Ecosystem Interactions Class Discussion Presentation in Blue Green Lined Styl...
Starbucks Wait Time Analysis
1. A Starbucks Beverage in Less
Than 5 Minutes?
Brandon Theiss
Brandon.Theiss@gmail.com
2. The Experiment
• Observe the Starbucks in New Brunswick from
~07:45 AM to ~09:20 AM Monday through
Friday for 5 weeks starting on March 18th 2013
until April 19th 2013
• Week 1 3/18- 3/22
• Week 2 3/15- 3/39
• Week 3 4/1- 4/5
• Week 4 4/8- 4/12
• Week 5 4/15- 4/19
• Measure the amount of time a customer waits in
line and the total amount of time it takes for a
customer to receive a drink.
3. Motivation
• Many people elect to purchase a
Starbucks Beverage prior to the start of
their work day and therefore must
effectively approximate the total cycle time
of obtaining their beverage. If an individual
allocates less than the actual amount they
are late to work. If they allocate more than
the required time they have forgone other
usages of the time.
4. Objective
•To determine the probability of receiving a beverage from
the Starbucks location in New Brunswick NJ between 8 and
9 AM Monday –Friday in less than 5 minutes
•To determine the optimal time to arrive between 8-9AM to
minimize the expected time to receive a drink
•To determine the optimal system configuration to make
either drip coffee or specialty drinks.
5. About Starbucks
•Founded 1971, in Seattle‟s Pike Place Market.
Original name of company was Starbucks Coffee,
Tea and Spices, later changed to Starbucks
Coffee Company.
•In United States:
•50 states, plus the District of Columbia
•6,075 Company-operated stores
•4,082 Licensed stores
•Outside US
•2,326 Company Stores
•3,890 Licensed stores
6. About New Brunswick
•New Brunswick is a city in Middlesex County, New Jersey. It has
a population of 55,181 with a median household income of
$36,080
•Home to Rutgers University and Johnson & Johnson
7. Starbucks in New Brunswick NJ
Standard Employee configuration consists of 3 Baristas.
1- Barista operating the cash register
1- Barista operating the espresso bar
1- Barista delivering the drip coffee
10. Measurement Procedure
1. Click Start on 1 of 12 timers in the Custom Application
(multiple instances of the program can be run to allow for
timers 13-24, 25-36 as needed)
2. Enter Identifying characteristic for the customer in
textbox
3. Click „Drink Ordered‟ when a customer if first speaks to
the Starbucks Barista
4. Click‟ Stop‟ when the customer receives their beverage
or leaves the store. Data is automatically recorded with
times measured in milliseconds
5. Click Reset for the next customer
15. An Anomaly in the Data Collection
Rutgers was sponsoring an event for High School Students.
This resulted in an anomalous measurements and it is
omitted from the analysis
16. Analysis of the Data
• The data was left and right truncated to
only include arrivals into the store between
8 AM and 9 AM.
• The data was processed in Minitab
Software.
20. Is the Variation Statistically
Significant?
Kruskal-Wallis Test: Total versus Week
Kruskal-Wallis Test on Total
Week N Median Ave Rank Z
W1 5 83.00 7.6 -1.74
W2 5 90.00 11.4 -0.39
W3 5 86.00 12.7 0.07
W4 5 95.00 14.4 0.68
W5 4 95.50 17.4 1.51
Overall 24 12.5
H = 4.79 DF = 4 P = 0.310
H = 4.80 DF = 4 P = 0.308 (adjusted for ties)
Implies there is not a statistically significant
difference in number of transactions due to week
21. What About Day?
Kruskal-Wallis Test: Total versus Day
Kruskal-Wallis Test on Total
Day N Median Ave Rank Z
Monday 5 86.00 12.4 -0.04
Tuesday 5 82.00 10.2 -0.82
Wednesday 5 94.00 16.1 1.28
Thursday 5 95.00 15.7 1.14
Friday 4 84.00 7.0 -1.70
Overall 24 12.5
H = 5.27 DF = 4 P = 0.261
H = 5.29 DF = 4 P = 0.259 (adjusted for ties)
Implies there is not a statistically significant
difference in number of transactions due to day
22. Conclusion about the Number of
Transactions
• There is not a statistically significant
difference in the number of transactions due
to day and week.
• Therefore it is reasonable to aggregate the
results.
