Skip to contents

The largest, the smallest and a quantile over the scenarios

Source: R/stochastic.R
scenario_max.Rd

The value a quantity takes in one particular scenario:

Usage

scenario_max(x)

scenario_min(x)

scenario_quantile(x, prob)

Arguments

x

A random expression (see is_random()).

prob

A number above 0 and at most 1. It cannot depend on a decision.

Value

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

Details

  • scenario_max(x) is the largest value of x among the scenarios. Minimizing it makes the worst scenario as good as possible.

  • scenario_min(x) is the smallest. Maximizing it does the same for a quantity where large is good, such as a profit.

  • scenario_quantile(x, prob) is the value that the share prob of the scenarios stays at or below. With n_scenarios scenarios it is the ceiling(prob * n_scenarios)-th smallest value, which is what quantile(x, prob, type = 1) returns for a sample. scenario_quantile(x, 1) is scenario_max(x). For a cost it is also known as the value at risk; cvar() at the same level is the average of the values above it.

These are different from max(), min() and quantile(). max(a, b) compares two expressions within each scenario, and the result is still random. scenario_max(x) compares the values of one expression across the scenarios, and the result is a single number.

A single scenario decides the largest or smallest value, so it changes more from one sample of scenarios to the next than an average does, and a larger sample usually contains a more extreme scenario. Check a solution found with these on new scenarios, with resample().

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)
cost <- 3 * stock + 10 * max(demand - stock, 0)
minimize(m, scenario_max(cost))                  # the cost of the worst scenario
add(m, scenario_quantile(cost, 0.95) <= 500)     # at most 500 in 95% of scenarios