Suppose the following disjunction with i terms:

(1)

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

	(2)
	(3)
	(4)

where M_i is a parameter whose value is large enough such that if y_i = 0, then (2) becomes redundant. If y_i = 1 then constraint a_i^Tx <= b_i must be satisfied. The tightest value for M_i 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: