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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