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Advanced LP models
column generation
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min
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max
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Bin packing example
bins of size K
items of different types
items of type i have size s(i) and there are
n(i) of them
problem
put all items into the bins minimizing the number
of bins
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feasible patterns
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........
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integer
knapsack !
otherwise add pattern maximizing knapsack
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example
bin capacity 20
3 types
type 1 size 7 quantity 50
type 2 size 5 quantity 100
type 3 size 3 quantity 70
y ( 0 1/4 1/2 )
y ( 1/3 1/4 1/6 )
0 1 5
y ( .35 .25 .15 )
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however, change quantities to 52 97
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how to get an integer solution?
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compute the 5 longest paths
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integer
V(j)optimal value for a knapsack of capacity j
V(j) max V(j - s(i)) y(i) i 1, ... , n
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min
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max b(i) y(i)
however this is the dual problem we need the
patterns which are in the primal
so lets make the dual of the above problem
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It turns out that the dual is a flow problem
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