NEW HEURISTIC FOR THREE DIMENSIONAL STRIP PACKING PROBLEM

Ha 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