Integer Linear Programing - Using Binary Vaviables

Some tips about ILP transformaion using binary variables.

- Logic
  - Conjunction, A and B, A∩B => a+b = 2
  - Disjunction, A or B, A∪B => a+b ≥ 1
  - if A then B, A→B, ~A∪B => a ≤ b
  - A if only if B, A↔B => a = b
  - A = ~B => a+b = 1
  - C = A∩B => c ≤ a, c ≤ b, c ≥ a+b-1
  - C = A∪B => c ≥ a, c ≥ b, c ≤ a+b

Integer Linear Programming - Duality

Main Resource: Applied Mathematical Programming by Bradley, Hax, and Magnanti (Addison-Wesley, 1977), provided by MIT

A canonical form of duality of an Integer Linear Programming problem: