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Wednesday, February 17, 2016

Strange restriction

In this post the question is posed how to model the restriction
x{1,2,3,4,5,6,8,10,12,..,100}.
Note that this is {1,2,3,4,5}{6,8,10,..,98,100}.  Never seen a thing like this, but here is a way to model this in a MIP model:
6(1δ)Mx5+δM2y(1δ)Mx2y+(1δ)M1x100xintegeryintegerδbinary
Note that this essentially means:
δ=0x5δ=1x6,x=2y
We can use M=100 (or even refine that a little bit).
 

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