• The average number of transactions in the 1
hour window is 88.83
25. Arrival Rates and Chi-Square for
Poisson for each observation
Each Arrival is has a P value >0.05 which
suggests that each days arrivals follow a
Poisson Distribution
27. Are the differences Significant?
General Linear Model: Arrivals versus Week, Day, Time Bucket
MANOVA for Week
s = 1 m = 1.0 n = 351.5
Test DF
Criterion Statistic F Num Denom P
Wilks' 0.99590 0.725 4 705 0.575
Lawley-Hotelling 0.00411 0.725 4 705 0.575
Pillai's 0.00410 0.725 4 705 0.575
Roy's 0.00411
MANOVA for Day
s = 1 m = 1.0 n = 351.5
Test DF
Criterion Statistic F Num Denom P
Wilks' 0.99563 0.774 4 705 0.542
Lawley-Hotelling 0.00439 0.774 4 705 0.542
Pillai's 0.00437 0.774 4 705 0.542
Roy's 0.00439
MANOVA for Time Bucket
s = 1 m = 14.0 n = 351.5
Test DF
Criterion Statistic F Num Denom P
Wilks' 0.93655 1.592 30 705 0.024
Lawley-Hotelling 0.06775 1.592 30 705 0.024
Pillai's 0.06345 1.592 30 705 0.024
Roy's 0.06775
The Arrival Rate is not statistically
affected by week and day
The Arrival Rate but
is affected by Arrival
Time
30. A Very Interesting Result
Goodness-of-Fit Test for Poisson Distribution
Data column: Arrival Rate
Poisson mean for Arrivals = 2.82392
N N* DF Chi-Sq P-Value
744 0 7 23.8414 0.001
31. What if we change the time Bucket?
Per minute time window
32. The Same Result!
Goodness-of-Fit Test for Poisson Distribution
Data column: Arrivals
Poisson mean for Arrivals = 1.41940
N N* DF Chi-Sq P-Value
1464 0 5 37.3578 0.000
33. Conclusions About Arrival Rate
• The arrival rate does not depend on Week or
Day
• The arrival rate is influenced by arrival time
• The average arrival rate is 1.42 customers
per minute
• Possible Violation of the assumption of
independence for a Poisson Process
41. A Non Parametric Approach
Comparison of Survival Curves
Test Statistics
Method Chi-Square DF P-Value
Log-Rank 121.876 4 0.000
Wilcoxon 105.831 4 0.000
Implies there is a statistically significant
difference in Time To Drink due to the week
42. Is the Difference Statistically
Significant?
Kruskal-Wallis Test: To Drink versus Week
Kruskal-Wallis Test on To Drink
Week N Median Ave Rank Z
W1 410 3.680 1009.4 -2.04
W2 441 3.958 1092.5 1.05
W3 439 3.236 857.0 -7.96
W4 461 3.932 1111.7 1.84
W5 378 4.691 1277.9 7.42
Overall 2129 1065.0
H = 102.49 DF = 4 P = 0.000
H = 102.49 DF = 4 P = 0.000 (adjusted for ties)
Implies there is a statistically significant
difference in Time To Drink due to the week
46. A Non Parametric Approach
Comparison of Survival Curves
Test Statistics
Method Chi-Square DF P-Value
Log-Rank 146.730 4 0.000
Wilcoxon 155.155 4 0.000
Implies there is a statistically significant
difference in Time To Drink due to the Day
47. Is the difference Statistically
Significant?
Kruskal-Wallis Test: To Drink versus Day
Kruskal-Wallis Test on To Drink
Day N Median Ave Rank Z
Monday 443 3.273 865.4 -7.68
Tuesday 437 3.481 989.4 -2.88
Wednesday 462 4.096 1142.4 3.06
Thursday 463 4.840 1331.3 10.54
Friday 324 3.365 949.1 -3.69
Overall 2129 1065.0
H = 159.03 DF = 4 P = 0.000
H = 159.03 DF = 4 P = 0.000 (adjusted for ties)
Implies there is a statistically significant
difference in Time To Drink due to the day
52. Is the difference Significant?
Kruskal-Wallis Test: To Drink versus Time Bucket
Kruskal-Wallis Test on To Drink
Time Bucket N Median Ave Rank Z
0 49 4.913 1302.2 2.73
2 60 4.166 1143.3 1.00
4 64 3.463 940.9 -1.64
6 55 3.366 936.3 -1.57
…
54 86 3.897 1033.1 -0.49
56 67 3.625 1014.1 -0.69
58 74 3.988 1070.6 0.08
60 46 3.884 1069.9 0.05
62 32 3.193 864.5 -1.86
Overall 2129 1065.0
H = 66.39 DF = 31 P = 0.000
H = 66.39 DF = 31 P = 0.000 (adjusted for ties)
Implies there is a statistically significant
difference in Time To Drink due to the arrival
time
53. Conclusions About Time to Drink
• The time a customer waits for their drink is well
described by a 3 Parameter Gamma distribution which
• The time a customer waits for a drink is influenced by
the day, week and time of arrival.
• The aggregated average Time to Drink is 4.21 minutes
58. Drip Coffee vs. Other Drinks
• Drip Coffee is a made to stock item that is stored
in large carafes with a very short cycle time for
the coffee to be poured into a cup
• Other Drinks (Lattes, Cappuccinos etc) are
made to order items with a long cycle time. The
process is specific to the drink but often requires
making espresso and steaming milk. Minimum
cycle time is greater than 1.5 minutes
62. Is Difference Statistically
Significant?
Kruskal-Wallis Test: % versus Week
Kruskal-Wallis Test on %
Week N Median Ave Rank Z
W1 5 0.3614 10.0 -0.89
W2 5 0.3956 9.4 -1.10
W3 5 0.5349 16.6 1.46
W4 5 0.4545 13.0 0.18
W5 4 0.4894 13.8 0.39
Overall 24 12.5
H = 3.42 DF = 4 P = 0.491
Implies there is a not a statistically
significant difference in the mix of drip
coffees by week
64. Is the difference Significant by Day
Kruskal-Wallis Test: % versus Day
Kruskal-Wallis Test on %
Day N Median Ave Rank Z
Monday 5 0.4857 14.6 0.75
Tuesday 5 0.5591 17.6 1.81
Wednesday 5 0.4189 9.6 -1.03
Thursday 5 0.3474 5.8 -2.38
Friday 4 0.5059 15.5 0.93
Overall 24 12.5
H = 9.09 DF = 4 P = 0.059
Implies there is a may be a statistically
significant difference in the mix of drip
coffees by day
70. Is the difference Significant?
Kruskal-Wallis Test on Make
Week N Median Ave Rank Z
W1 410 1.744 1089.2 0.89
W2 441 2.089 1136.8 2.76
W3 439 1.495 982.4 -3.16
W4 461 1.803 1062.7 -0.09
W5 378 1.633 1053.7 -0.39
Overall 2129 1065.0
H = 14.72 DF = 4 P = 0.005
H = 14.72 DF = 4 P = 0.005 (adjusted for
ties) Implies there is a statistically significant
difference in time to make a drink by week
72. Is the difference Significant?
Kruskal-Wallis Test: Make versus Day
Kruskal-Wallis Test on Make
Day N Median Ave Rank Z
Monday 443 1.618 1017.0 -1.85
Tuesday 437 1.432 944.9 -4.58
Wednesday 462 1.850 1096.7 1.25
Thursday 463 2.125 1211.0 5.78
Friday 324 1.554 1038.8 -0.83
Overall 2129 1065.0
H = 47.33 DF = 4 P = 0.000
H = 47.33 DF = 4 P = 0.000 (adjusted for ties)
Implies there is a statistically significant
difference in time to make a drink by day
74. Conclusions About the Process
to Make a Drink
• There are actually two processes being observed. The process to make a drip coffee and the
process to make all other coffee drinks
• The mix of Drip Coffee and Non Drip coffee is constant over week and day
• The time to make a drink varies by both day and week
77. Looking at the Problem Differently
• A failure occurs when a drink is received in
greater than 5 minutes.
• So let us look at the failure rates to see if
there is a statistically significant difference
by day and week.
80. Is the difference Significant?
General Linear Model: % >5 versus Week, Day
MANOVA for Week
s = 1 m = 1.0 n = 6.5
Test DF
Criterion Statistic F Num Denom P
Wilks' 0.68284 1.742 4 15 0.193
Lawley-Hotelling 0.46447 1.742 4 15 0.193
Pillai's 0.31716 1.742 4 15 0.193
Roy's 0.46447
MANOVA for Day
s = 1 m = 1.0 n = 6.5
Test DF
Criterion Statistic F Num Denom P
Wilks' 0.60502 2.448 4 15 0.091
Lawley-Hotelling 0.65285 2.448 4 15 0.091
Pillai's 0.39498 2.448 4 15 0.091
Roy's 0.65285 Implies there does not appear to be a
statistically significant difference in failures
rates and the day and week
82. Answering Research Questions
(What is the probability of receiving a drink in > 5 Minutes)
• The 95% Confidence interval for receiving
a drink in a less than 5 minutes is from
67.41% to 71.37% with a mean of 69.42%
91. About Control Charts
• The Control Limit on a Shewhart Control chart
represents a +/- 3 Sigma Confidence Interval.
• This implies that there is a 99.7% chance that a
randomly fluctuating observation will be
observed within the control limits.
• Or conversely there is only a 0.3% chance of
observing a more extreme observation than the
control limits.
• As the limits are symmetric 0.15% of the
observation being below the mean
92. Answering Research Questions (What
time should you arrive to minimize the expected to receive your drink)
• An individual should arrive at 8:08 to
minimize the expected time they will wait
to receive their drink.
93. Conclusion
Time Wasted
•4.21 minutes that a customer spends in Starbucks each day
• 4.21 min* 5 working days = 21.05 minutes in a work
week
• 21.05 min * 50 weeks = 1,052.5 minutes in a work year
• 1,052.5 minutes = 17.54 hours/yr spent in waiting in
Starbucks
IF THE AVERAGE CUSTOMER SPENDS 4 MINUTES IN
STARBUCKS, 5 DAYS WEEK, THEN THEY LOSE 2 FULL
8.5 HOUR WORK DAYS IN A YEAR BY GOING TO
STARBUCKS.
94. Conclusion
# of customers in 1 hr
•Average of 88.9 customers comes into Starbucks from 8 AM - 9 AM
•There are about 6,075 Starbucks in the US
• Assuming # of consumers are constant from 8AM - 9AM in every
store.
88.9* 6,075= 540,067 customers spend their time in Starbucks from 8
AM - 9 AM
Which means 2,273,684 minutes (37,895 hours) are wasted each day
at Starbucks!
At an average wage of $25/hr that is $236,842,101.56 nationally in lost
productivity
95. Overall Conclusions
• The best time to arrive at the New Brunswick
Starbucks between 8AM and 9AM is 08:08
• The probability of receiving a drink under 5
minutes is roughly 70%
96. Further Research
Using the Collected Data
Based upon the observed data, the task
was then to develop a computer simulation
for the system that would allow for
evaluation of
• Optimal Number of Employees
• Optimal Queue Configuration
• Optimal Employee Allocation
100. Simulation Model vs Observed
Sim Model
Description Value Unit
Avg time in syst (W) 2.71
(+6.2%)
min
Observed Situation
Description Value Unit
Avg time in syst (W) 2.89 min
Regular coffee
Description Value Unit
Avg time in syst (W) 5.94
(+12.5%)
min
Description Value Unit
Avg time in syst (W) 5.28 min
Other drinks
Description Value Unit
Avg time in syst (W) 4.42
(+5%)
min
Description Value Unit
Avg time in syst (W) 4.21 min
Combined drinks
102. Comparison of Measured Values
with Simulated
Kruskal-Wallis Test: Avg versus Factor
Factor N Median Ave Rank Z
Observed 24 3.848 24.1 -0.19
Simulation 24 4.112 24.9 0.19
Overall 48 24.5
H = 0.03 DF = 1 P = 0.853
Not significant. Simulated = Measured
103. Measured Values vs Simulated
Test Statistics
Method P-Value
Log-Rank 0.365
Wilcoxon
0.510
104. Measured Values vs Simulated
Conclusion
• Krushall Wallis test is not significant
• Log Rank and Wilcoxon tests are not significant
Simulation Model can be used to reproduce
observed situation for further analysis.
