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Topic: disjunctive constraints in integer linear programming
Replies: 9   Last Post: Apr 14, 2013 2:43 AM

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RGVickson@shaw.ca

Posts: 1,645
Registered: 12/1/07
Re: disjunctive constraints in integer linear programming
Posted: Apr 12, 2013 3:56 AM
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On Thursday, April 11, 2013 12:24:57 PM UTC-7, d.inf...@gmail.com wrote:
> I have an integer linear programming problem as follows:
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> The constraints are either
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> x >= 0
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> y = u
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> z = x + v
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> or
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> x < 0
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> y = u - x
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> z = v
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> where y, z, u, v range over non-negative integers. There are other unrelated constraints associated with u, v, y, z.
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> What's the most simple way to encode the disjunctive case? Does any linear encoding where all co-efficients are -1, 0, 1 exist?
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> Thank you!


If x is real valued (or even rational) the strict inequality x < 0 cannot be modelled exactly; instead, one must replace it by x <= =e, where e > 0 is "small". If x is also integer (<>0) then, of course, x < 0 is the same as x <= -1, so that is again OK.



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