How to replicate excel solver in R

Question

I used excel solver to solve an optimization problem, and I am trying to replicate it in R.

I found many packages like optim, ROI etc., but it seems all of them only

Answer 1

You need to construct a vector for the objective function and a constraint matrix, finally solving with one of the R LP solvers:

library(lpSolve)
costs <- matrix(c(9, 10, 11, 4, 5, 10, 1, 3, 5, 7, 5, 4), nrow=3)
nr <- nrow(costs)
nc <- ncol(costs)
columns <- t(sapply(1:nc, function(x) rep(c(0, 1, 0), c(nr*(x-1), nr, nr*(nc-x)))))
rows <- t(sapply(1:nr, function(x) rep(rep(c(0, 1, 0), c(x-1, 1, nr-x)), nc)))
mod <- lp("max", as.vector(costs), rbind(columns, rows), "<=", rep(1, nr+nc), binary.vec=rep(TRUE, nr*nc))

Now you can grab the solution and the objective function:

mod$objval
# [1] 27
matrix(mod$solution, nrow=nr)
#      [,1] [,2] [,3] [,4]
# [1,]    0    0    0    1
# [2,]    1    0    0    0
# [3,]    0    1    0    0

Note that functions like optim are not well suited for this problem both because they don't consider matrices of constraints and also because they cannot limit to binary variable values.