In PulP modeling, I have an integer variable s that can take on values 0, 1, or 2. I want a binary indicator variable y such that y=1 if s=0 or s=2, and y=0 if s=1.
I tried defining three binary variables z1, z2, and y, and setting up these constraints:
z1 <= s <= 2 * z1
2*z2 <= s
s < 2*z2 + 2
y = z1 * (1 - z2)
Essentially, z1=1 means s>0, and z2=0 means s<2. Hence y=1 means s=1, and y=0 means s=0 or 2.
However, this makes y non-linear, since it is a product of 2 variables.
Is there a way to define y using only linear constraints?
My suggestion sticks with constraint types available to Linear Programming. Therefore, non-linear constraints and modulo operators are not available.
You could introduce y and s1 as binary variables.
The constraints:
y == 1 - s + 2*s1
0 <= y <= 1
0 <= s1 <= 1
Three cases for s:
s = 0: s1 = 0, y = 1
s = 1: s1 = 0, y = 0
s = 2: s1 = 1, y = 1