Try our new documentation site.


diet.R


# Copyright 2023, Gurobi Optimization, LLC
#
# Solve the classic diet model, showing how to add constraints
# to an existing model.

library(Matrix)
library(gurobi)

# display results
printSolution <- function(model, res, nCategories, nFoods) {
  if (res$status == 'OPTIMAL') {
    cat('\nCost: ',res$objval,'\nBuy:\n')
    for (j in nCategories + 1:nFoods) {
      if (res$x[j] > 1e-4) {
        cat(format(model$varnames[j],justify='left',width=10),':',
            format(res$x[j],justify='right',width=10,nsmall=2),'\n')
      }
    }
    cat('\nNutrition:\n')
    for (j in 1:nCategories) {
      cat(format(model$varnames[j],justify='left',width=10),':',
          format(res$x[j],justify='right',width=10,nsmall=2),'\n')
    }
  } else {
    cat('No solution\n')
  }
}

# define primitive data
Categories      <- c('calories', 'protein', 'fat', 'sodium')
nCategories     <- length(Categories)
minNutrition    <- c(     1800 ,       91 ,    0 ,       0 )
maxNutrition    <- c(     2200 ,      Inf ,   65 ,    1779 )

Foods           <- c('hamburger', 'chicken', 'hot dog', 'fries', 'macaroni',
                     'pizza', 'salad', 'milk', 'ice cream')
nFoods          <- length(Foods)
cost            <- c(2.49, 2.89, 1.50, 1.89, 2.09, 1.99, 2.49, 0.89, 1.59)
nutritionValues <- c( 410, 24, 26 ,  730,
                      420, 32, 10 , 1190,
                      560, 20, 32 , 1800,
                      380,  4, 19 ,  270,
                      320, 12, 10 ,  930,
                      320, 15, 12 ,  820,
                      320, 31, 12 , 1230,
                      100,  8, 2.5,  125,
                      330,  8, 10 ,  180 )
# Build model
model     <- list()
model$A   <- spMatrix(nCategories, nCategories + nFoods,
               i = c(mapply(rep,1:4,1+nFoods)),
               j = c(1, (nCategories+1):(nCategories+nFoods),
                     2, (nCategories+1):(nCategories+nFoods),
                     3, (nCategories+1):(nCategories+nFoods),
                     4, (nCategories+1):(nCategories+nFoods) ),
               x = c(-1.0, nutritionValues[1 + nCategories*(0:(nFoods-1))],
                     -1.0, nutritionValues[2 + nCategories*(0:(nFoods-1))],
                     -1.0, nutritionValues[3 + nCategories*(0:(nFoods-1))],
                     -1.0, nutritionValues[4 + nCategories*(0:(nFoods-1))] ))
model$obj         <- c(rep(0, nCategories), cost)
model$lb          <- c(minNutrition, rep(0, nFoods))
model$ub          <- c(maxNutrition, rep(Inf, nFoods))
model$varnames    <- c(Categories, Foods)
model$rhs         <- rep(0,nCategories)
model$sense       <- rep('=',nCategories)
model$constrnames <- Categories
model$modelname   <- 'diet'
model$modelsense  <- 'min'

# Optimize
res <- gurobi(model)
printSolution(model, res, nCategories, nFoods)

# Adding constraint: at most 6 servings of dairy
# this is the matrix part of the constraint
B <- spMatrix(1, nCategories + nFoods,
              i = rep(1,2),
              j = (nCategories+c(8,9)),
              x = rep(1,2))
# append B to A
model$A           <- rbind(model$A,       B)
# extend row-related vectors
model$constrnames <- c(model$constrnames, 'limit_dairy')
model$rhs         <- c(model$rhs,         6)
model$sense       <- c(model$sense,       '<')

# Optimize
res <- gurobi(model)
printSolution(model, res, nCategories, nFoods)

# Clear space
rm(res, model)

Try Gurobi for Free

Choose the evaluation license that fits you best, and start working with our Expert Team for technical guidance and support.

Evaluation License
Get a free, full-featured license of the Gurobi Optimizer to experience the performance, support, benchmarking and tuning services we provide as part of our product offering.
Academic License
Gurobi supports the teaching and use of optimization within academic institutions. We offer free, full-featured copies of Gurobi for use in class, and for research.
Cloud Trial

Request free trial hours, so you can see how quickly and easily a model can be solved on the cloud.

Search