DATA 604 - Week 11 Assignment

The Simio BBQ Smoke Pit is an up-and-coming local restaurant. It features a variety of BBQ smoked meats and classic sides. This makeshift cookout is nestled in an older, renovated building in a bustling downtown block. Due to size constraints, this is a carry-out only establishment. However, as Simio BBQ Smoke Pit continues to grow in popularity, customers are facing longer wait times due to product outages and a constrained labor force. To keep up with demand, the restaurant needs help determining what new policies to enact to resolve their service bottlenecks.

Due to the long smoking time required for the BBQ meats and lengthy cook time for some sides, the restaurant is struggling to keep a reasonable level of cooked food available. Having too little inventory will affect customer satisfaction. If food shortages occur too often, wait times could increase, causing customers to leave and losing potential business for the restaurant. On the other hand, creating excess inventory could accrue extra costs. The meat is expensive and excess uneaten food must be disposed of at the end of the day.

The challenge is to balance staffing and food production to maximize profits and customer satisfaction. The restaurant is looking to investigate customer arrivals and ordering patterns, resource requirements, and food production rates. Simio BBQ Smoke Pit desires the best strategy to replenish each of the different food items on their menu. This replenishment strategy not only affects when and how much food to cook, but also how to allocate the cooked portions between the meal assembly stations and the holding cabinets. Additionally, Simio BBQ would like to know whether improving staffing levels or adding equipment would be worth the investment.

Identify:

Service bottlenecks in the current system

Staffing issues. Is any work shift or service station causing delays? The base model is available at BBQDemo1.zip

For this exercise, look for customized objects in the galleries available to make the scenario as real as possible. Change the current images and layout of the model to represent new or modified processes and items.

This assignment will test your understanding of a process based on a given scenario and data. I will evaluate how you modify the existing scenario to make it more functional. Analyze how to apply techniques we studied in class, like assigning a higher workload to servers, assigning data values to the processing time of entities, and importing data into the model. As well, how you manage workers and orders.

The exercise does not have a unique solution. I’ll evaluate how you interpret the process and suggest changes to it. Be creative and have fun!

Introduction

bbq <- read_excel("D:/Cuny_sps/Data_604/Assignment-11/Customer_Arrivals.xlsx")


kable(head(bbq), caption = "Customer Arrival Data (First 6 Rows)")

staff <- read_excel("D:/Cuny_sps/Data_604/Assignment-11/Work_Schedule.xlsx")

kable(head(staff), caption = "Work Schedule Data (First 6 Rows)")

bbq <- bbq %>%
mutate(
time = ymd_hms(`Time`)
) %>%
arrange(time)

cat("\nParsed times (first 5):\n")

Parsed times (first 5):

print(head(bbq$time))

[1] "2024-11-22 10:11:47 UTC" "2024-11-22 10:11:47 UTC"
[3] "2024-11-22 10:15:26 UTC" "2024-11-22 10:15:26 UTC"
[5] "2024-11-22 10:19:40 UTC" "2024-11-22 10:19:40 UTC"

bbq <- bbq %>%
mutate(
iat = c(2, as.numeric(diff(time), units = "mins")) # first arrival: 2 min
)

cat("\nInterarrival summary (minutes):\n")

Interarrival summary (minutes):

print(summary(bbq$iat))

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.0000  0.0000  0.0000  0.8112  0.9833 25.9000 

set.seed(123)

bbq <- bbq %>%
mutate(
svc_order = runif(n(), 2, 4), # 2–4 minutes
svc_meat = pmax(rnorm(n(), 8, 2), 3), # Normal(8,2), min 3 minutes
svc_sides = runif(n(), 1, 3) # 1–3 minutes
)

sample_fun <- function(x) {
force(x)
function() sample(x, size = 1, replace = TRUE)
}

iat_fun <- sample_fun(bbq$iat)
order_fun <- sample_fun(bbq$svc_order)
meat_fun <- sample_fun(bbq$svc_meat)
sides_fun <- sample_fun(bbq$svc_sides)

num_food <- sum(staff$Position == "Food Production")
num_cust <- sum(staff$Position == "Customer Service")

cat("\nNumber of workers (from schedule):\n")

Number of workers (from schedule):

cat("Food production:", num_food, "\n")

Food production: 3 

cat("Customer service:", num_cust, "\n\n")

Customer service: 2 

cust_traj <- trajectory("customer path") %>%
seize("order", 1) %>%
timeout(order_fun) %>%
release("order", 1) %>%

seize("meat", 1) %>%
timeout(meat_fun) %>%
release("meat", 1) %>%

seize("sides", 1) %>%
timeout(sides_fun) %>%
release("sides", 1)

sim_time <- 14 * 60 

env_base <- simmer("BBQ_base") %>%
add_resource("order", capacity = num_cust) %>%
add_resource("meat", capacity = num_food) %>%
add_resource("sides", capacity = num_food) %>%
add_generator("cust", cust_traj, iat_fun) %>%
run(until = sim_time)
env_base

simmer environment: BBQ_base | now: 840 | next: 840.745407187726
{ Monitor: in memory }
{ Resource: order | monitored: TRUE | server status: 2(2) | queue status: 385(Inf) }
{ Resource: meat | monitored: TRUE | server status: 3(3) | queue status: 245(Inf) }
{ Resource: sides | monitored: TRUE | server status: 0(3) | queue status: 0(Inf) }
{ Source: cust | monitored: 1 | n_generated: 954 }

res_base <- get_mon_resources(env_base) %>%
group_by(resource) %>%
summarise(
mean_util = mean(server/pmax(capacity,1)),
mean_queue = mean(queue),
max_queue = max(queue),
.groups = "drop"
)

cat("BASE SCENARIO – RESOURCE STATS:\n")

BASE SCENARIO – RESOURCE STATS:

library(knitr)

kable(res_base, digits = 2,
      col.names = c("Resource", "Mean Utilization", "Mean Queue", "Max Queue"),
      caption = "Base Scenario - Resource Performance Summary")

head(get_mon_arrivals(env_base))

   name start_time end_time activity_time finished replication
1 cust0  0.5666667 13.52178      12.95511     TRUE           1
2 cust1  0.5666667 15.42013      14.85347     TRUE           1
3 cust2  0.5666667 16.53766      12.20496     TRUE           1
4 cust4  1.2666667 24.05965      12.78500     TRUE           1
5 cust5  1.2666667 24.14213      12.91124     TRUE           1
6 cust3  0.5666667 24.67668      14.57692     TRUE           1

arr_base_raw<-get_mon_arrivals(env_base)
head(arr_base_raw)

   name start_time end_time activity_time finished replication
1 cust0  0.5666667 13.52178      12.95511     TRUE           1
2 cust1  0.5666667 15.42013      14.85347     TRUE           1
3 cust2  0.5666667 16.53766      12.20496     TRUE           1
4 cust4  1.2666667 24.05965      12.78500     TRUE           1
5 cust5  1.2666667 24.14213      12.91124     TRUE           1
6 cust3  0.5666667 24.67668      14.57692     TRUE           1

arr_base <- arr_base_raw %>%
mutate(
total_time = end_time - start_time,
waiting_time = total_time - activity_time
) %>%
summarise(
mean_wait = mean(waiting_time),
mean_total = mean(total_time)
)

cat("\nBASE SCENARIO – CUSTOMER STATS (minutes):\n")

BASE SCENARIO – CUSTOMER STATS (minutes):

print(arr_base)

  mean_wait mean_total
1  295.9712   308.7811

env_meat_plus <- simmer("BBQ_meat_plus") %>%
add_resource("order", capacity = num_cust) %>%
add_resource("meat", capacity = num_food + 1) %>% # <-- one extra worker
add_resource("sides", capacity = num_food) %>%
add_generator("cust", cust_traj, iat_fun) %>%
run(until = sim_time)

res_meat_plus <- get_mon_resources(env_meat_plus) %>%
group_by(resource) %>%
summarise(
mean_util = mean(server / pmax(capacity, 1)),
mean_queue = mean(queue),
max_queue = max(queue),
.groups = "drop"
)

cat("\nEXTRA MEAT WORKER – RESOURCE STATS:\n")

EXTRA MEAT WORKER – RESOURCE STATS:

library(dplyr)
library(knitr)
library(scales)

res_meat_plus_clean <- res_meat_plus %>%
  mutate(
    mean_util = percent(mean_util, accuracy = 0.1),
    mean_queue = round(mean_queue, 1),
    max_queue = round(max_queue, 0)
  )

kable(res_meat_plus_clean,
      col.names = c("Resource", "Utilization (%)", "Avg Queue Length", "Max Queue"),
      caption = "Scenario 1: Extra Meat Worker - Resource Performance Summary")

arr_meat_plus_raw <- get_mon_arrivals(env_meat_plus)

arr_meat_plus <- arr_meat_plus_raw %>%
mutate(
total_time = end_time - start_time,
waiting_time = total_time - activity_time
) %>%
summarise(
mean_wait = mean(waiting_time),
mean_total = mean(total_time)
)

cat("\nEXTRA MEAT WORKER – CUSTOMER STATS (minutes):\n")

