Part of a model's data is often unknown when the decision has to be made: demand, prices, yields, arrival times. Declare that data as random variables carrying distributions, and the model is solved over a sample of scenarios drawn from them.
Details
Two rules describe the whole surface:
A variable declared with
rand_var()is a random variable, not a decision variable. Every use of it references the same sample.An expression containing a random variable is itself random, and cannot serve as an objective or a constraint until an aggregator reduces it over the scenarios:
expectation()for the mean,cvar()for the tail,prob()for a chance constraint.
set_scenarios() sets how many scenarios are drawn and from which seed.
Both belong to the model, so repeated solves see the same sample. The
drawing happens in the service, from the model's own seed — R's
set.seed() plays no role here.
Examples
if (FALSE) { # \dontrun{
# Order x units at 3 apiece against a demand learned later, pay 10 per unit
# of shortfall, and meet demand in at least 90% of scenarios:
m <- model()
x <- num_var(m, "x", 0, 200)
demand <- rand_var(m, "demand", normal(100, 15))
set_scenarios(m, 512, seed = 42)
minimize(m, 3 * x + 10 * expectation(max(demand - x, 0)))
add(m, prob(demand - x <= 0) >= 0.9)
solve(m)$solution
} # }