Roots Café MIE 380 Project Final
Report
William AndrewsEric Wright
Hugh LavelleStatement of the Problem
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From the start of the day through the late hours it’s open, many of the students
living at the honors college and across campus go through the Roots Café to get
breakfast, lunch, dinner and snacks. Roots is a small Café style eatery with a main
entrance on the first floor and a smaller entrance at the top of the stairs leading to the
second floor. The service area is a semi-circle with registers at both ends. The hours
are from 7:00 AM to 1:00 AM, but the quesadilla and sandwich grill is only open until
10:30 PM. Grab and Go serves breakfast in the morning until 10:00 AM. The rest of the
area contains round tables that seat four each and high tables that seat six. Adjacent is
an auditorium with furniture allowing for overflow. Our team consists of Eric Wright,
William Andrews, and Hugh Lavelle; all industrial engineering majors. Through data
collection, observation, and optimization methods we sought to make suggestions for
improvements of the café. Roots is very busy from 6:00 to 11:00 PM when the line to
order, pay for, and receive the sandwiches from the grill turns into a severe cluster
which often results in people having to pay before they receive their food or getting their
food and having to wait to pay, which could prompt them to leave without paying at all.
Many people also just walk out if the wait is too long. When customers enter roots, they
are prompted with four options, order pizza, go to the deli, go to the grill side, or pick up
an entrée and choose which side to pay for it on. The pizza and deli share the same
register on the same side. At the grill, customers order food, pay for it, and then pick it
up. At all other stations, customers order food, pick it up, and then pay. Recycling, trash
disposal, and dish return is a non-issue as there are no lines for that and many people
take their food to go. The two sides at which customers can order are unevenly utilized,
and the workspace organization of the cafe also has great room for improvement.
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We modeled the system ultimately as a Jackson network, consisting of multiple
M/M/c queues including the separate stations such as the grill, pizza, and deli. While the
roots system as whole is very complicated and dynamic, we did our best to model it
accurately with the information and skills we have acquired over the course of the
semester and use these models to alter the parameters of the system to see if an
benefits could come from doing so. We chose to divide the system into two main
components, the grill station side and the pizza and deli side. The two sides each have
their own cashier for service, even though the customer flow is far greater on the grill
side, as backed by the sales data we received from Van Sullivan (attached in the
appendix). With a few changes to the system we believe Roots Cafe could be much
further optimized to increase services times and improve customer traffic flow.
Background
In order to prepare for this project, the first item on our agenda was to familiarize
ourselves with the dining area that we would be studying. This wasn’t very hard as we
all had been to Roots Cafe many times before. However, in order to immerse ourselves
in the area of study, all group meetings were held in Roots Cafe to stimulate thought
and allow easy visualization of questions raised, possible solutions, and other
miscellaneous ideas. While the area itself was familiar, its specific layout was not. A
blueprint of Roots Cafe was critical in preparing to take measurements and specify
queuing and buffer areas. After spending some time in the cafe, Roots was portioned of
into several designated queuing systems and a peak time was estimated. The grill, the
pizza oven, and the deli were all separated into their own queuing systems. The points
were identified by precedence and what needed the most focus. Based on general
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observation, the grill was the most problematic and had the most intricate queuing
system out of all the possible systems contained in the cafe. In addition, a request was
sent for any possible sales data that Mr. Van Sullivan might have had pertaining to the
cafe. He obliged and provided some extensive and specific data that would end up
being critical to the many future calculations that were made. Before any time
measurements were taken, each group member was charged with a separate task
Methodology
After becoming familiar with the system being used at Roots, it was time to collect
data. In order to obtain the most accurate results possible, data was collected during the
peak hour time (7:00pm to 8:00pm), from a table situated directly across from the queue
area. Since there were three people taking data, for each customer, one person
obtained the arrival time, one person obtained the time to reach departure from the
queue, and one person obtained the time to reach departure from the system. Each
data point was timed on an electronic stopwatch, and the time was then entered into
one Excel file in the appropriate column. After one collection of data, a second collection
was taken using the same methods in order to eliminate lurking variables. For example,
if there were extenuating circumstances that influenced the arrival/service processes
during the first collection, the second collection ensured that the data would be accurate
and true of the system.
Once the data was collected and stored in an Excel file, several mathematical
models were utilized to give perspective on the effectiveness of the queuing system at
Roots. First, in order to provide a visual representation of the data, a PDF (probability
density function) and an empirical CDF (cumulative distribution function) of the
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interarrival times were created using the software program Minitab. These graphs
showed an exponential distribution of interarrival times with a mean of 1.265 minutes
between arrivals. A PDF and CDF of the service times were also created using Minitab,
and resulted in a normal distribution with a mean of 3.671 minutes and a standard
deviation of 1.792 minutes.
Little’s Law was also used as a mathematical model in order to calculate the
necessary characteristics of the queuing system at Roots. To obtain the accurate
calculations, the proper queuing system for each service area had to be determined.
The grill system was determined to be an M/M/6 system because the maximum
capacity for the grill is 6 sandwiches at a time, meaning 6 customers can be served at
any one time. After the grill, some items (namely, hot sandwiches) would be placed in
an oven for secondary heating. This oven was an M/M/4 system as it could fit up to 4
items. On the other side of Roots, the pizza oven was determined to be an M/M/4
system because it could fit 4 items at one time. Next to the pizza oven, the deli is able to
serve only one person at a time, making it an M/M/1 system. Using all of this
information, along with Little’s Law, it was possible to calculate the average number of
customers in the system, average number of customers in the queue, average time
spent in the system, and average time spent in the queue.
In order to optimize the system, the addition of a second oven should be considered.
This second oven would be modeled by another M/M/4 system in addition to the
existing one, and thus, would improve the flow through the queue that is currently
hampered by the limitations of the service system in use now. This second oven would
also help balance the amount of customers who go to each side of the register. At the
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present, most of the customers go to the left side, creating a larger than needed queue.
If an additional oven were to be added on the other side of Roots, the length of the
queue would be halved, and a more standard service time could be achieved.
The final model that was used to evaluate this system was a cost benefit
analysis. In order to finance a new oven, the details of the cost savings from the
proposed changes needed to be calculated. First, the average unit price of relevant food
items was calculated using the menu from Roots, then using the mean service times
that were collected during the data collection process, the profit per hour was able to be
calculated for each side of Roots (the grill side and the deli/pizza oven side). These
relevant food items were grill items, heated sandwiches/subs, entrees, pizza, and deli
items. In our layout change, the entrees and hot sandwiches/subs were moved over to
the deli side to be exclusively sold and prepared there. After researching the oven
model used at Roots, an estimated price of an additional oven was calculated. Finally,
using the profit per hour after the changes, and the price of a new oven and a new
employee, it was possible to calculate the time to pay off the new oven: 10.5 work days
(19 hours per day).
Results
Essential to creating a visual representation of the system, we used building layout
plans and artistic software to visualize the flow of customers and where each part of the
system is with respect to each other. This representation, along with layout with
dimensions is attached in the appendix. Our first step with our data was to create the
cumulative grill diagram, along with graphs of the CDFs and PDFs of both the service
and arrival. We determined the arrival rates to be of an exponential distribution, and
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found our service times to be a normal distribution. All statistical graphs can be located
in the statistical section of the appendix. Because the system follows a Poisson system,
we used the Markovian model of an M/M/c to represent the system and calculate the
various parameters including the waiting times and average number of people in both
the system and the queue using the appropriate formulas. Since the system was an
M/M/c system, we were able to model it as a Jackson network divided into two main
components, being the grill side and pizza/deli side. We proceeded to use Mathematica
to compare the changes resulting from adding an extra oven to the deli/pizza side to
more evenly distribute customer flow and orders. From sales data we concluded that
hot sandwiches would be the best choice to double up on service because it’s the
second highest grossing product sold at Roots. With the current set up the total arrival
rate is .82 customers/minute and for the grill .5289 customers/minute. When we choose
to add a second oven and evenly split the percentage of people getting hot sandwiches
(calculated from acquired sales data), not only did this more evenly distribute the
arrivals, decreasing them to .4838 customers/minute, it also more evenly distributed the
probabilities of each customer going to the grill side or pizza/deli side. In its current set
up we calculated 64.5% of customers go to the grill side but if the extra oven were
added to the other side, and if it were theoretically drawing half of the hot sandwich
orders, then only 38.95% of customers would go to the grill and 30.42% would go to the
deli, versus only 20% of customers going to the deli in the current system. For the profit
per hour, our changes increased the profit per hour (of relevant items only) from 164.99
dollars per hour to 178.99 dollars per hour. The deli is most busy during lunch while the
hot sandwiches are busy later at night. This means that one worker could operate both
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systems. However, we factored in the possibility of another employee to work the oven.
At a pay of 9.00 dollars per hour, this would bring the new profit down to 169.99 dollars
per hour, which is still five dollars an hour more than the previous profit margin. Once
again, at this rate it would only take 10.5 days to pay off the oven.
Conclusions
We concluded that our changes are worth the cost. While an improvement of five
dollars an hour may not seem worthwhile to some, it starts to make more sense when
the system is looked at as a whole. First, the obvious improvement in profit and short
breakeven time after implementation is enough to warrant a consideration of this
change. Second, this change completely evens out the arrival times on both sides,
allowing for maximum utilization of all stations in the cafe. This would relieve a great
burden from the employees as the grill chefs no longer need to scramble to complete
orders while the employees at the deli and pizza station sit idly by. The employees can
now work at a more sustainable rate and customers will be more satisfied by the speedy
and efficient service and will no longer be disgruntled by long queues. While these
benefits don’t have a dollar sign, they affirm that our changes are well worth
implementing. Going into this project, we knew that Roots had issues with long queues
but we weren’t sure why. Our first guess was that the actual grill was slowing the whole
process down but over time, we learned that it was actually the oven causing the hold
up. We learned that it is vital to talk to the people that were having the problem.
Speaking with Van Sullivan yielded information that was critical to our analysis. We also
learned the importance of gathering multiple sets of data. As we gathered more data our
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results evolved but we were able to have more confidence in those results with data to
back it up and it added consistency to our findings.
Critique Throughout the course of the project, our team dealt with a few minor issues that lead
longer hours than expected to get the information needed. In our first attempt to collect
data on arrival and service times, we quickly realized the difficulty in keeping track of
each customer in line during the peak hours of the Roots during which it is mere chaos.
One group member wrote a small description each person the data was being collected
on just to differentiate each person as they made their way through the system. As the
term project carried on, we learned just how extensive the amount of data collection can
be, and the fact that there is a great variety in parameters to collect data on. For
example not only did we need service and arrival time data, we found that data like how
long it takes for a pizza to be on average to be useful. This is just one example of the
many points of possible data collection. Once we collected data on two separate
occasions, using the actual programs to visualize and model our system proved to be
quite difficult. As mentioned previously, we used Minitab rather than Arena to great our
PDF and CDF graphs because the program was far more straight forward and the
graphics it produced were higher in quality and depth. Since for the most part we did not
actually use the softwares such as Mathematica in class, there was a learning curve just
to get started and figure out how to use the program to alter our Jackson network
parameters to get the results we needed. We’d recommend to future students to
become as familiar with the softwares like Arena and Mathematica so that when it
comes time to crunch numbers the process will be much smoother since you have
already had minor experience with the programs. Other than these few issues, the
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project ran smoothly and we had the tools necessary to model our system and make
suggestions for improvement based on our knowledge from what was learned in class.
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Appendix
General Layout Of System
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Current Network Diagram
M/M/1
M/M/1
M/M/4
M/M/6
Register
.66 c/min
Oven
.17 c/min
.53 Customers/min
Grill
.36 c/min
M/M/1
M/M/4
.126 Customers/min
.164 Customers/min
Register
.66 c/min
Pizza Oven
.19 c/min
Deli
.657 c/min
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Mathematica Results
Grill side before
Deli side before
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Grill side after changes
New Deli/Hot sandwich side after changes
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Network Diagram After Changes
M/M/1
M/M/4
M/M/6
Register
.66 c/min
Oven
.17 c/min
.39 Customers/min
Grill
.36 c/minDeli/Sandwiches
.17 c/min
Pizza Oven
.19 c/min
Register
.66 c/min
.126 Customers/min
.304 Customers/min
M/M/4
M/M/1
M/M/4
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Sales Data from Van Sullivan (data from
April 4th to 11th)
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Food $46,747.72 11,405 $4.10Grill $15,343.25 2,723 $5.63Sandwiches $7,194.25 943 $7.63Pizza $6,845.00 1,129 $6.06Breakfast $4,701.72 1,526 $3.08Deli $2,621.50 714 $3.67Harvest $2,373.96 503 $4.72Entrees $2,058.75 305 $6.75Snacks $1,766.34 1,514 $1.17Bakeshop $1,255.25 848 $1.48Salad $786.10 287 $2.74Fried Foods $316.75 181 $1.75Grab N Go $307.57 103 $2.99Burgers $218.75 125 $1.75Chips/Candy/Bars $173.63 97 $1.79Groc Nutri Bars $107.07 43 $2.49Miscellaneous $102.39 7 $14.63Fruit $37.13 47 $0.79Condiments $21.00 21 $1.00Yogurt $517.31 289 $1.79
Beverages $13,221.63 5,415 $2.44Prep Drinks $4,884.00 1,648 $2.96Coke $4,334.83 1,968 $2.20Bev, Other $2,717.33 1,556 $1.75Bottled Nutri $1,285.47 243 $5.29Grab and Go Swipes 4,326
Total (net of swipes) $59,969.35 16,820 $3.57
Raw Data collection and m at Roots from 7-8 pm (peak hours)
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