Exploring COFF[IE]: An Industrial Engineering Analysis
Kenneth Acquah Colin Courchesne Sheela Hanagal [email protected] [email protected] [email protected]
Kenneth Li Caroline Potts [email protected] [email protected]
Mentor: Juilee Malavade, Brandon Theiss, PE
RTA: Juilee Malavade
Abstract
Waiting in lines for extended periods
of time results in inconveniences and a
waste of what may be the most important
resource of all, time, for all consumers.
Thus, reducing wait times within Starbucks
and Dunkin' Donuts and optimizing a
simulation of the processes within those
restaurants could result in shorter wait times
for customers and larger profits for the
restaurants. Data of the wait times in line
and the service times were collected at
Starbucks and Dunkin' Donuts restaurants
within New Brunswick through
observational studies. Minitab® statistical
analysis software was then used to analyze
the data and obtain the probability
distributions and descriptive statistics. The
results from the Minitab software were then
used to create simulations of the queuing
processes for both Starbucks and Dunkin'
Donuts using Arena Simulation Software®.
The simulations were run and analyzed to
see whether the simulated data accurately
reflected the data which was collected at the
two restaurants. The simulated data reflected
some of the collected data but not all
depending on what queue we were obtaining
simulated data from. It was found that
queues in Starbucks were longer than the
queues in Dunkin’ Donuts. Upon evaluation
of the parameters which could shorten wait
times in each restaurant, the simulation
could be manipulated to change resource
values and process orders, deriving an
optimal model of increased efficiency and
increased profitability for both restaurants
which could potentially decrease wait times
for both Starbucks and Dunkin’ Donuts.
1. Introduction
Standing in queues is not only an
inconvenience for customers everywhere, it
is also costly to firms and to the overall
economy. A person who spends five minutes
waiting for coffee each day who otherwise
earns ten dollars an hour would lose over
three hundred dollars every year due to the
opportunity cost of waiting in line. When
this cost is applied to the three million
customers served in Dunkin' Donuts alone
daily,1
millions of dollars are lost every year
due to Dunkin' Donuts coffee lines.
Extending this to Starbucks restaurants and
customers as well, the loss only multiplies.
Minimizing queue length by improving
efficiency and productivity in Starbucks and
Dunkin' Donuts coffee shops has the
potential to save millions of people both
time and money.
This research seeks to create a
working simulation of both a Dunkin'
Donuts and a Starbucks restaurant and
predict how the processes observed in each
restaurant could be improved. A simulation
that accurately represents the waiting and
service processes in Dunkin' Donuts and
Starbucks locations could be used to analyze
ways to potentially increase efficiency and
decrease queue length.
By changing parameters of an
accurate simulation, one could analyze the
additional costs and benefits of altering store
operation systems, such as increasing or
decreasing the number of employees
working at the cash registers or making
specialty drinks. This would allow owners
to determine if a particular change would
improve or detract from the service provided
to customers without actually testing it in a
real store, preventing a decline in the quality
and profitability of the company during the
testing phase. To obtain data to compare to
the values output by the simulation, data was
collected regarding the amount of time
customers waited to order and to receive
their drinks at both a Dunkin' Donuts and a
Starbucks restaurants located in New
Brunswick, New Jersey.
2. Background
2.1 History of Starbucks
The first Starbucks was opened in
Pike Place Market in Seattle, Washington, in
1971 by Jerry Baldwin, Zev Siegl, and
Gordon Bowker. The company grew slowly
and soon hired Howard Schultz as Director
of Retail Operations and Marketing in
1982.2 Schultz eventually bought the
company and, borrowing ideas from the
coffeehouse culture of Milan, Italy, worked
to build a coffee shop that was more of a
restaurant than a retail store. He had a lofty
vision for Starbucks; he wanted it to be a
national company with values and ethics of
which employees could be proud and “to
build a company with soul" by making sure
the company would never stop pursuing “the
perfect cup of coffee” for the consumers.3
The service aspect of customer service was
also a main block of the new Starbucks
model. Starbucks grew rapidly, recording
millions of dollars in sales from thousands
of locations annually.
2.2 Starbucks Business Model
Starbucks is a coffee retailer that has
its main location in Seattle, Washington.
There are over twenty-two thousand
Starbucks restaurants worldwide. It reported
a net revenue of $12,977.9 million from
company operated restaurants and $1,588.6
million from licensed restaurants in 2014.
The majority of Starbucks’ sales come from
beverages, with company operated stores
reporting this category to account for
seventy-eight percent of sales.4 In the United
States, Starbucks has 7,400 co-operated
restaurants and 4,823 licensed restaurants.5
The 2014 net revenue from the Americas
was $11,980.5 million.4 Starbucks focuses
on expanding its geographic locations,
having diversified products, and creating the
semblance of an authentic neighborhood
coffee shop.
Starbucks strives to be the place to
which people retreat from home and work
and thus encourages customers to stay in-
shop by providing attractive services, such
as free WiFi, and a welcome atmosphere.
To promote this atmosphere, Starbucks
emphasizes service and customer
satisfaction.6 When it comes to beverage
choices, Starbucks is well known for its
wide, accommodating range. The drinks
available at Starbucks include hot drip
coffees, iced coffees, teas, Frappuccinos,
espressos, lattes, cappuccinos, and clovers,
which are hot coffees that can be highly
specialized and are made in a machine that
individualizes each cup.
The typical process once in a
Starbucks is to wait in line (see 2 in Figure
2.2.1 below) and then place an order with a
cashier (5), who then passes the order on to
the barista by marking a cup with the order
if the order is not a drip coffee (7b). The
customer then pays (8b) and proceeds to the
designated pickup area (9b). The barista
then makes the coffee (10c) and hands it to
the customer (11c). If the order is a drip
coffee, the cashier makes the coffee (8a) and
hands it directly to the customer (9a). Once
this occurs, the customer typically chooses
to stay in the shop and drink the coffee,
rather than leaving immediately.
The Starbucks business model
focuses on consumer satisfaction, increased
distribution, partnerships, and international
expansion to encourage customers to stay
with Starbucks as loyal customers. This
model has worked well as the company’s
annual growth rate from 2010 to 2014 was
eleven percent.7
2.3 History of Dunkin’ Donuts
The original Dunkin’ Donuts,
excluding all affiliated brands such as
Dunkin’ Coffee and Baskin-Robbins, was
started in 1950 by William Rosenburg in
Quincy, Massachusetts. However, it was
not until 1955 that Dunkin’ Donuts began to
license franchises, consequently leading to
the development and growth of the chain as
a nationally recognized brand.1
Dunkin’ Donuts has since
experienced exponential growth, leading to a
total of over 8,000 restaurants in the United
States and 11,300 restaurants globally.1
Much of the recent growth can be attributed
to the brand’s recent shift away from food
items, namely donuts, and instead towards
coffee, effectively transitioning from being
mainly a restaurant to being mainly a coffee
shop.
This change is generally attributed to
CEO Jon Luther who, in 2003, was forced to
adapt to changing market tastes in order to
keep afloat what was then a struggling
business. Luther introduced a series of new
coffee-based products, including espresso,
and expanded the menu to cater to a diverse
range of customers.8 Dunkin’ Donuts has
since continued to follow this business
model, which has brought it great success,
almost doubling its stock price since its IPO
in 2011.9
2.4 Dunkin’ Donuts Business Model
Figure 2.2.1 – Process Map of Starbucks Operations
Dunkin’ Donuts focuses on service,
emphasizing the quick delivery of food and
drink items. The Dunkin Donuts system
does not definitively delineate roles of
cashier and barista; cashiers are
simultaneously baristas. The workload is
often divided depending on the nature of the
drink, either hot specialty, cold specialty, or
drip, which is premade stock hot coffee.
Dunkin’ Donuts does prioritize customer
experience in the restaurant. Instead, service
speed, convenience, and value are
prioritized, which can be seen in the brand
motto which is to “Make and serve the
freshest, most delicious coffee and donuts
quickly and courteously in modern, well-
merchandised stores.” This can also be seen
in the limited space inside restaurants which
indicates a model which primarily caters to
customers who purchase food and drinks
and then leave rather than those who stay in
the store after receiving their drinks and
spend time socializing at the tables.8 Due to
high franchising rates, values and focuses
may deviate from store to store; however,
the original motto for the Dunkin’ Donuts
brand remains expressly to "Make and serve
the freshest, most delicious coffee and
donuts quickly and courteously in modern,
well-merchandised stores,” indicating that
speed, convenience, and value trump
customer experience.1
To begin the service process at a
typical Dunkin’ Donuts store, customers
enter and begin queuing (see 1 and 2 in
Figure 2.4.1). After waiting a variable
amount of time to reach the counter, the
customer served by one of two available
cashiers at either cashier’s earliest
convenience (3/4). The customer then
proceeds to place his or her order
(5/6a/6b/6c), pay for the aforementioned
order and then wait for his order to be filled.
If the placed order is drip coffee or tea,
either cold or hot, the customer pays (7a)
and is immediately served (9a). If the drink
is a Coolatta®, or a frozen ice-based drink
and the equivalent of a Frappucino® at
Starbucks, the customer pays (7b), and the
cashier then takes roughly three minutes to
personally make the drink (9b). If the drink
is a warm specialty drink, the order is passed
down to a third employee who continually
works the latte, cappuccino, and espresso
machines (8). This worker then creates the
drink to give to the customer (9c), a process
whose time depends on the type of drink
ordered.
Dunkin’ Donuts currently focuses its
business model on cost-optimization,
seeking to capture a lower-income segment
of the market by offering products of similar
quality to competitors for lower prices.
Though no official information has been
released pertaining to profit margins per
item, most speculate coffee to be the most
profitable item sold by Dunkin’ Donuts,
with economists believing that roughly 95%
of coffee sales serving as pure profit.10
Dunkin’ Donuts has also publically stated
that it wishes to reach such cost optimization
through economies of scale, wherein the
Figure 2.4.1 – Process Map of Dunkin’ Donuts Operations
company is able to minimize the individual
cost-per-unit by producing beverage and
food products in large quantities. This
minimization of cost allows Dunkin’ Donuts
to reduce prices and therefore undercut
competitive companies while maintaining
healthy profit margins.11
The growth of the Dunkin’ Donuts
companies has remained healthy over the
past 5 years, namely thanks to the individual
strength of the domestic Dunkin’ Donuts
brand. Sales for Dunkin’ Donuts brands,
including Baskin-Robbins and international
subsidiaries reached an annual total of
$748.709 million in 2014. Dunkin’ Donuts
is heavily franchised, with roughly 7,000 of
current restaurants serving as franchises.
Dunkin’ Donuts currently operates locally in
41 states while maintaining an international
presence in 36 countries, serving an average
of roughly 3,000,000 customers daily.1 Their
current menu offers an eclectic variety of
food and beverages, including upwards of
50 donut options and over a dozen coffee-
based drink products.
Overall, Dunkin’ Donuts is heavily
franchised, has seen steady growth over the
past 10 years, and has a business model
centered on providing comparatively low
price items to undercut competitors and
attract customers of a lower income bracket.
2.5 Comparison of Starbucks and
Dunkin’ Donuts
To elucidate the distinctions between
Starbucks and Dunkin’ Donuts, this section
will provide side by side comparison of
various aspects of the two chains (Figures
2.5.1, 2.5.2).
2.6 Queueing Theory
Most businesses in the food industry
deliver their products to customers through
service. The study of queueing theory can
be used to understand the different
mechanisms used by companies to deliver
their products to customers. Queueing
theory is the mathematical theory and
analysis of waiting in queues. It was
originally used to optimize the number of
telephone operators working at any given
time; however, it can be applied to myriad
other industries including the food service
industry and medical facilities.
Mathematical models and operational
measurements can then evaluate and
increase customer flow.13
Results obtained through studies of
queueing theory in the service industry can
improve everyday life of customers. By
predicting wait times at various
establishments, consumers can optimize
their time, a highly prized resource.
Customer satisfaction from purchases is
largely dependent on queuing and
transaction time;14
therefore, minimizing
waiting time through queueing theory can be
very beneficial to companies.
Queueing theory can be applied to
the foodservice industry to analyze the
methods used by companies such as Dunkin’
Donuts and Starbucks to deliver products to
their customers. Random variables such as
arrival and service time along with details
concerning the method of delivering the
service characterize queueing models. It is
typically assumed that the system is
memoryless, in that each arrival is
independent of the previous arrival, and that
the variables are identically distributed.
Queueing theory can be used to distinguish
the sequence of requests for service and the
order in which customers are served. There
are numerous possibilities for serving order,
such as first in first out (FIFO), in which the
customer who arrives first receives service
first, last in first out (LIFO), in which the
customer who arrives last receives service
first, priority, in which some customers take
precedence over others, and random service
(RS), in which the order in which customers
are served is independent of arrival time or
priority.15
The notation used to identify
different types of queues is called Kendall’s
notation. This notation follows the form
A/B/m where A is the type of arrival
process, B is the type of service process, and
m is the number of servers. The most
common model used to represent the arrival
process is called the Poisson Process. This
process refers to a discrete model of arrival,
meaning that customers arrive as individual
units. Because customers cannot be
separated into non-whole number units, the
graph of arrival will not be continuous. The
Poisson Process details the distribution of
events independent of each other as
exponential with a parameter λ. In Kendall’s
notation, the Poisson Process is represented
by an M. An M can also be used to
represent an exponential distribution of
service times. Service times can be
represented by a continuous exponential
distribution due to the ability to quantify
time in very small increments.15
One basic queueing model is the
M/M/1 system. As the notation indicates,
this refers to a queue in which customer
arrivals follow the Poisson Process, service
times are exponentially distributed, and
there is one server. Variations of this model
include M/M/2, which is identical to the
M/M/1 model except it includes two
servers.15
The M/M/c system serves as an
extension of the M/M/1 model, where c
represents a variable number of servers.
Variability of servers allows for idling when
the load is below c.
The M/G/1 system denotes a single server
with a general distribution time as opposed
to the memoryless service time model of
M/M/1. The change in service time
distribution indicates a different firm-side
response to the Poisson process.
As was determined in a 2005 paper
by Gregor Hohpe, the queueing process in
coffee shops such as Starbucks is an
example of an asynchronous processing
model. The asynchronicity enters the model
when the cashier places the cup in a
secondary queue for the barista to make the
drink. This allows the cashier to continue
serving customers when the barista is not
ready or multiple baristas to serve one line
of customers, which increases the amount of
customers that can be served in a given
amount of time. Additionally, the barista
can begin to make the next drink in the
queue before the customer retrieves the
drink. In a process with one server per
customer, also known as a two-phase-
commit approach, the process is linear, one
step follows after another. This process is
less efficient than an asynchronous model,
so it is not used in stores such as
Starbucks.16
The asynchronous model results in
the customers not necessarily receiving their
orders in the same order in which they were
placed. Because some drinks take longer to
prepare than others, a drink that can be
prepared faster but was ordered later can be
delivered to the customer before a drink that
has a longer preparation time but was
ordered earlier. This creates a difficulty in
matching the order to the customer;
customers cannot simply wait in line for
their drink to appear because the drink of
someone behind them may appear before
their own. Starbucks resolves this
complication by writing the names of the
customers on the cups and calling out the
name when the drink is ready. This
solution, however, adds time to the
customer’s wait because the cashier has to
take time to write on the cup.16
This system also increases the
probability of needing to correct an error, as
the presence of multiple servers adds
possibilities for mistakes.16
2.7 Similar Research
Simulations have been used in
previous research to optimize processes in
various fast food restaurants.17, 18, 19, 20
Reducing Service Time at a Busy Fast Food
Restaurant on Campus indicated that
simulations are a useful tool for accurately
modeling and improving processes in a
restaurant.17
Additionally, Using Queueing
Theory and Simulation Model to Optimize
Hospital Pharmacy Performance revealed
that Arena Simulation Software is an
effective platform to construct simulations
and that statistical analysis software is
necessary to properly analyze queue
distributions.13
Finally, the paper Computer
Simulation: An Important Tool in the Fast
Food Industry presented the technique of
building a preliminary simulation and then
adapting it by using observed data to set
parameters.18
This approach, as well as the
use of Arena, was adopted in the research of
Dunkin’ Donuts and Starbucks.
3. Data Collection and Simulation
Creation
3.1 Data Collection Methodology
In order to collect the data needed to
create simulations and analyze wait times,
trips to Dunkin’ Donuts and Starbucks shops
located in New Brunswick were taken. An
equal amount of time of three days was
spent in both locations taking data. Tables
were set up in each location in order to
collect data regarding the wait times of
customers while in line and while waiting
Figure 3.1.1 – Starbucks Store Layout
for an ordered drink. In order to get accurate
information, tables were chosen that were in
view of the entrance of the shop, the
cashier’s counter, and the waiting area.
In order to record the times spent in
the queues within the store, a timing
application was used. This application
provided a timer that was pressed once a
customer entered the store, once a customer
ordered a drink, and once a customer
received a drink. The total time a customer
spends in the system is called the sojourn
time. Also provided within the application
was the ability to record which drink a
customer recorded as well as a text box that
allowed a description of the customer to be
taken, which was helpful in ensuring that the
data recorded using the timers was not
mixed up between different customers. All
of the information being recorded was sent
to a spreadsheet that organized each of the
different categories. Recording the times
spent in queues allows analysis of wait times
that customers spend in each store.
Recording the type of drink ordered was
also important because different drinks have
different average preparation times. Within
the application the drinks were separated
into categories that reflect similar
preparation times. The five options that
could be selected for drinks were Hot
Drip/Tea, Ice Drip/Tea, Frappuccino,
Espresso/Latte/Cappuccino, and Clover.
3.1.1 Store Layouts
The Starbucks store in New
Brunswick that was visited to collect data
had a comfortable atmosphere with a strong
coffee scent. There were many tables open
for seating and high-chair areas right next to
the barista’s coffee-making area. As seen in
Figure 3.1.1, as soon as a person enters the
Starbucks store, they can see the cash
registers in front. There are areas available
for seating on either side of the store. The
cashiers have the hot drip machines behind
them for easy access. The baristas are
located to the right with access to all of the
other machines such as the Clover and
Espresso makers. The queue to order can be
seen below (represented by a black line).
