Client for the Quicopt Optimization Service • quicopt

quicopt lets you write an optimization model in R and solve it with the Quicopt service. You state what you can decide, what you want to achieve, and which conditions have to hold, and the service finds the best decision. Nothing needs to be installed besides the package: the model is sent to the service, and the answer comes back as an R list.

quicopt is built in particular for decisions under uncertainty. When part of the data, such as demand, prices or travel times, is not known in advance, you describe it by a probability distribution or by observations in a data frame, and the service finds the decision that does best across many possible outcomes.

Install

install.packages("quicopt", repos = c("https://quicopt.r-universe.dev",
                                      "https://cloud.r-project.org"))

or from the source repository, which needs no compiler either, since the package is written in plain R:

pak::pak("Quicopt/quicopt-r")

A first model

A workshop makes tables and chairs. A table earns 50 and takes 3 hours of carpentry, a chair earns 20 and takes 1 hour. There are 41 hours available and wood for 18 pieces. How many of each should it make?

library(quicopt)

m <- model()
tables <- int_var(m, "tables", lower = 0)
chairs <- int_var(m, "chairs", lower = 0)

maximize(m, 50 * tables + 20 * chairs)    # profit
add(m, 3 * tables + chairs <= 41)         # hours of carpentry
add(m, tables + chairs <= 18)             # wood

res <- solve(m)
res$solution                              # 12 tables, 5 chairs
res$objective                             # a profit of 700

A decision under uncertainty

A shop orders stock at 3 per unit before it knows the day’s demand, which is roughly normal with mean 100 and standard deviation 15. Each unit of demand it cannot meet costs 10. The shop wants the lowest expected cost, and enough stock to meet demand on at least 90% of days:

m <- model()
stock  <- num_var(m, "stock", lower = 0, upper = 200)   # decided now
demand <- rand_var(m, "demand", normal(100, 15))       # learned later
set_scenarios(m, 512, seed = 42)                       # 512 simulated days

minimize(m, 3 * stock + 10 * expectation(max(demand - stock, 0)))
add(m, prob(demand <= stock) >= 0.9)

res <- solve(m)
res$solution[["stock"]]                                # 118.7

The stock was chosen to work on those 512 simulated days. resample() checks it on new ones, and add(..., margin = 2) builds in a safety margin for what it finds. With observed history in a data frame instead of a distribution, set_empirical(m, history) makes each column a random variable and each row a scenario.

Minimum loads, fees and groups

A delivery is often either nothing or at least a minimum load: semi = TRUE says so, and active() is 1 when such a delivery takes place, so a fee per delivery is one term. holds() charges a fee once a total reaches a level, and block() names the variables of one subproblem, such as one customer’s deliveries. Three warehouses supply three customers:

demand  <- c(40, 30, 20)                                # units, customers 1 to 3
price   <- rbind(c(1, 3, 4), c(3, 1, 3), c(4, 2, 1))    # per unit, price[warehouse, customer]
opening <- c(60, 50, 40)                                # fee of warehouses 1 to 3

m <- model()
ship <- int_var(m, "ship", lower = 10, upper = 25, length = 9, semi = TRUE)   # none, or 10 to 25 units
to   <- function(c) ship[3 * (c - 1) + 1:3]             # to customer c, from warehouses 1 to 3
from <- function(w) ship[w + c(0, 3, 6)]                # from warehouse w, to customers 1 to 3
for (c in 1:3) {
  block(m, paste0("customer_", c), to(c))
  add(m, sum(to(c)) >= demand[c])
}
sent <- c(sum(from(1)), sum(from(2)), sum(from(3)))     # units leaving each warehouse
minimize(m, sum(as.vector(price) * ship)                # price per unit
            + 5 * sum(active(ship))                     # 5 per delivery
            + sum(opening * holds(sent >= 1)))          # a warehouse that ships pays its fee

res <- solve(m)
res$objective                                           # 300: warehouse 2 stays closed

part_var() splits items into groups, such as people into teams, read through part_of() and size_of().

Learn more

Get started: variables, objectives, constraints and the answer, step by step.
Deciding before the data arrives: random variables, expected costs, chance constraints, and checking a solution on new scenarios.
Orderings and assignments: routes, schedules and assignments.
Reference: every function.

quicopt

Install

A first model

A decision under uncertainty

Minimum loads, fees and groups

Learn more

License