In dirkdegel/simplexR: Simplex Algorithm

optimality_check <- function(t) {
  if (min(t[nrow(t), 1:(ncol(t) - 1)]) < 0) {
    return(FALSE) # not optimal
  }
  else {
    return(TRUE) # optimal
  }
}

get_pivot_column <- function(t) { # pricing
  return(which.min(t[nrow(t), 1:(ncol(t) - 1)]))
}

get_pivot_row <- function(t, pivot_column) {
  lhs <- t[1:(nrow(t) - 1), pivot_column]
  rhs <- t[1:(nrow(t) - 1), ncol(t)]
  if (max(lhs) < 0) {
    print("Problem is unbounded -> stop execution")
    # break
    return(-1)
  }
  else {
    theta <- vector(mode = "double", length = (nrow(t) - 1))
    for (i in 1:(nrow(t) - 1)) {
      if (lhs[i] > 0) {
        theta[i] <- rhs[i] / lhs[i]
      } else {
        theta[i] <- Inf
      }
    }
    return(which.min(theta))
  }
}

pivot <- function(t, pivot_row, pivot_column) {
  pivot_element <- t[pivot_row, pivot_column]
  t[pivot_row, ] <- t[pivot_row, ] / pivot_element
  for (r in 1:nrow(t)) {
    if (r != pivot_row) {
      t[r, ] <- t[r, ] - t[r, pivot_column] * t[pivot_row, ]
    }
  }
  return(t)
}

simplex <- function(tableau, max_iter = 100) {
  print("Initial Tableau (Tableau 0)")
  print(tableau)
  iter <- 1
  while (!optimality_check(tableau) & iter < max_iter) {
    print("----------------------------------------------")
    print(paste("Iteration", iter))
    print("----------------------------------------------")
    pivot_column <- get_pivot_column(tableau)
    print(paste("Pivot column:", pivot_column))
    pivot_row <- get_pivot_row(tableau, pivot_column)
    if (pivot_row == -1) {
      break()
    }
    print(paste("Pivot row:", pivot_row))
    tableau <- pivot(tableau, pivot_row, pivot_column)
    print(paste("New tableau at the end of iteration", iter))
    print(tableau)
    iter <- iter + 1
  }
  print("----------------------------------------------")
  print("Status: End")
  print("----------------------------------------------")
}

simplexR <- function(A, b, c, sense = 1, relation = rep("<=", length(b)), max_iter = 100) {
  tableau <- construct_tableau(A, b, c, sense, relation)
  simplex(tableau = tableau, max_iter = max_iter)
}