The Dunkin’ Donuts store in New
Brunswick that was visited to collect data
had a few tables for seating that were
intended as a drink and then go accessory.
As seen in Figure 3.1.2, when a person
comes into a Dunkin’ Donuts store, there are
cash registers located directly in front of the
customers. There are areas available for
seating on either side of the store although
some of the tables are more isolated in a
corner. The cashiers and baristas have
access to all of the machines, and the hot
drip machines are located behind the cash
registers. The queue to order can be seen
below in the figure.
3.1.2 Errors in Data Collection and
Observation
When collecting data, there were
some variations in methodology from person
to person. The first variation occurred with
differences in the interpretation of when a
person counts as entering the store. Some
Baristas
Cashiers Points of
Observation /
Data Collection
Figure 3.1.2 – Dunkin’ Donuts Store Layout
Queueing
Line
data points were collected with the timer
being started when the customer opened the
door and entered. Other data points were
collected with the timer being started when
the customer started to wait on line. The
next variation occurred with differences in
the interpretation of when a person was
considered to have ordered a drink. Some
data points were collected with the timer
being pressed when a person told the cashier
the order. Some were collected when a
person paid the cashier. Another variation
occurred when considering people who
ordered multiple drinks. Some data points
were collected when a person had finished
collecting all ordered drinks while others
were collected when a person got the first
drink ordered.
Some difficulties with the data
collection included interpreting the start
time of timers, keeping track of customers
throughout the order process, and
accounting for people who only entered the
store for other purposes rather than ordering
beverages. Since the data collected only
applies to the order of beverages within
Starbucks and Dunkin’ Donuts, data
collected of people who entered the store
only to use the toilet facilities and the data
collected of people who ordered food rather
than beverages had to be disregarded.
Additionally, the researchers collecting data
were inexperienced in this work which may
have added to human error in the data.
3.2 Simulation Methodology
Rockwell Arena Simulation
Software® is used for compiling and
incorporating collected empirical data to
accurately create virtual simulations of
scenarios in businesses which can be
evaluated and manipulated. Simulation is a
method that presents information obtained
from a constructed model based on
observing work flow rotation from the
current situation and other related
variables.18
The three main components used in
Arena simulations to represent various
components of actual operations are entities,
processes, and resources. Entities are the
objects upon which processes are performed
and must be defined first. Processes, which
act as operations performed upon the entities
and often incur delays within the queue,
must be defined next. Lastly, resources
must be created in order to perform the
processes upon the entities. The nature of
resources can be altered to allow for the
prioritization of entities or to permit
multitasking. With proper classification of
such objects, computer simulation provides
an accurate way to evaluate changes in the
restaurant without disturbing the normal
day-to-day operations.18
In order for these
simulations to reflect the observed business
operations, corresponding data and
components must be inputted as factors of
the simulated process. Since the average
service times of different drink orders are
very different from each other, the
probabilities of each drink order are
calculated to represent product variety at the
respective stores. Furthermore, data
collected of service times for various
observed drinks may reflect certain
distributions. Thus, statistical evidence such
as probability distribution models and
certain respective parameters are required
for the simulation to adopt a specified
distribution that would reflect firm
operations based on empirical evidence.
For both restaurants, the simulation
consists of customers and drinks as entities,
drink production and cashier service as
processes, and floor employees as resources.
The simulations both begin through the
perspective of a customer but transition to
assume the position of a drink from its
inception as an order into delivery to the
customer. As customers become largely
independent from the process after their
drink orders are processed, the drink
production process essentially equals the
length of the customer’s total wait after the
order. Some processes involving cashier
service after the order is placed are
accounted for as resource usage for more
than one process and can accurately be
represented in Arena although individual
employee behavior cannot be modeled.
Since it had been decided that the simulation
of the ordering queue would be most
accurately represented by an M/M/c queue
with a c-value of two, an Arena Simulation
with two servers completing the process of
placing a drink order and a set queue with
values of wait times calculated with queuing
theory was created. Arena simulations apply
principles of queuing theory with statistical
evidence that may accurately reflect real-
time processes and components of the
Starbucks and Dunkin’ Donuts stores.21
Figures 2.2.1 and 2.4.1 show general flow
charts of service systems. Arena Simulation
Software was used to model these processes
(Figures A.1, A.2).
3.3 Data Analysis Methodology
Microsoft®
Excel was utilized in
order to sort all recorded data. After
completing all necessary data
measurements, the resulting figures were
then organized using a series of processes.
Sort functions in the Microsoft®
Excel
software were first used to organize the data
based on such parameters as alphabetic or
numeric order. Likewise, the “Delete
Duplicates” function in Excel was able to
identify and delete any duplicate data.
Finally, manual sorting was also used to
determine any faulty or misrepresented data
caused by human error in recording
procedures as well as any double-counted
data inherent to the data recording
techniques. For certain measurements,
including line waiting time and drink
preparation time, the Excel software was
also used to convert the times from
milliseconds to seconds.
After sorting the data, Minitab
software, a conditionally free analytics
system, was then used to provide statistical
analysis for the data. Through data analysis,
one can identify patterns in data which may
not be immediately obvious, then utilize
such patterns to better understand the
systems which produced the data.
By entering the collected data points
and using the tools offered by the software,
basic descriptive statistics were collected for
each establishment, Dunkin Donuts and
Starbucks, as well as for each individual
drink type. These statistics include mean,
median, maximum, minimum, standard
deviation, and quartile figures. Such
statistics were found both for times spent
waiting in line as well as time waiting for
drinks to be prepared. Descriptive statistics
can be used to determine, isolate, and
analyze outliers in data as well as general
trends, such as skewness or symmetry.
Once such descriptive statistics were
determined, the Minitab software was then
used in order to perform significance tests to
determine appropriate probability
distributions for the time spent in line at
each establishment as well as the required
time to prepare each drink item, dependent
on the drink ordered as well as the
restaurant. Minitab offers a total of 16
possible probability distribution models,
including Weibull, Gamma, and Normal,
among 13 others. The appropriateness of
each proposed data distribution model
comparative to the actual data distribution
can be gauged by comparing the P-values
and Anderson-Darling values provided by
the software for each proposed distribution.
