Skip to main content
SpringerLink
Log in

A GRASP algorithm for multi container loading problems with practical constraints

  • Research Paper
  • Published:
4OR Aims and scope Submit manuscript

Abstract

We consider the multicontainer loading problem of a company that has to serve its customers by first putting the products on pallets and then loading pallets onto trucks. When a large number of units of a product have to be shipped, the company requires that homogeneous pallets, with only one product, are built first, then weakly heterogeneous pallets, in which each layer corresponds to a single product, and finally strongly heterogeneous pallets with the remaining units of the products. To be useful in practice, the solutions have to satisfy five types of constraints: geometric constraints, so that pallets are completely inside the trucks and do not overlap; weight constraints, limiting the total weight a truck can bear and the maximum weight supported by each axle; constraints limiting the position of the centre of gravity of the cargo; dynamic stability constraints, to avoid cargo displacement when the truck is moving; and constraints ensuring that the delivery dates of products are respected. We have developed a Greedy Randomized Adaptive Search Procedure, including some improvement methods tailored to the problem, among them an adaptation of ejection chains. The approach has been tested on a benchmark of real problems and it has been shown to be capable of finding high-quality, realistic solutions in short computing times. We also provide a comparison with an integer programming formulation that justifies the use of a metaheuristic algorithm.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  • Alonso MT, Alvarez-Valdes R, Parreño F, Tamarit JM (2016) Algorithms for pallet building and truck loading in an inter-depot transportation problem. Math Probl Eng. Article ID 3264214

  • Alonso MT, Alvarez-Valdes R, Iori M, Parreño F, Tamarit JM (2017) Mathematical models for multicontainer loading problems. Omega 66:106–117

    Article  Google Scholar 

  • Baldi MM, Perboli G, Tadei R (2012) The three-dimensional knapsack problem with balancing constraints. Appl Math Comput 218:9802–9818

    Google Scholar 

  • Bischoff EE, Ratcliff MSW (1995) Issues in the development of approaches to container loading. Omega 23(4):377–390

    Article  Google Scholar 

  • Bortfeldt A (2012) A hybrid algorithm for the capacitated vehicle routing problem with three-dimensional loading constraints. Comput Oper Res 39(9):2248–2257

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Contreras I, Tanash M, Vidyarthi N (2017) Exact and heuristic approaches for the cycle hub location problem. Ann Oper Res 258:655–677

    Article  Google Scholar 

  • Correcher JF, Alonso MT, Parreño F, Alvarez-Valdes R (2017) Solving a large multicontainer loading problem in the car manufacturing industry. Comput Oper Res 82(1):139–152

    Article  Google Scholar 

  • Doerner KF, Fuellerer G, Gronalt M, Hartl RF, Iori M (2007) Metaheuristics for the vehicle routing problem with loading constraints. Networks 49(4):294–307

    Article  Google Scholar 

  • Fanslau T, Bortfeldt A (2010) A tree search algorithm for solving the container loading problem. INFORMS J Comput 22(2):222–235

    Article  Google Scholar 

  • Feo T, Resende MGC, Smith SH (1994) A greedy randomized adaptive search procedure for maximum independent set. Oper Res 42(5):860–878

    Article  Google Scholar 

  • Gendreau M, Iori M, Laporte G, Martello S (2006) A tabu search algorithm for a routing and container loading problem. Transp Sci 40:342–350

    Article  Google Scholar 

  • Glover F (1996) Ejection chains, reference structures and alternating path methods for traveling salesman problems. Discrete Appl Math 65:223–253

    Article  Google Scholar 

  • Iori M, Martello S (2010) Routing problems with loading constraints. TOP 18(1):4–27

    Article  Google Scholar 

  • Iori M, Salazar González JJ, Vigo D (2007) An exact approach for the vehicle routing problem with two-dimensional loading constraints. Transp Sci 41:253–264

    Article  Google Scholar 

  • Junqueira L, Morabito R, Yamashita DS (2012) Three-dimensional container loading models with cargo stability and load bearing constraints. Comput Oper Res 39(1):74–85

    Article  Google Scholar 

  • Knopp S, Dauzere-Peres S, Yugma C (2017) A batch-oblivious approach for complex job-shop scheduling problems. Eur J Oper Res 263:50–61

    Article  Google Scholar 

  • Lim A, Ma H, Qiu C, Zhu W (2013) The single container loading problem with axle weight constraints. Int J Prod Econ 144(1):358–369

    Article  Google Scholar 

  • Lopez-Sanchez AD, Hernandez-Diaz AG, Gortazar F, Hinojosa MA (2018) A multiobjective GRASP/VND algorithm to solve the waste collection problem. Int Trans Oper Res 25:545–567

    Article  Google Scholar 

  • Moon I, Nguyen TVL (2014) Container packing with balance constraints. OR Spectr 36:837–878

