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

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