“SOC InfoComm Camps”
‰ Computational Problem Solving
™ Packing Problems and Algorithmic Solutions
‹What are Packing Problems
‹Types of Packing Problems
‹PSA Berth Allocation Problem
Quickly get up to speed…
Hon Wai Leong, SoC, NUS
(Packing Problems) Page 1
Copyright © 2007 by Leong Hon Wai
Large Variety of Packing Problems
Capital Budgeting
Memory Allocation
Assembly Line Balancing
Layout & Partition
Container Loading
Vehicle Loading
Loading your BAG
Bin
Packing
Cutting Stock
Trim Loss
Assortment Problems
Hon Wai Leong, SoC, NUS
(Packing Problems) Page 2
Copyright © 2007 by Leong Hon Wai
The Packing / Nesting “industry”
‰ Industry Applications
™ Manufacturing industry (ship building)
™ Construction industry
™ Furniture industry
™ Packing and Moving industry
™ Garment industry
‰ Vendor Solutions
™ AutoNEST, RNest, BarNest (Radan System)
™ FastNEST
(Fagan…)
™ SIGMANEST
(SigmaTech Inc)
Hon Wai Leong, SoC, NUS
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Copyright © 2007 by Leong Hon Wai
Vendor solution…
‰ AutoNEST (from Radan Systems)
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Copyright © 2007 by Leong Hon Wai
Vendor solution (an example)
AutoNEST (from Radan Systems)
Optimize use of stock sheet
Can handle complicated shapes
Can do “picture-in-picture”
Hon Wai Leong, SoC, NUS
Industries
Shipbuilding
Heavy engineering,
Fabrication,
Leather/fabrics, furniture
(Packing Problems) Page 5
Copyright © 2007 by Leong Hon Wai
Packing problems are everywhere
™ Packing books into shelves
‹ different height, width, thickness, classification
™ Packing books into your school bag
™ Packing apples into boxes
™ Packing squares, rectangles, hexagons
‹ tessellations?
™ Packing songs into your MP4 player
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Copyright © 2007 by Leong Hon Wai
1-D Packing Problems
‰ You are going on a trip
™ You have a list of songs (mp3 files)
‹ A long, long list of your favorite song
http://mixitup987.blogspot.com/2008/01/top-10-songs-of-month.html
‹ Each of different file sizes
™ You want to store into your MP3 player
‹ But you cannot fit them all in
™ You want to store as many song as possible
‹ What are your preferences (by favourites, by singers)
‰ Photos from your trips
™ You are storing “different collections of photos,
video from various trip” onto CDs / DVDs
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Copyright © 2007 by Leong Hon Wai
1-D Bin Packing Algorithms
‰ Most “well-solved” packing problem
™ Many software solutions can be found
‹ Google “1-D packing software” [here]
‰ Some algorithms for 1-D bin packing
‰ Interval Packing (2 of Everything)
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(Packing Problems) Page 8
Copyright © 2007 by Leong Hon Wai
2D Packing Problems
‰ Construction Industry
™ Cutting glass/aluminium panels for windows
™ Sign boards, Furnitures
‰ Media Industry
™ Advertisements layout in newspaper
™ Leather, Fabrics
‰ Shipbuilding, Engineering Industry
™ Parts of a ship, machine, car
™ (Often irregular shapes)
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(Packing Problems) Page 9
Copyright © 2007 by Leong Hon Wai
3-D Packing Problems
‰ Many examples:
™ Packing suitcases for a trip
™ Container loading
Hon Wai Leong, SoC, NUS
(Packing Problems) Page 10
Copyright © 2007 by Leong Hon Wai
An un-expected packing problem…
‰ Berth Allocation Problem in PSA
™ Allocate berths to ships
™ similar to 2-D packing (after suitable modelling)
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(Packing Problems) Page 11
Copyright © 2007 by Leong Hon Wai
Thank you!
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(Packing Problems) Page 12
Copyright © 2007 by Leong Hon Wai