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