105. Scenario 2 - Two baristas spec drinks;
1 Register/Drip
106. Queuing Performance
Base Line Simulation
Avg CT system
Regular 2.71 min
Special 5.94 min
Combined 4.42 min
Cost / unit (regular) $0.27
Cost / unit (special) $0.33
Total Cost (1 hr) $24
Extra Barista; Reg/Drip
Avg CT system
Regular 8.84 min (+226%)
Special 9.60 min (+62%)
Combined 9.26 min (+109%)
Cost / unit (regular) $0.27
Cost / unit (special) $0.33
Total Cost (1 hr) $24
Avg CT significantly increased. Cost remains the same.
This scenario is not a valid option.
108. Scenario 3 - Speeding Up the Drip
Coffee Process
Currently the barista must walk a minimum of 17.9 feet to complete a drip coffee
transaction.
This barista is walking 2/3 of a mile per week during the 08:00-09:00
window to make the drip coffees!
109. Move the Drip Coffee to Directly
Beyond the Register
By locating the drip coffee directly behind the cash register the total distance
traveled for the process is reduced to 8 feet. A 61.2% reduction in the distance
traveled.
The 15th percentile for mixed gender walkers is 1.15 ft/s. Which means the drip
coffee cycle time could be reduced by 8.6 seconds
110. Queuing Performance
Base Line Simulation
Avg CT system
Regular 2.71 min
Special 5.94 min
Combined 4.42 min
Cost / unit (regular) $0.27
Cost / unit (special) $0.33
Total Cost (1 hr) $24
Speeding up drip process
Avg CT system
Regular 2.45 min (-9.6%)
Special 5.82 min (-2%)
Combined 4.30 min (-2.7%)
Cost / unit (regular) $0.27
Cost / unit (special) $0.33
Total Cost (1 hr) $24
Only improvement from Base Line is the Avg CT.
Cost remains the same.
This scenario is a valid option
111. Scenario 4 - One Barista Spec Drink;
One Register/Drip w/ faster drip
112. Queuing Performance
Base Line Simulation
Avg CT system
Regular 2.71 min
Special 5.94 min
Combined 4.42 min
Cost / unit (regular) $0.27
Cost / unit (special) $0.33
Total Cost (1 hr) $24
Register/Drip
Avg CT system
Regular 7.85 min (+263%)
Special 10.47 min (+76%)
Combined 9.93 min (+125%)
Cost / unit (regular) $0.21 (-22%)
Cost / unit (special) $0.28 (-337%)
Total Cost (1 hr) $16 (-33%)
113. Scenario 5 - Base line w/ extra barista spec
drinks
114. Queuing Performance
Base Line Simulation
Avg time in queue
Special 3.70 min
Avg CT system
Special 5.94 min
Cost / unit (regular) $0.27
Cost / unit (special) $0.33
Total Cost (1 hr) $24
Base Line (extra barista)
Avg time in queue
Special 0.18 min (-95%)
Avg CT system
Special 2.50 min (-58%)
Cost / unit (regular) $0.35 (+30%)
Cost / unit (special) $0.42 (+27%)
Total Cost (1 hr) $32 (+33%)
Avg CT significantly decreased. Cost increased.
This scenario can be a potentially an option
115. Queuing Performance
Base Simulation
Resource Utilization
Register 70.7%
Barista Reg 53.4%
Barista Special 81.7%
Cost Used Res
Barista Special $6.54
Cost Unused Res
Barista Special $1.46
Base with extra barista
Resource Utilization
Register 70.7%
Barista Reg 53.4%
Barista Special 43.9% (-46%)
Cost Used Res
Barista Special $7.02 (+7%)
Cost Unused Res
Barista Special $8.98 (+515%)
116. Queuing Performance
Conclusion
Two valid options
Baseline with Faster Drip
• Avg CT Drip (9.6%)
• Total Cost
Baseline with Extra Barista
• Avg CT (58%)
• Total Cost (33%)
• Cost Unused Res (515%)
• Queue Specialty Drink
117. How many more customers would
be required?
• Starbucks Gross Operating Margin is 15.4%
with an average drink cost of $3.00.
• To justify the additional baristas an
additional $8/ (3*15.4%) = ~18 customers
per hour
Can the system handle the additional 18
customers per hour?
118. Yes the System Can
• 100 Simulations Result in
o Drip Coffee Time to Drink - 3.9
o Non Drip Time to Drink- 3.3
o Total Time to Drink (55/45) - 3.63
Drip Coffee is now longer! And its
cycle time has increased by a minute!
But the overall cycle time is still
improved from 4.42 min