A similar problem is one in which some minimum level is required before an activity is undertaken. For example, a firm may have to buy a minimum quantity of at least 50 units of a certain product. Let x be the number of units bought. Then either x = 0 or x 50.
This situation can be formulated with a zero/one integer variable y by using constraints as follows:
where M is penalty cost (a very large number).
Note that if y = 0, then, by the first constraint, x must be 0. If y = 1, then, by the second constraint, x must be at least 50.