I think you have two options - turn them alphabetical, or make a factor.
library(tidyverse)
dat <- tribble(
~Scenario, ~Iteration, ~LB, ~UB, ~Eps,
"BP = 0, BI = 50", 1, 1, 4.60880829 ,3.60880829,
"BP = 0, BI = 50", 2, 4.60880829 ,4.60880829, 0,
"BP = 0, BI = 50", 3, 4.60880829 ,4.60880829, 0,
"BP = 0, BI = 100", 1, 1, 7.294041451 ,6.294041451,
"BP = 0, BI = 100", 2, 7.292746114 ,7.294041451, 0.00017762,
"BP = 0, BI = 100", 3, 7.292746114 ,7.294041451, 0.00017762,
"BP = 0, BI = 150", 1, 1, 10.16450777 ,9.164507772,
"BP = 0, BI = 150", 2, 10.1619171 ,10.16450777, 0.000254939,
"BP = 0, BI = 150", 3, 10.1619171 ,10.16450777, 0.000254939,
"BP = 0, BI = 200", 1, 1, 12.89248705 ,11.89248705,
"BP = 0, BI = 200", 2, 12.89248705 ,12.89248705, 0,
"BP = 0, BI = 200", 3, 12.89248705 ,12.89248705, 0
)
dat %>%
mutate(Scenario = str_replace_all(Scenario, "BI = 50", "BI = 050")) %>%
ggplot(aes(x = Iteration)) +
geom_line(aes(y = LB), color = "cornflowerblue", lwd = 0.9) +
geom_line(aes(y = UB),
color = "chocolate1",
linetype = "twodash",
lwd = 0.9) +
facet_wrap( ~ Scenario, ncol = 4)

dat %>%
mutate(Scenario = fct_inorder(Scenario)) %>%
ggplot(aes(x = Iteration)) +
geom_line(aes(y = LB), color = "cornflowerblue", lwd = 0.9) +
geom_line(aes(y = UB),
color = "chocolate1",
linetype = "twodash",
lwd = 0.9) +
facet_wrap( ~ Scenario, ncol = 4)

Created on 2022-06-21 by the reprex package (v2.0.1)