Whether a variable is in use

active(x) is 1 when the variable x is not 0, and 0 when it is. It is meant for a variable declared with semi = TRUE (see num_var()), which is either 0 or between its bounds: a delivery of either nothing or 10 to 25 units, say. A fee charged for every delivery that takes place is then fee * active(delivery), and a limit on how many deliveries take place is a constraint on sum(active(delivery)).

Usage

active(x)

Arguments

x

A decision variable, or elements of one, such as x[2:3].

Value

An expression with one 0/1 element per element of x.

Details

For such a variable, a model that is otherwise linear is still solved to a proven optimum. On any other variable, active(x) means the same, 1 when x is not 0, but the model is then solved by a search.

Examples

m <- model()
delivery <- int_var(m, "delivery", lower = 10, upper = 25, length = 3, semi = TRUE)
fee <- c(30, 10, 5)
minimize(m, sum(c(1, 2, 3) * delivery) + sum(fee * active(delivery)))
add(m, sum(delivery) >= 40)                     # the customer needs 40 units
add(m, sum(active(delivery)) <= 2)              # at most two deliveries