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ISE 336 ART OF MATHEMATICAL
MODELLING
INTRODUCTION TO MATHEMATICAL
MODELING AND IBM ILOG CPLEX
OPTIMIZATION STUDIO
2014-2015 SPRING TERM
Dr. M. Arslan Örnek
LECTURE #7
THIS WEEK...
• CUTTING STOCK PROBLEM
• Programming applications
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CUTTING STOCK PROBLEM
• The determination of how to cut the (larger) standard
sizes into the (smaller) sizes at min cost is called the
“cutting stock problem”.
• If all ordered sizes are cut horizantally or vertically, the
problem is one dimensional.
• If an ordered size is made by both horizantal and vertical
cuts, the problem is two dimensional.
• For a given standard width (or length), the way of cutting
it into ordered widths (or lengths), is called a “cutting
pattern”.
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CUTTING STOCK PROBLEM
ONE DIMENSIONAL
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CUTTING STOCK PROBLEM
TWO DIMENSIONAL
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CUTTING STOCK PROBLEM
• A one dimensional cutting stock problem is to determine how
to cut rolls of the standard width into various ordered widths
so that the required no of rolls (assuming trim pieces are
useless) is minimal while satisfying the ordered quantity of
each width.
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CUTTING STOCK PROBLEM
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CUTTING STOCK PROBLEM
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CUTTING STOCK PROBLEM
MODEL FORMULATION
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CUTTING STOCK PROBLEM
TUPLE MODEL FORMULATION
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CUTTING STOCK PROBLEM
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