(1) |

The "Big-M" relaxation for the previous disjunction can be defined as follows:

(2) | |

(3) | |

(4) |

Where Mi is a parameter whose value is large enough such that if yi = 0, then (2) becomes redundant. If yi = 1 then constraint aiTx <= bi must be satisfied. The tightest value for Mi is given by:

Example:

As an illustration, consider the following disjunction:

(5) |

The feasible region for the disjunction is:

The Big-M relaxation of (5) is given by:

(BM1) |

The feasible region of the BigM relaxation is: