Exploring COFF[IE]: An Industrial Engineering Analysis

Kenneth Acquah Colin Courchesne Sheela Hanagal aquariusacquah@gmail.com colin.courchesne55@gmail.com shhanagal@gmail.com

Kenneth Li Caroline Potts kenneth.june.li@gmail.com carolinepotts164@gmail.com

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