If condition in Integer Programming

Question

I am solving an integer programming problem with the condition

if a=0 then b=0 else b=1

where a is integer while b is binary

I looked on previous question similar to this but could not find solution. please help to define constraint equation in integer programming for above conditions.

a is integer while b is binary – shariq mohammad Dec 05 '16 at 17:33 — shariq mohammad, Dec 05 '16 at 17:33

score 1 · Answer 1 · answered Dec 05 '16 at 17:58

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The first constraint is easy: a=0 ⇒ b=0 can be written as a ≥ b. The second constraint (a ≥ 1 ⇒ b=1) is more complicated. If a ≤ M where M is relatively small, then you can write this as M ⋅ b ≥ a. Otherwise, you will need to use a solver feature called indicator constraints.

answered Dec 05 '16 at 17:58

Greg Glockner

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thanks for reply , constraint a ≥ b does not hold true if a is negative integer – shariq mohammad Dec 05 '16 at 18:04
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Typically, there are no negative integers in Integer Programming. A lower bound of zero is assumed if not stated otherwise. – mattmilten Dec 06 '16 at 06:37

score 1 · Answer 2 · answered Dec 14 '16 at 16:13

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Use these two constraints:

a<=bM
b<=aM

where M is a big number (M>a). When a=0, the 1st constraint is redundant, 2nd one gonna impose b=0. If a>0 then 2nd constraint is redundant, but the 1st one gonna force the b gets the value of 1 (if M is enough big).

answered Dec 14 '16 at 16:13

Faraz Ramtin

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Since b is binary, you should simplify the second constraint to b <= a. – Greg Glockner Dec 15 '16 at 16:07
Greg, It was my misreading of your previous answer, I though the (dot) you put after M is a colon. Basically, I just anwsered what you already did.M is not necessary in the 2nd constraint as you mentioned. – Faraz Ramtin Dec 16 '16 at 20:36

If condition in Integer Programming

2 Answers2