P-Values range between 0 and 1 and should
exceed an arbitrary alpha value of between
0.05 and 0.10 to ensure that the distribution
accurately represents the data. Meanwhile,
the Anderson-Darling Value can exceed 1
but should be as low as possible, as
relatively lower values comparative to other
distributions are indicative that the model
more accurately reflects the data. The
Anderson-Darling value can be used to
generally reaffirm the consensus indicated
by the P-value. By using these two values in
conjunction, one can find an appropriate
probability distribution for any set of data.
Once the appropriate probability distribution
was determined, the Minitab software was
then used to determine the parameters
required by the Arena software in order to
run the distribution in the simulation. The
required parameters were dependent on the
chosen probability distribution; however,
they were most often either mean and
standard deviation or alpha and beta values
for scale and shape.
4. Data Discussion
4.1 Starbucks Data
It is generally accepted in the study
of queueing theory that arrivals follow the
Poisson Process. This model assumes all
arrivals to be independent, which can be
problematic in the case of the Dunkin’
Donuts and Starbucks data because it was
observed that many customers did not arrive
independently; they either arrived with a
group of friends or would be drawn away
from or towards the store dependent on the
size of the queue upon approach. The Chi-
square test for goodness of fit was used to
compare the distribution of arrival rates of
the observed data to the Poisson distribution.
By performing a Chi-square test in Minitab,
the p-value, or probability of independence,
can be calculated. A p-value of under 0.05
generally indicates that the two inputs are
dependent on one another, while a p-value
of over 0.05 indicates that the events are
independent. This means that a p-value of
over 0.05 would be needed to conclude that
the arrivals followed the Poisson Process
distribution. The p-value obtained from this
test was practically zero, indicating that the
arrivals were not following the Poisson
Process. The results of the Chi-square test
(Figure A.21) revealed that arrivals of four
or more people weighed more heavily than it
should have, indicating that people did not
arrive independently and giving a possible
reason why the Poisson Process would not
perfectly fit the data. When the expected
and observed counts were compared (Figure
A.22) for every category, the number of
times zero or three or more people arrived
was too high, while the number of times one
or two people arrived was too low. This
demonstrates that the arrival process does
not perfectly follow the Poisson distribution.
After analysis, it was determined that
Starbucks queues followed a Weibull
distribution, demonstrating a strong right
skew and a median value of 82.275 seconds,
a maximum value of 325.024 seconds, and a
minimum value of 4.205 seconds. For all
distributions with rightward skew, median
values of center will be used in order to
compensate for the rightward skew, while
mean values of center will be used for
symmetric probability distributions. Queue
wait time distributions also varied by day,
wherein observed Mondays displayed a
normal distribution, Tuesdays showed a
gamma distribution, and Wednesdays
exhibited a Weibull distribution. Such
differences can be attributed to differences
in customer inflow dependent on the day of
the week. However, it was found to be
appropriate to group data for all days into
one collective data set, for both the data sets
of Dunkin’ Donuts and Starbucks, as not
enough data was collected for each day to
determine whether each day truly has a
different probability distribution for queuing
times, which could have been determined
with more observational studies, or if the
differences in probability distributions are
simply abnormalities in the regular flow of
business.
The probability distributions for each
Starbucks drink were variable. For hot drip
coffees, the data indicated a Weibull
distribution, containing a strong right skew
with a mean value of 69.093 seconds, a
maximum value of 325.024 seconds and a
minimum value of 8.028 seconds (Figure
A.9). Frappucinos demonstrated a gamma
distribution, which also contains a rightward
skew but has a more severe skew
comparative to the Weibull distribution
(Figure A.11). Frappucino wait times had a
median value of 78.888 seconds and a
maximum value of 290.499 seconds. Lattes
exhibited a normal distribution, symmetric
around the mean value of 94.656 seconds
with a standard deviation of 64.194 seconds
(Figure A.10). Lastly, iced coffee wait times
demonstrated a Weibull distribution, once
more showing a rightward skew with a
median value of 80.629 seconds and a
maximum value of 276.817 seconds (Figure
A.12).
4.2 Dunkin’ Donuts Data
Probability distributions for Dunkin’
Donuts wait times, both for queues and
drinks, differed from their Starbucks
counterparts, indicative of the manifestation
of the previously outlined differences in the
business policies and structures for each
respective company. Queues at Dunkin’
Donuts had a gamma distribution, with a
median value of 42.055 seconds and a
maximum value of 317.714 seconds. Like
Starbucks, the queue wait time distribution
also varied depending on the day of the
week. Mondays demonstrated a lognormal
distribution, while Tuesday observations
varied and were first believed to be gamma
but were then seen to be lognormal. Lastly,
Thursdays exhibited a gamma distribution.
Just as at Starbucks, drink wait times
also varied depending on the type of drink
ordered. Hot drip coffees were
demonstrative of a lognormal distribution,
which contains a slight rightward skew
(Figure A.4). Hot drip coffee wait times had
a median value of 59.838 seconds and a
maximum value of 196.668 seconds.
Coolattas held a Weibull distribution with a
median value of 157.427 seconds and a
maximum value of 648.792 seconds (Figure
A.6). Lattes showed a lognormal distribution
with a median value of 102.919 seconds and
an upper-bound maximum value of 267.075
seconds (Figure A.5). Finally, iced coffees
demonstrated a gamma distribution with a
median value of 107.871 seconds and a
maximum value 350.140 seconds (Figure
A.7).
4.3 Starbucks vs. Dunkin’ Donuts
Starbucks queue waiting times
tended to be generally longer than queue
waiting times at Dunkin’ Donuts, as
minimum, median, mean, and maximum
values for Starbucks queue waiting times
were all greater than their Dunkin’ Donuts
counterparts. This data reflects Dunkin’
Donuts’ devotion to quick service being
greater than that of Starbucks. Likewise,
preparation times for hot drip coffees were
longer at Starbucks than at Dunkin’ Donuts,
wherein such aforementioned descriptive
statistics were all greater at Starbucks
comparative to Dunkin’ Donuts. However,
for all other drinks, including iced coffees,
lattes, and frappuccinos, Starbucks tended to
be quicker, exhibiting lower mean and
median values for all such drinks. Starbucks
also tended to be more consistent in its drink
preparation times compared to Dunkin
Donuts as, for all drink preparation times
exclusive of hot drip coffee, standard
deviation values were lower at Starbucks
than at Dunkin’ Donuts.
