OMPR (Optimization Modeling Package) is a DSL to model and solve Mixed Integer Linear Programs. It is inspired by the excellent Jump project in Julia.

Here are some problems you could solve with this package:

• What is the cost minimal way to visit a set of clients and return home afterwards?
• What is the optimal conference time table subject to certain constraints (e.g. availability of a projector)?
• Sudokus

The Wikipedia article gives a good starting point if you would like to learn more about the topic.

I am always happy to get bug reports or feedback.

## Install

### CRAN

install.packages("ompr")
install.packages("ompr.roi")

### Development version

To install the current development version use devtools:

devtools::install_github("dirkschumacher/ompr")
devtools::install_github("dirkschumacher/ompr.roi")

## Available solver bindings

Package Description Build Linux Build Windows Test coverage
ompr.roi Bindings to ROI (GLPK, Symphony, CPLEX etc.)

## A simple example:

library(dplyr)
library(ROI)
library(ROI.plugin.glpk)
library(ompr)
library(ompr.roi)

result <- MIPModel() %>%
add_variable(y, type = "continuous", lb = 0) %>%
set_bounds(x, lb = 0) %>%
set_objective(x + y, "max") %>%
add_constraint(x + y <= 11.25) %>%
solve_model(with_ROI(solver = "glpk"))
get_solution(result, x)
get_solution(result, y)

## API

These functions currently form the public API. More detailed docs can be found in the package function docs or on the website

### DSL

• MIPModel() create an empty mixed integer linear model (the old way)
• MILPModel() create an empty mixed integer linear model (an alternative way; experimental, especially suitable for large models)
• add_variable() adds variables to a model
• set_objective() sets the objective function of a model
• set_bounds() sets bounds of variables
• add_constraint() add constraints
• solve_model() solves a model with a given solver
• get_solution() returns the column solution (primal or dual) of a solved model for a given variable or group of variables
• get_row_duals() returns the row duals of a solution (only if it is an LP)
• get_column_duals() returns the column duals of a solution (only if it is an LP)

### Backends

There are currently two backends. A backend is the function that initializes an empty model.

• MIPModel() is the standard MILP Model
• MILPModel() is another backend specifically optimized for linear models and is about 1000 times faster than MIPModel(). It has slightly different semantics, as it is vectorized. Currently experimental.

### Solver

Solvers are in different packages. ompr.ROI uses the ROI package which offers support for all kinds of solvers.

• with_ROI(solver = "glpk") solve the model with GLPK. Install ROI.plugin.glpk
• with_ROI(solver = "symphony") solve the model with Symphony. Install ROI.plugin.symphony
• with_ROI(solver = "cplex") solve the model with CPLEX. Install ROI.plugin.cplex
• … See the ROI package for more plugins.

## Further Examples

Please take a look at the docs for bigger examples.

### Knapsack

library(dplyr)
library(ROI)
library(ROI.plugin.glpk)
library(ompr)
library(ompr.roi)
max_capacity <- 5
n <- 10
weights <- runif(n, max = max_capacity)
MIPModel() %>%
add_variable(x[i], i = 1:n, type = "binary") %>%
set_objective(sum_expr(weights[i] * x[i], i = 1:n), "max") %>%
add_constraint(sum_expr(weights[i] * x[i], i = 1:n) <= max_capacity) %>%
solve_model(with_ROI(solver = "glpk")) %>%
get_solution(x[i]) %>%
filter(value > 0)

### Bin Packing

An example of a more difficult model solved by symphony.

library(dplyr)
library(ROI)
library(ROI.plugin.symphony)
library(ompr)
library(ompr.roi)
max_bins <- 10
bin_size <- 3
n <- 10
weights <- runif(n, max = bin_size)
MIPModel() %>%
add_variable(y[i], i = 1:max_bins, type = "binary") %>%
add_variable(x[i, j], i = 1:max_bins, j = 1:n, type = "binary") %>%
set_objective(sum_expr(y[i], i = 1:max_bins), "min") %>%
add_constraint(sum_expr(weights[j] * x[i, j], j = 1:n) <= y[i] * bin_size, i = 1:max_bins) %>%
add_constraint(sum_expr(x[i, j], i = 1:max_bins) == 1, j = 1:n) %>%
solve_model(with_ROI(solver = "symphony", verbosity = 1)) %>%
get_solution(x[i, j]) %>%
filter(value > 0) %>%
arrange(i)