1. Gomory’s cutting plane algorithm for integer programming
Prepared by Shin-ichi Tanigawa
(Revised by DA, June )

2. Rounding does not give any useful result

3. Solve the following Integer Program

4. We first solve the LP-relaxation

5. Optimize using primal simplex method

6. The optimal solution is fractional

7. Generating an objective row cut
(1)
(weakening)
(2)
(for integers)
(2) - (1)
(substitute for slacks)

8. The new cut is added to the optimum dictionary

9. Re-optimize using dual simplex method

10. A new fractional solution has been found

11. Generating a constraint row cut
(1)
(2)
(2) – (1)

12. The new cut is inserted into the optimum dictionary

13. Re-optimize using dual simplex method

14. The new optimum solution is integral