5. Simulation Results and Analysis
Simulating the processes within
Starbucks and Dunkin’ Donuts requires
input of the time it takes from entering the
store to ordering, the time it takes to
complete a transaction with a cashier, and
the time it takes from ordering to receiving a
drink. Data was collected on all of those
processes except for the time it takes to
complete a transaction with a cashier. Time
Efficiency of Point-of-Sale Payment
Methods: Empirical Results for Cash, Cards
and Mobile Payments relates data taken of
how long a transaction with a cashier takes.
The data in the paper is separated by
payment method. It was observed while
collecting data that around half of the
customers paid with cash and half paid with
credit cards so the times given in the
research paper for these methods of
payments were averaged to gain the total
time of transaction inputted into the
simulation. The paper listed the time for
cash as 28.86 seconds and it listed the time
for credit as 40.26 seconds.22
Therefore, the
time put into the simulation was an average
34.56 seconds.
In order to validate the simulation
results in relation to the data collected
within the actual Starbucks and Dunkin’
Donuts stores, the two-sample Kolmogorov-
Smirnov test was used. This same test was
used by researchers who published
Development and Application of a
Validation Framework for Traffic
Simulation and Statistical Validation of
Traffic Simulation Models. These two papers
used the two-sample Kolmogorov-Smirnov
test to validate the traffic simulation models
in relation to actual traffic.23, 24
When analyzing some of the results
of the simulation using the Kolmogorov-
Smirnov test, it was found that parts of the
simulation did not accurately match the
queue processes observed in the Starbucks
restaurant. When running the simulations for
Starbucks, there were some clear differences
between the simulation results and the
collected data. The distribution for the
collected data of the Hot Drip was best fit
mathematically by the Weibull distribution,
which provided the lowest relative P and
Anderson-Darling values. Even though the
Weibull distribution empirically provided
the best fit for the data, the frequency
histogram with fitted Weibull distribution
demonstrated that a Weibull distribution
would not be appropriate for use within the
simulation, as the aforementioned
distribution would too heavily weight Hot
Drip times trending around the zero value.
This would cause the mean values for hot
drip times to be unrealistically low; for
example, a run of the simulation with the
Weibull distribution as a parameter
produced times of three seconds, which
cannot be possible in reality.
After matching the distribution for
the data to the second-best mathematical fit,
an exponential fit, the distribution was more
reasonable, and, within the simulation,
provided results more reflective of the
observed data. The same error and analysis
process was applied to the Iced Coffee data
for Starbucks, where the mathematically
appropriate distribution was forsaken in
favor of a distribution which returned
simulation results more reflective of real
data. Many of these errors could have been
avoided had more data been collected;
however, time constraints rendered this
option an impossibility.
After making the necessary
adjustments to the simulation probability
distributions, the validity of the simulation
results were tested by the Kolmogorov-
Smirnov test, which tests whether the
distributions of two data sets match given
certain parameters. Given that the
Kolmogorov-Smirnov test confirms the
hypothesis that the distributions match, the
simulation results can be taken to accurately
simulate the processes that take place within
the two stores. Thus, analysis of the
simulation data would be taken to reflect the
random queue processes that would occur
within the two stores.
For Dunkin’ Donuts and Starbucks, a
simulation was run of the sojourn time, the
overall time from entering the store to
getting a drink. Running the Kolmogorov-
Smirnov test for the data in Minitab showed
that the collected and simulated data had
matching distributions for all of the
Starbucks data (Figure 5.1). The same test
showed that the collected and simulated data
for Dunkin’ Donuts had matching
distributions for only the Latte and the
Coolatta (Figure 5.1). Whenever the K-S
value is less than the critical value, the
distributions match. When the K-S value is
greater than the critical value, the
distributions do not match, which happened
with the Dunkin’ Donuts Hot and Iced
Coffee. Another way to see whether the
distributions match is by looking at
empirical cumulative distribution functions.
Figure 5.1.1 - CDF and Histogram for Starbucks Latte Simulated Data of Service Time vs Collected
Data
Figures A.13- A.20 in the Appendix show
the empirical cumulative distribution
functions side by side for the collected data
and the simulated data which show the
difference in distributions for the other
drinks. The Dunkin’ Donuts Hot and Iced
Coffee simulation data did not match what
was collected in store because not all of the
values inputted into the simulation were
collected experimentally. Some of the values
such as the time of the cashier transaction
had to be taken from other sources such as
established papers, which could have caused
a difference in the simulation data versus the
collected data.
5.1 Starbucks Service Time Simulation
Analysis
Simulations were also run for the
service times, the times from when the
customer ordered the drink to when the
drink was received, in Starbucks and
Dunkin’ Donuts. Histograms, empirical
cumulative distribution functions, and
Kolmogorov-Smirnov tests were done for all
of the service time data for each of the
drinks within each store.
As seen in Figure 5.1.1, both the
histogram curves and the the empirical
cumulative distribution functions for the
simulated data and the collected data for
Starbucks Espresso/Latte/Cappuccino
service time abide closely to the same
profiles. The Kolmogorov-Smirnov test was
run for the data, and the K-S value is 0.193
while the critical value is 0.225. Since the
K-S value is less than the critical value, it is
implied that the distributions for both sets of
data match. The distribution for both sets of
data is Normal.
Figure 5.1.2 shows both the
histogram curves and the empirical
cumulative distribution functions for the
simulated data and the collected data for
Starbucks Frappuccino service time which
abide closely to the same curves. The
Kolmogorov-Smirnov test was run for the
data, and the K-S value is 0.196 while the
critical value is 0.269. Since the K-S value is
less than the critical value, it is implied that
the distributions for both sets of data match.
The distribution for both sets of data is
Gamma.
As seen in Figure 5.1.3, both the
histogram curves and the empirical
cumulative distribution functions for the
simulated data and the collected data for
service time of Starbucks Hot Drip abide
closely to the same profiles. The
Kolmogorov-Smirnov test was run for the
Figure 5.1.4 - CDF and Histogram for Starbucks Iced Drip Simulated Data of Service Time vs
Collected Data
Figure 5.1.2 - CDF and Histogram for Starbucks Frappuccino Simulated Data of Service Time
vs Collected Data
Figure 5.1.3 - CDF and Histogram for Starbucks Hot Drip Simulated Data of Service Time vs
Collected Data
data and the K-S value is 0.128 while the
critical value is 0.262. Since the K-S value is
less than the critical value, it is implied that
the distributions for both sets of data match.
