Declare decision variables

A decision variable is a quantity the service chooses. num_var() declares one that can take any value between its bounds, int_var() one that must be a whole number, and bin_var() a yes-or-no decision, which is either 0 or 1.

Usage

num_var(
  m,
  name,
  lower = -Inf,
  upper = Inf,
  length = 1,
  start = 0,
  semi = FALSE,
  n
)

int_var(
  m,
  name,
  lower = -Inf,
  upper = Inf,
  length = 1,
  start = 0,
  semi = FALSE,
  n
)

bin_var(m, name, length = 1, start = 0, n)

add_var(
  m,
  name,
  lower = -Inf,
  upper = Inf,
  length = 1,
  start = 0,
  domain = c("num", "int", "bin"),
  semi = FALSE,
  n
)

Arguments

m

A model().

name

The variable's name, used for it in the answer. It must be unique within the model.

lower, upper

The smallest and the largest value allowed. -Inf and Inf, the defaults, leave that side open.

length

How many variables to declare under this name.

start

The value the service's search starts from (see set_start()).

semi

Whether the variable may also be 0 when 0 lies outside its bounds (see above).

n

The former name of length, still accepted for now, with a warning.

domain

For add_var(): "num", "int" or "bin", to declare the variable as num_var(), int_var() or bin_var() would.

Value

The variable, an expression with length elements.

add_var() returns the model, invisibly.

Details

Each returns the variable, for use in expressions such as 50 * tables + 20 * chairs; m$tables retrieves it from the model too. add_var() declares a variable in the same way but returns the model, for use in a pipe (see model()).

With semi = TRUE, the variable is either 0 or between its bounds, never in between: a delivery of either nothing or 10 to 25 units is int_var(m, "delivery", lower = 10, upper = 25, semi = TRUE). Solvers for mixed-integer programs call such a variable semi-continuous, or semi-integer when it must be a whole number. The bounds must then be finite. When 0 already lies between them, semi changes nothing. active() is 1 when such a variable is not 0, which is how a fixed fee per delivery is written: fee * active(delivery).

With length greater than 1, one call declares that many variables under one name, and they behave like an R vector: x[3] is the third, arithmetic works element by element, and sum(x) adds them up. lower, upper and start may then be vectors with one value per element. In the answer the elements are named "x[1]", "x[2]", and so on; a single variable is named "x".

Examples

m <- model()
tables <- int_var(m, "tables", lower = 0)
take   <- bin_var(m, "take", length = 6)                    # six yes-or-no decisions
share  <- num_var(m, "share", lower = 0, upper = 1, length = 3)
sum(share)
#> (share[1] + share[2] + share[3])
take[2]
#> take[2]
delivery <- int_var(m, "delivery", lower = 10, upper = 25, semi = TRUE)   # none, or 10 to 25