DATA 604 - Week 7 Assignment

For this assignment, the pharmacy queue model created in Week 3 was extended by incorporating more realistic operational features. In a typical pharmacy environment, customer arrivals fluctuate throughout the day, and staffing levels are adjusted to handle busy periods.

This Week 7 model builds upon the pharmacy queue simulation developed in the Week 3 assignment. The original model assumed a constant arrival rate and a single pharmacist, while the updated model introduces variable arrival rates, additional service steps, and a dynamic staffing schedule.

In this model, a rush hour period between 4 PM and 7 PM was introduced. During this time, customer arrival rates increase significantly, and additional pharmacists are scheduled to manage the increased workload. The objective of this simulation is to evaluate how these operational changes affect system performance, particularly waiting times and overall service efficiency.

Load all required packages

The necessary R libraries are loaded to support data processing, visualization, and modeling tasks.
Loading these packages ensures all required functions are available for the analysis.

library(simmer)

library(dplyr)

library(ggplot2)

Define Pharmacist Schedule

set.seed(123)

# ---- Pharmacist schedule (more staff during rush hour 4–7 PM) ----
pharmacist_schedule <- schedule(
  t = c(0, 960, 1140),
  values = c(1, 2, 1),
  period = 1440
)

# ---- Customer trajectory ----
cust_traj <- trajectory("patient path") %>%
  seize("pharmacist", 1) %>%
  timeout(function() rnorm(1, mean = 4, sd = 1)) %>%   # prescription review
  timeout(function() rnorm(1, mean = 1, sd = 0.3)) %>% # verification step
  release("pharmacist", 1)

run_scenario <- function(name, gen_dist, until_min = 1440){

env <- simmer(name) %>%
add_resource("pharmacist", capacity = pharmacist_schedule) %>%
add_generator("patient", cust_traj, distribution = gen_dist)

env %>% run(until = until_min)

arr <- get_mon_arrivals(env)

summ <- arr %>%
mutate(
sojourn = end_time - start_time,
wait = pmax(sojourn - activity_time, 0)
) %>%
summarise(
customers = n(),
avg_wait_min = mean(wait),
p95_wait_min = quantile(wait,0.95),
avg_system_min = mean(sojourn),
avg_service_min = mean(activity_time)
) %>%
mutate(scenario=name,.before=1)

list(env=env,arrivals=arr,summary=summ)
}

# ---- Baseline scenario ----
baseline <- run_scenario(
name="Baseline Pharmacy System",
gen_dist=function()6
)

# ---- Rush hour scenario (4 PM – 7 PM) ----
rush_times <- c(
seq(0,959,by=6),
seq(960,1139,by=2),
seq(1140,1440,by=6)
)

rush_dist <- at(rush_times)

rush <- run_scenario(
name="Pharmacy Rush Hour 4PM–7PM",
gen_dist=rush_dist
)

resource_data <- get_mon_resources(rush$env)

comparison <- bind_rows(baseline$summary,rush$summary) %>%
dplyr::select(scenario,customers,avg_wait_min,p95_wait_min,
avg_system_min,avg_service_min)

knitr::kable(comparison)

ggplot(comparison,aes(x=scenario,y=avg_wait_min))+
geom_bar(stat="identity")+
labs(
title="Average Waiting Time: Normal vs Rush Hour",
x="Scenario",
y="Average Waiting Time (Minutes)"
)+
theme_minimal()

ggplot(resource_data, aes(x = time, y = queue)) +
  geom_line() +
  labs(
    title = "Pharmacy Queue Length Over Time",
    x = "Simulation Time (minutes)",
    y = "Number of Patients Waiting"
  ) +
  theme_minimal()