The distribution for both sets of data is
Weibull.
As seen in Figure 5.1.4, neither the
histogram curves nor the empirical
cumulative distribution functions for the
simulated data and the collected data for
service time of the Starbucks Iced Drip
abide as closely to the same curve is
expected when the distributions match. The
Kolmogorov-Smirnov test was run for the
data, and the K-S value is 0.352 while the
critical value is 0.215. Since the K-S value is
greater than the critical value, it is implied
that the distributions for both sets of data do
not match. The reason for the difference in
distribution is that the process to make the
Iced drip coffee is in the same queue as that
of the Espresso drinks in the real world, but
this is not represented in the simulation. An
espresso drink takes more time to make than
an Iced Drip Coffee (which is a relatively
short process), and the time spent in the
espresso queue substantially affects the
amount of time between when the order is
placed and when a customer receives the
drink.
5.2 Dunkin’ Donuts Service Time
Simulation Analysis
Figure 5.2.1 shows both the
histogram curves and the empirical
cumulative distribution functions for the
simulated data and the collected data for
service time, which do abide closely to the
same curves. The Kolmogorov-Smirnov test
was run for the data and the K-S value is
0.868 while the critical value is 0.227. Since
the K-S value is less than the critical value,
it is implied that the distributions for both
sets of data do match. The distribution of the
collected data is lognormal. Seen in the
histogram, the distributions are intuitively
different, indicating that there exists a
discrepancy within the structure of
simulation itself that does not affect service
time distributions of Iced and Coolatta
drinks to such a large degree.
Figure 5.2.2 shows both the
histogram curves and the empirical
cumulative distribution functions for the
simulated data and the collected data for
service time, which do not abide closely to
the same curves. The Kolmogorov-Smirnov
test was run for the data and the K-S value is
0.220 while the critical value is 0.166. Since
the K-S value is greater than the critical
value, it is implied that the distributions for
both sets of data do not match. The
distribution of the collected data is weibull.
Figure 5.2.3 shows both the
histogram curves and the empirical
cumulative distribution functions for the
simulated data and the collected data for
service time, which do not abide closely to
the same curves. The Kolmogorov-Smirnov
test was run for the data and the K-S value is
0.962 while the critical value is 0.163,
exemplifying a sharp distinction between the
two data sets as the K-S value is larger than
the critical value by a large degree. The
distribution of the collected data is
lognormal.
Figure 5.2.4 shows both the
histogram curves and the empirical
cumulative distribution functions for the
simulated data and the collected data for
service time, which do abide closely to the
same curves. The Kolmogorov-Smirnov test
was run for the data and the K-S value is
0.080 while the critical value is 0.110. Since
the K-S value is less than the critical value,
it is implied that the distributions for both
sets of data do match. The distribution of the
collected data is gamma.
Figure 5.2.1 - CDF and Histogram for Dunkin’ Donuts Latte Data of Service Time vs Collected Data
Figure 5.2.2 - CDF and Histogram for Dunkin’ Donuts Coolatta Data of Service Time vs
Collected Data
Figure 5.2.3 - CDF and Histogram for Dunkin’ Donuts Drip Simulated Data of Service Time vs
Collected Data
Figure 5.2.4 - CDF and Histogram for Dunkin’ Donuts Iced Drink Data of Service Time vs
Collected Data
These results in statistical matching of
sojourn and service times result in a diverse
set of combinations. While Latte and
Coolatta drinks matched for sojourn times,
they did not match for service times. While
Iced and Drip did not match for sojourn
times, only Iced matched for service times.
Thus, a case where a drink order fit both
distributions was nonexistent and implies a
considerable margin of error in this Dunkin’
Donuts simulation. Structurally, the DD
simulation is slightly more complex than
that of Starbucks as the payment processes
as observed were oriented towards
efficiency and frequent process overlaying,
which may be difficult to correctly replicate
given the flat, disassembled environment of
Arena. Since only sojourn times matched
with the Latte and Coolatta distributions, the
payment and ordering processes incorrectly
accounted for actual service times of those
drink orders that were not represented within
the simulation. This discrepancy is more
evident in the Latte (Figure 5.2.1) that
exhibits a clear disparity in distribution,
indicating that simulation structure directly
deviated from actual operational structures.
As the payment and ordering processes were
represented by constant delays, the simple
translations in Coolatta service time
distribution (Figure 5.2.2) can be accounted
for by said payment/ordering processes. The
results for Iced drink indicate that the
payment and ordering processes inaccurately
represented cashier interaction times in a
consistent manner as marked by a shift in
distribution curves (Figure ___ graph for
DD Iced sojourn time CDF). Thus, general
process of this production was correctly
observed and translated yet payment and
ordering processes could not be consistent
with this drink specifically. Such an error is
coincidental in nature. As Drip does not
match for neither sojourn nor service times,
there was quite possibly an unobserved
detail of workflow rotation and resource
management in the drink production that
was distinct from that of all other drink
orders. Given the Drip product’s qualities
itself and how they directly align with
Dunkin’s expedited business model, a more
complex or specialized process may have
actually been conducted. However, the same
orientation of workflow rotation as in all
other drinks was simulated, which may have
resulted in such deviated results.
Structural error implies that some
actual firm operations were unobserved or
unaccounted for when translating the
process onto the simulation platform.
Concepts such as worker rotation, general
workflow, and a behavioral aspect of
employee behavior were unobserved and
thus not translated into the simulation. The
simulation employed default parameters to
resource management which may directly
interfere with realistic modelling. Such
inconsistency can propagate itself
throughout each of the simulated customers
and result in larger deficiencies in
distribution matching through such an
extended effect. In the case of workflow
rotation, it is necessary to retain both a
uniform and similar pattern within the
simulation as the concept of queues itself
requires arrival times via Poisson process.
As there are multiple processes as seen in
the simulation, irregular or distinct
workflow rotation affects the value of
inputted distributions from data analysis.
