Gomory’s cutting plane algorithm for integer programming

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Presentation transcript:

Gomory’s cutting plane algorithm for integer programming Prepared by Shin-ichi Tanigawa (Revised by DA, June 14 2012)

Rounding does not give any useful result

Solve the following Integer Program

We first solve the LP-relaxation

Optimize using primal simplex method

The optimal solution is fractional

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

The new cut is added to the optimum dictionary

Re-optimize using dual simplex method

A new fractional solution has been found

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

The new cut is inserted into the optimum dictionary

Re-optimize using dual simplex method

The new optimum solution is integral

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