The average over the scenarios

expectation(x) is the average of x over the model's scenarios: an estimate of its expected value. It turns a random expression into a single number, which can be used in the objective or in a constraint.

Usage

expectation(x)

Arguments

x

A random expression (see is_random()).

Value

An expression of the same length as x, no longer random.

Details

Minimizing an average makes the typical scenario good, and says little about the bad ones; cvar() looks at those instead. For a vector x, each element is averaged separately.

Examples

m <- model()
stock  <- num_var(m, "stock", lower = 0, upper = 200)
demand <- rand_var(m, "demand", normal(100, 15))
set_scenarios(m, 512, seed = 42)
shortfall <- max(demand - stock, 0)        # units short, in each scenario
minimize(m, 3 * stock + 10 * expectation(shortfall))