NEW HEURISTIC FOR THREE DIMENSIONAL STRIP PACKING PROBLEMHa Thai Duong Supervisor: Edmund Burke, Graham Kendall

Overview Problem Definition Literature Review Currently Used Heuristic Tested Result Conclusion

Problem Definition Pack all boxes into a smallest open

container Min (Optimal Volume/Actual Volume)

Open Container

Boxes

Problem Definition Logistic

Container Storage

Cutting Material Space allocation

Problem Definition Dyckhoff (1990)

3/B/O/F, 3/B/O/M or 3/B/O/R 3: three-dimensional, B/O: one

object/container and selection of items, F: few items of different types, M: many items of many different types, R: many items of relatively few different types).

Wascher et al. (2007) Three-dimensional cuboids open-

dimension-problem

Literature Review Exact method

Dudzinski, K. and Walukiewicz, S., 1987 Heuristic

Heuristic Heuristic & Search Method

Literature Review Layer Building

Moura and Oliveira, 2005 A. Bortfeldt and D. Mack 2007

Literature Review Box Arrangement

Bortfeldt and Gehring, 1998 Eley 2002 Bortfeldt et al., 2003

Literature Review Best Fit

E. K. Burke, G. Kendall, and G. Whitwell. 2004 S. Allen E. K. Burke G. Kendall

And manymore ...

GAP

Literature Review Heuristic & Search Method

Tabu Search T.G. Crainic, G. Perboli and R. Tadei 2009 E.E. Zachariadis, C.D. Tarantilis and C.T.

Kiranoudis 2009 Genetic Algorithms

Gehring, H., Bortfeldt, A., 2002. ....

Literature Review Each heuristic suitable for some cases Constructive heuristic is more important

than search method Addition Constraints:

Orientation constraint Weight distribution Loading stability

Currently Used Heuristic Max Surround Touching Min Rotation Score Min Volume Percentage Max Contact Area & Max Volume (S.

Allen E. K. Burke G. Kendall)

Max Surround Touching Touching top of the box

Max Surround Touching

Max Surround Touching Touching top of the box

Min Rotation Score Box with less rotation is harder to pack Packing box with min rotation score Rotation Score

(Number Possible Rotation * Number Box)/ Total Number Box

Min Rotation Score

No Rotation

Min Rotation Score

No Rotation

Min Rotation Score

No Rotation

Min Rotation Score

No Rotation

Min Rotation Score

No Rotation

Min Volume Percentage Optimal Volume/ Actual Volume

Min Volume Percentage

Min Volume Percentage

Tested Result BR dataset – OR Library

BR10 – 87.2% (Best 87.6)

Viewer created by Sam Allen

Conclusion & Future Work New heuristic particular good in some

cases Multiple heuristic run Different data set Application hyper-heuristic

References A New Hybrid Placement Strategy for the

Three-Dimensional Strip Packing Problem (S. Allen E. K. Burke G. Kendall)

An improved typology of cutting and packing problems Gerhard Wa¨scher *, Heike Hausner, Holger Schumann

A heuristic for the three-dimensional strip packing problem, Andreas Bortfeldt, Daniel Mack

Thank you

Questions