Integer Linear programming formulation if then condition

Question

I want to create constraints such that I can implement the following condition:

Let A be an integer variable>= 0 with an upper bound of 12

I want to introduce the following variable B also an integer:

if A = 1 then B = 0 else B = A

• D.W.: Have you looked at other questions in the integer-programming tag, and the questions in the related list? Have you looked at cs.stackexchange.com/questions/51025/… and cs.stackexchange.com/q/12102/755 and cs.stackexchange.com/q/76549/755? I suspect you'll find that the question is answered there. Also please edit your question to indicate whether you know of an upper bound on A or not.
• Tobias Dekker: I checked all these topics but could not found a solution for this question. Most of the answers are about boolean variables and not integers, which makes it more complicated.
• user1543037: You need Boolean algebra blog.adamfurmanek.pl/2015/08/22/ilp-part-1 + multiplication blog.adamfurmanek.pl/2015/08/29/ilp-part-2 + comparisons blog.adamfurmanek.pl/2015/09/12/ilp-part-4 + conditional operator blog.adamfurmanek.pl/2015/10/17/ilp-part-9 and you can do whatever you like.
• D.W.: The first question I linked is about integers. The second also discusses about integers; see "cast to boolean". There are also other questions in the tag that are about integers. I suggest spending a little more time to read through that material and learn about the typical techniques used there, and I suspect that will give you some ideas how to handle your particular situation.

Answer 1

you can introduce a binary variable z verifying the following constraints :

• (A-1) <= 12*z

• z<= 0.5*A

• -(1-z)*12 <= B-A <= (1-z)*12

• -12*z <= B <= 12*z