    Article  Google Scholar 

  • Morabito R, Morales S (1998) A simple and effective recursive procedure for the manufacturer’s pallet loading problem. J Oper Res Soc 49(8):819–828

    Article  Google Scholar 

  • Morabito R, Morales S, Widmer J (2000) Loading optimization of palletized products on trucks. Transp Res Part E Logist Transp Rev 36(4):285–296

    Article  Google Scholar 

  • Moura A, Bortfeldt A (2017) A two-stage packing problem procedure. Int Trans Oper Res 24:43–58

    Article  Google Scholar 

  • Moura A, Oliveira JF (2005) A GRASP approach to the container-loading problem. IEEE Intell Syst 20(4):50–57

    Article  Google Scholar 

  • ORTEC (2018) Company. www.ortec.com. Accessed 04 Mar 2018

  • Parreño F, Alvarez-Valdes R, Oliveira JF, Tamarit JM (2010) A hybrid GRASP/VND algorithm for two- and three-dimensional bin packing. Ann Oper Res 179:203–220

    Article  Google Scholar 

  • Peng B, Liu M, Lu Z, Kochengber G, Wang H (2016) An ejection chain approach for the quadratic multiple knapsack problem. Eur J Oper Res 253:328–336

    Article  Google Scholar 

  • Pisinger D (2000) A minimal algorithm for the bounded knapsack problem. INFORMS J Comput 12(1):75–82

    Article  Google Scholar 

  • Pollaris H, Braekers K, Caris A, Janssens G, Limbourg S (2016) Capacitated vehicle routing problem with sequence-based pallet loading and axle weight constraints. EURO J Transp Logist 5:231–255

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Queiroz T, Miyazawa F (2014) Order and static stability into the strip packing problem. Ann Oper Res 223:137–154

    Article  Google Scholar 

  • Ramos AG, Oliveira JF, Gonçalves JF, Lopes MP (2015) Dynamic stability metrics for the container loading problem. Transp Res Part C Emerg Technol 60:480–497

    Article  Google Scholar 

  • Ramos AG, Oliveira JF, Gonçalves JF, Lopes MP (2016) A container loading algorithm with static mechanical equilibrium stability constraints. Transp Res Part B Methodol 91:565–581

    Article  Google Scholar 

  • Ramos AG, Silva E, Oliveira JF (2018) A new load balance methodology for container loading problem in road transportation. Eur J Oper Res 266(3):1140–1152

    Article  Google Scholar 

  • Resende MGC, Werneck RF (2004) A hybrid heuristic for the p-median problem. J Heuristics 10:59–88

    Article  Google Scholar 

  • Sheng L, Hongxia Z, Xisong D, Changjian C (2016) A heuristic algorithm for container loading of pallets with infill boxes. Eur J Oper Res 252:728–736

    Article  Google Scholar 

  • Takahara S (2005) Loading problem in multiple containers and pallets using strategic search method. In: Torra V, Narukawa Y, Miyamoto S (eds) Modeling decisions for artificial intelligence, vol 3558. Lecture notes in computer science. Springer, Berlin, pp 448–456

    Chapter  Google Scholar 

  • Toffolo T, Esprit E, Wauters T, Vanden Berghe G (2018) A two-dimensional heuristic decomposition approach to a three-dimensional multiple container loading problem. Eur J Oper Res 257(2):526–538

    Article  Google Scholar 

  • Wäscher G, Haußner H, Schumann H (2007) An improved typology of cutting and packing problems. Eur J Oper Res 183(3):1109–1130

    Article  Google Scholar 

  • Zachariadis EE, Tarantilis CD, Kiranoudis CT (2012) The pallet-packing vehicle routing problem. Transp Sci 46:341–358

    Article  Google Scholar 

  • Zhao X, Bennell J, Betkas T, Dowsland K (2016) A comparative review of 3D container loading algorithms. Int Trans Oper Res 23:287–320

    Article  Google Scholar 

Download references

Acknowledgements

This study has been partially supported by the Spanish Ministry of Science and Technology DPI2014-53665-P and by Consejeria de Educacion y Ciencia, Junta de Comunidades de Castilla-La Mancha SBPLY/17/180501/000282.

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Castilla-La Mancha, Albacete, Spain

    M. T. Alonso & F. Parreño

  2. Department of Statistics and Operations Research, University of Valencia, Burjassot, Valencia, Spain

    R. Alvarez-Valdes

Authors
  1. M. T. Alonso
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Alvarez-Valdes
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. F. Parreño
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. T. Alonso.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Alonso, M.T., Alvarez-Valdes, R. & Parreño, F. A GRASP algorithm for multi container loading problems with practical constraints. 4OR-Q J Oper Res 18, 49–72 (2020). https://doi.org/10.1007/s10288-018-0397-z

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10288-018-0397-z

Keywords

Mathematics Subject Classification

Search

Navigation