Abstract
This paper presents a logistical study using a mathematical model based on the Three-dimensional Open Dimension Rectangular Packing Problem (3D-ODRPP) to optimize the arrangement of products in a packaging with the practical constraint “product stability”. The proposed model aims at seeking the minimal volume rectangular bounding box for a set of rectangular products. Our model deals with orthogonal rotation, static stability and overhang constraints of products, three of the most important real-world conditions that ensure the feasibility of solution. Literature test instances are given to demonstrate that the proposed method can find the feasible global optimum of a 3D-ODRPP. Experimental results show the improvement of solution quality in terms of box volume and packaging stability comparing to existing models in the literature.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bischoff, E.E., Ratcliff, M.: Issues in the development of approaches to container loading. Omega 23(4), 377–390 (1995)
Bortfeldt, A., Gehring, H.: A hybrid genetic algorithm for the container loading problem. Eur. J. Oper. Res. 131(1), 143–161 (2001)
Chen, C., Lee, S.M., Shen, Q.: An analytical model for the container loading problem. Eur. J. Oper. Res. 80(1), 68–76 (1995)
Gonçalves, J.F., Resende, M.G.: A parallel multi-population biased random-key genetic algorithm for a container loading problem. Comput. Oper. Res. 39(2), 179–190 (2012)
Junqueira, L., Morabito, R.: On solving three-dimensional open-dimension rectangular packing problems. Eng. Optim. 49(5), 733–745 (2017)
Pedruzzi, S., Nunes, L.P.A., de Alvarenga Rosa, R., Arpini, B.P.: A mathematical model to optimize the volumetric capacity of trucks utilized in the transport of food products. Gest. Prod. 23, 350–364 (2016)
Ramos, A.G., Oliveira, J.F., Gonçalves, F.J., Lopes, M.P.: A container loading algorithm with static mechanical equilibrium stability constraints. Transp. Res. Part B: Methodol. 91, 565–581 (2016)
Ramos, A.G., Oliveira, J.F., Lopes, M.P.: A physical packing sequence algorithm for the container loading problem with static mechanical equilibrium conditions. Int. Trans. Oper. Res. 23(1–2), 215–238 (2016)
Silva, J., Soma, N., Maculan, N.: A greedy search for the three-dimensional bin packing problem: the packing static stability case. Int. Trans. Oper. Res. 10(04), 141–153 (2003)
Truong, C.T.T., Amodeo, L., Farouk, Y., Hautefaye, J.C., Birebent, S.: A product arrangement optimization method to reduce packaging environmental impacts. In: International Conference on Sustainable Energy and Green Technology (2019)
Tsai, J.F., Wang, P.C., Lin, M.H.: A global optimization approach for solving three-dimensional open dimension rectangular packing problems. Optimization 64(12), 2601–2618 (2015)
Vielma, J.P., Nemhauser, G.L.: Modeling disjunctive constraints with a logarithmic number of binary variables and constraints. Math. Program. 128(1–2), 49–72 (2011)
Wäscher, G., Haussner, H., Schumann, H.: An improved typology of cutting and packing problems. Eur. J. Oper. Res. 183(3), 1109–1130 (2007)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Truong, CTT., Amodeo, L., Yalaoui, F. (2020). A Mathematical Model for Three-Dimensional Open Dimension Packing Problem with Product Stability Constraints. In: Dorronsoro, B., Ruiz, P., de la Torre, J., Urda, D., Talbi, EG. (eds) Optimization and Learning. OLA 2020. Communications in Computer and Information Science, vol 1173. Springer, Cham. https://doi.org/10.1007/978-3-030-41913-4_20
Download citation
DOI: https://doi.org/10.1007/978-3-030-41913-4_20
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-41912-7
Online ISBN: 978-3-030-41913-4
eBook Packages: Computer ScienceComputer Science (R0)