Optimization of unit load formation taking into account the mass of packaging units

Kamil Popiela; Mariusz Wasiak

doi:10.5604/08669546.1147002

Authors

Kamil Popiela Warsaw University of Technology, Faculty of Transport, Division of Logistics and Transport Systems, Warsaw, Poland Author
Mariusz Wasiak Warsaw University of Technology, Faculty of Transport, Division of Logistics and Transport Systems, Warsaw, Poland Author

DOI:

https://doi.org/10.5604/08669546.1147002

Keywords:

optimalization, unit loads, formation of loading units

Abstract

This article presents a mathematical formulation of the optimization problem of loading unit formation taking into account the mass of packaging units. Proposed model can be applied to optimize the arrangement of non-uniform cubical loading units in loading spaces. The model ensures possibility of defining various dimensions, masses, resistances of particular packaging units and their vertical axis rotation. Within the constraints of formulating optimization problem, taking into account masses and resistances ensures that all packaging units will rest on a pallet or on other packaging units, and the surface of contact between loading units guarantees stability of units arranged in subsequent layers. The mathematical model was verified. The paper provides an appropriate calculation example.

References

Alian W., Baisong Ch., Zhang J., Liangfeng L., Three-dimensional Packing by Tabu Search Algorithm in Military Airlift Loading, 2010 International Conference on Optoelectronics and Image Processing, IEEE, 2010.

Bomba I., Woźniak G., Kwiecień K.: Wykorzystanie programowania liniowego w projektowaniu paletowej jednostki ładunkowej, Czasopismo Logistyka 3/2012, s. 157-162.

Chen C.S., Lee S.M., Shen Q.S., An analytical model for the container loading problem, Theory and Methodology, European Journal of Operational Researc, No. 80,pp.68-76, Elsevier, 1995.

Dahmani N., Krichen S., On solving the biobjective aircraft cargo loading, 5th International Conference on Modeling, Simulation and Applied Optimization (ICMSAO), IEEE, 2013.

Hifi M., Kacem I., Negre S., Wu L.,A Linear Programming Approach for the Three-Dimensional Bin-Packing Problem, Electronic Notes in Discrete Mathematics, No. 36, pp. 993–1000, 2010.

Lodi A., Martello S., Monaci M., Two-dimensional packing problems: A survey, European Journal of Operational Research, No. 141,pp. 241-252, Elsevier Science Ltd., 2002

Lodi A., Martello S., Vigo D., Models and Bounds for Two-dimensional Level Packing Problems, Journal of Combinatorial Optimization, No.8, pp. 363-379, Kluwer Academic Publishers, 2004 the Netherlands.

Mongeau M., Bes Ch., Optimization of Aircraft Container Loading, IEEE Transactions on Aerospace and Electronic Systems, Vol.39, No 1., IEEE, 2003.

Pargas R.P., Jain R., A Parallel Stochastic Optimization Algorithm for Solving 2D Bin Packing Problems, AIA, IEEE, 1993 Orlando Florida United States.

Piekarska M., Mrozek-Kantak J., Lewandowska J., Rozwiązania najważniejszych problemów współczesnych łańcuchów dostaw FMCG w Polsce, w: Najlepsze praktyki w logistyce, Polski kongres Logistyczny Instytut Logistyki. Materiały konferencyjne, Poznań 2006, s. 177-126

Pisinger D., Sigurd M., The two-dimensional bin packing problem with variable bin sizes and costs, Discrete Optimization, No. 2, pp.154 – 167, Elsevier Science Ltd., 2005.

Popiela K., Wasiak M., Optymalizacja formowania jednostek ładunkowych, Czasopismo Logistyka 4/2014, s. 2335-2344.

Ratkiewicz A., Rozprawa doktorska – Optymalizacja procesu komisjonowania w ustalonej klasie łańcuchów transportowo-magazynowych, Wydział Transportu Politechniki Warszawskiej, Warszawa 2002.

Savić A., Sukilović T., Filipović V., SOLVING THE TWO-DIMENSIONAL PACKING PROBLEM WITH m-M CALCULUS, Yugoslav Journal of Operations Research 21, No. 1, pp. 93-102, 2011.

Tlili T., Faiz S., Krichen S., A particle swarm optimization for solving the one dimensional container loading problem, 5th International Conference on Modeling, Simulation and Applied Optimization (ICMSAO), IEEE, 2013.

Yao Ch., Jia-Zhen H., Hu L., Optimal Model, Algorism and Desicion Support System of Bulk Ship Loading Problem, IEEE, 2008.