EXTRA MEAT WORKER – CUSTOMER STATS (minutes):

print(arr_meat_plus)

  mean_wait mean_total
1  280.3354   293.3103

scenario_comp <- bind_rows(
Base = arr_base,
Extra_Meat_Worker = arr_meat_plus,
.id = "Scenario"
)

library(knitr)

scenario_comp %>%
  kable(
    caption = "Comparison – Mean Wait & Total Time (minutes)",
    digits = 2,
    align = "c"
  )

env_meat_plus2 <- simmer("BBQ_meat_plus") %>%
add_resource("order", capacity = num_cust+1) %>% # <-- one extra order worker
add_resource("meat", capacity = num_food + 2) %>% # <--  extra worker
add_resource("sides", capacity = num_food ) %>%
add_generator("cust", cust_traj, iat_fun) %>%
run(until = sim_time)

res_meat_plus2 <- get_mon_resources(env_meat_plus2) %>%
group_by(resource) %>%
summarise(
mean_util = mean(server / pmax(capacity, 1)),
mean_queue = mean(queue),
max_queue = max(queue),
.groups = "drop"
)

cat("\nSCENARIO 2 – RESOURCE STATS:\n")

SCENARIO 2 – RESOURCE STATS:

library(dplyr)
library(knitr)
library(scales)

res_meat_plus2_clean <- res_meat_plus2 %>%
  mutate(
    mean_util = percent(mean_util, accuracy = 0.1),
    mean_queue = round(mean_queue, 1),
    max_queue = round(max_queue, 0)
  )

kable(res_meat_plus2_clean,
      col.names = c("Resource", "Utilization (%)", "Avg Queue Length", "Max Queue"),
      caption = "Scenario 2: Two Extra Meat Workers + One Extra Order Worker - Resource Performance Summary")

arr_meat_plus_raw <- get_mon_arrivals(env_meat_plus2)

arr_meat_plus2 <- arr_meat_plus_raw %>%
mutate(
total_time = end_time - start_time,
waiting_time = total_time - activity_time
) %>%
summarise(
mean_wait = mean(waiting_time),
mean_total = mean(total_time)
)

cat("\nEXTRA MEAT WORKER – CUSTOMER STATS (minutes):\n")

EXTRA MEAT WORKER – CUSTOMER STATS (minutes):

print(arr_meat_plus)

  mean_wait mean_total
1  280.3354   293.3103

scenario_comp <- bind_rows(
Base = arr_base,
Two_Extra_Meat_Worker_and_Extra_Order = arr_meat_plus2,
.id = "Scenario"
)

library(knitr)

scenario_comp %>%
  kable(
    caption = "Comparison – Mean Wait & Total Time (minutes)",
    digits = 2,
    align = "c"
  )

# Simulate inventory levels for demonstration
library(ggplot2)
library(dplyr)
library(lubridate)

# Example time points (minutes from opening)
time_points <- seq(0, sim_time, by = 10)  # every 10 minutes

# Simulated customer arrivals (cumulative)
cust_cum <- cumsum(sample(0:5, length(time_points), replace = TRUE))

# Simulated prepared food inventory
food_inventory <- pmax(0, 50 - cumsum(sample(0:3, length(time_points), replace = TRUE)) + 5*round(time_points/60))

inventory_df <- data.frame(
  Time = time_points,
  Customers = cust_cum,
  PreparedFood = food_inventory
)

# Plot: Customer Arrivals vs Prepared Food
ggplot(inventory_df, aes(x = Time)) +
  geom_line(aes(y = Customers, color = "Customers Arrived"), size = 1.2) +
  geom_line(aes(y = PreparedFood, color = "Prepared Food Inventory"), size = 1.2) +
  labs(
    title = "Customer Arrivals vs Prepared Food Inventory",
    x = "Time (minutes from opening)",
    y = "Count",
    color = ""
  ) +
  theme_minimal() +
  scale_color_manual(values = c("Customers Arrived" = "steelblue", "Prepared Food Inventory" = "darkorange"))

# Create summary data for plotting
time_df <- data.frame(
  Scenario = c("Base", "Improved"),
  Mean_Wait = c(296, 194),
  Mean_Total = c(309, 207)
)

# Convert to long format
library(tidyr)

time_long <- time_df %>%
  pivot_longer(cols = c(Mean_Wait, Mean_Total),
               names_to = "Metric",
               values_to = "Value")

# Plot
ggplot(time_long, aes(x = Metric, y = Value, fill = Scenario)) +
  geom_bar(stat = "identity", position = "dodge") +
  geom_text(aes(label = Value),
            position = position_dodge(width = 0.9),
            vjust = -0.3,
            size = 4) +
  labs(
    title = "Customer Time Comparison: Base vs Improved Scenario",
    x = "",
    y = "Time (minutes)"
  ) +
  theme_minimal()

# Create percentage improvement data
improve_df <- data.frame(
  Metric = c("Waiting Time", "Total Time"),
  Improvement = c(
    (296 - 194) / 296 * 100,
    (309 - 207) / 309 * 100
  )
)


ggplot(improve_df, aes(x = Metric, y = Improvement)) +
  geom_bar(stat = "identity") +
  geom_text(aes(label = paste0(round(Improvement, 1), "%")),
            vjust = -0.3,
            size = 5) +
  labs(
    title = "Percentage Improvement in System Performance",
    x = "",
    y = "Improvement (%)"
  ) +
  theme_minimal()