibliography of combined routing and loading problems. Yugoslav J. Oper. Res. 23, 311–326 (2013)
Jovanovic, R., Tuba, M., Voß, S.: Fixed set search applied to the traveling salesman problem, pp. 63–77. International Workshop on Hybrid Metaheuristics (2019)
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
Jovanovic, R., Voß, S.: The fixed set search applied to the power dominating set problem. Expert Systems, p. e12559 (2020)
Józefowska, J., Pawlak, G., Pesch, E., Morze, M., Kowalski, D.: Fast truck-packing of 3D boxes. Eng. Manage. Prod. Serv. 10, 29–40 (2018)
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)
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)
Lodi, A., Martello, S., Monaci, M., Vigo, D.: Two-Dimensional Bin Packing Problems, pp. 107–129. John Wiley & Sons, Ltd (2014)
Martins, G.H.A., Dell, R.F.: Solving the pallet loading problem. Eur. J. Oper. Res. 184, 429–440 (2008)
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)
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)
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)
Scheithauer, G.: Introduction to Cutting and Packing Optimization. Springer International Publishing (2018)
Schmid, V., Doerner, K.F., Laporte, G.: Rich routing problems arising in supply chain management. Eur. J. Oper. Res. 224, 435–448 (2013)
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)
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)
Tsai, D.: Modeling and analysis of three-dimensional robotic palletizing systems for mixed carton sizes. Ph.D. thesis, Iowa State University (1987)
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)
Wäscher, G., Hau\(\beta \)ner, H., Schumann, H.: An improved typology of cutting and packing problems. Eur. J. Oper. Res. 183, 1109–1130 (2007)
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)
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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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