The Arena Simulations for Dunkin
Donuts did not very accurately resemble the
restaurant observed. While some of the
“time-to-make” simulation data came close
to achieving the goal of the Simulation, for
the most part they are not accurate enough to
sufficiently represent the restaurants. One
reason for this could be that our data set is
relatively small, especially once the data is
split into separate drink types. The lack of
data points prevented Minitab from
accurately defining the distribution and
parameters for the Dunkin Donuts
restaurant, and because of the low precision
of these inputs into Arena the data points
from the simulation lacked precision as well.
6. Conclusion
A simulation that properly reflected
the processes within Starbucks and Dunkin’
Donuts was created that could be altered to
accurately represent changes in firm
operations that may increase process
efficiency and profitability without changing
actual employment or resource
management.Process-charts representing the
consumer purchase process were utilized to
form simulation structures that were
comprised of entities, processes, and
resources that mirrored that of actual firms
and configured with analysis of relevant
data. The Minitab statistical package and
data analysis of queue times for individual
drink orders coupled with mutable modules
enabled simulations to be statistically
accurate.The simulation can be tested for
validity using the Kolmogorov-Smirnov test
which compares distributions of the
simulated data to that of the collected data.
Adaptable modules of the simulation allows
for alterations to experiment in resource
utilization to increase efficiency and
profitability. This modelling of firm
operations through simulations holds
potential for such software and methodology
that optimize usage of computational
resources to apply from an industrial
engineering perspective that invites quality
control and other aspects.
Error is evident in some datasets but
is conjecturally accounted for through
extended analysis of empirical observations
and the issue with imposing such factors
into a simulation platform. It was recognized
that employee behavior within each firm can
be unpredictable and invites a larger degree
of error and nonuniform resource
management which opposes the consistent
processes within the simulation.
Furthermore, inconsistency in communal
data collection allowed for a larger degree of
error that propagates into erroneous time
distributions. Some graphs exhibit evidence
that there exist distinct fundamental errors in
simulation structure. Increased expertise
with the software that may enable more
complex modelling is a valid method for
future improvement.
A holistic analysis supported the
claim that Dunkin’ Donuts had lower queue
and service times following their expedient
business model as opposed to the enriched-
like nature of the Starbucks experience. It
was observed within each site that the
amount of customer-oriented amenities were
representative of each firm’s business model
and data analysis further corroborated the
notion that Dunkin’ Donuts operations are
overall quicker than that of Starbucks in
light of business models.
After confirming that the simulation
data accurately represents the processes
within the stores, any occurrences in the
simulation after changes are made to it could
be taken to accurately represent what would
actually happen in the restaurants. The
simulation could be changed to allow for
more efficient and profitable processes
within the restaurants. These changes could
be implemented by testing different amounts
of resources that are employed within the
various processes. Changing the amounts of
cashiers or baristas can result in changes
within the queue times due to resources
being employed in different areas. By
testing multiple variations of resources, an
optimal model for efficiency and
profitability for Starbucks and Dunkin’
Donuts restaurants may be found.
Acknowledgements
The completion of this project
required the collaborative effort of
numerous outside parties. As such, the
authors would specifically like to express
their deepest gratitude towards project
mentor Juilee Malavade for dedicating her
time towards aiding in all project efforts and
without whom completion of this project
would not have been possible. The authors
would also like to extend their thanks to
project mentor Brandon Theiss for providing
guidance and invaluable help in all aspects
of data analysis and simulation creation. The
authors would also like to thank the New
Jersey Governor’s School of Engineering
and Technology as well as all of its
sponsors, including Silverline Windows,
Lockheed Martin, South Jersey Industries,
Novo Nordisk Pharmaceuticals, Inc., and NJ
Resources. The authors would also like to
extend a special thanks to Deans Ilene
Rosen and Jean Patrick Antoine, directors of
the New Jersey Governor’s School of
Engineering and Technology, for providing
the opportunity to perform this study.
Finally, the authors would like to
acknowledge the New Brunswick Dunkin’
Donuts and Starbucks establishments for
allowing the research to be conducted,
Rutgers University and Rutgers School of
Engineering for hosting the Governor’s
School program, as well as the State of New
Jersey for providing the necessary resources
to perform the study.
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Appendix
Figure A.1 - Dunkin’ Donuts Arena Program
Figure A.2 - Starbucks Arena Program
Figure A.3 - Dunkin' Donuts (DD) Line Time Probability Distribution with Fit
Figure A.4 - Dunkin' Donuts Hot Drip Preparation Probability Distribution with Fit
Figure A.5 - Dunkin' Donuts Latte Preparation Probability Distribution with Fit
Figure A.6 - Dunkin' Donuts Frappucino Preparation Probability Distribution with Fit
Figure A.7 - Dunkin' Donuts Iced Coffee Preparation Probability Distribution with Fit
Figure A.8 - Starbucks Line Time Probability Distribution with Fit
Figure A.9 - Starbucks Hot Drip Preparation Probability Distribution with Fit
Figure A.10 - Starbucks Latte Preparation Probability Distribution with Fit
Figure A.11 - Starbucks Frappuccino Preparation Probability Distribution with Fit
Figure A.12 - Starbucks Iced Coffee Preparation Probability Distribution with Fit
Figure A.13 - CDF for the Espresso/Latte/Cappuccino Starbucks Simulation Data compared to
the Collected Data
Figure A.14 -CDF for the Frappuccino Starbucks Simulation Data compared to the Collected
Data
Figure A.15 -CDF for the Hot Drip Starbucks Simulation Data compared to the Collected Data
Figure A.16 -CDF for the Iced Drip Starbucks Simulation Data compared to the Collected Data
Figure A.17 -CDF for the Latte Dunkin’ Donuts Simulation Data compared to the Collected Data
Figure A.18 -CDF for the Iced Coffee Dunkin’ Donuts Simulation Data compared to the
Collected Data
Figure A.19 -CDF for the Drip Dunkin’ Donuts Simulation Data compared to the Collected Data
Figure A.20 -CDF for the Coolatta Dunkin’ Donuts Simulation Data compared to the Collected
Data
Figure A.21 -Chi-Square Value Graph
Figure A.22 -Observed vs. Expected Values Graph