Projects A, B, C, D, ... with associated binary variables a, b, c, d, ... which are 1 if we decide to do the project and 0 if we decide not to do the project.
| At most N of A, B, C,... |
a + b + c + ...≤ N |
| At least N of A, B, C,... |
a + b + c + ...≥ N |
| Exactly N of A, B, C,... |
a + b + c + ... = N |
| If A then B |
b ≥ a |
| Not B |
b- = 1-b |
| If A then not B |
a + b ≤ 1 |
| If not A then B |
a + b ≥ 1 |
| If A then B, and if B then A |
a = b |
| If A then B and C; A only if B and C |
b ≥ a and c ≥ a |
|
or alternatively: a ≤ (b + c)/2 |
| If A then B or C |
b + c ≥ a |
| If B or C then A |
a ≥ b and a ≥ c |
| |
or alternatively: a ≥
· (b+c) |
| If B and C then A |
a ≥ b + c - 1 |
| If two or more of B, C, D or E then A |
a ≥
· (b + c + d + e - 1) |
| If M or more of N projects (B, C, D, ...) then A |
a ≥
| b + c + d + ... -M +1 |
| N-M+1 |
|
