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A Starbucks Beverage in Less
Than 5 Minutes?
Brandon Theiss
Brandon.Theiss@gmail.com
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.
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.
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.
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
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
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
Starbucks New Brunswick Store Layout
The Starbucks Process
(Customer Perspective)
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
Measurement System
The Measurements of the Process
Arrive
Wait
in
Line
Order
Drink
Drink
Delivered
Wait
For
Drink
To Order To Make
To Drink
Time Stamp
The Measurement Process in the Space
STARBUCK’S
DATA COLLECTION
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
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.
Characterizing the Arrivals(number of
transactions per day in hour window)
Is the Number of transactions
constant?
The Number of Transactions
appears to vary by Week
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
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
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
Arrival Rates
( Per Every 2 Minutes)
Is the Arrival Rate Constant?
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
Which Factors Matter to the
Arrival Rate?
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
Arrival Rates by Arrival Time
Does the Aggregated Process
follow a Poisson?
Per two minute time window
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
What if we change the time Bucket?
Per minute time window
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
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
Time To Drink
What Distribution Characterizes the
Data?
3 Parameter Gamma and Johnson
Transformation adequately describe the
observed data
3 Parameter Gamma Fit to the
Data
Which Factors Influence the
Time to Drink?
Time to Drink By Week
Distribution of Time to Drink
By Week
How different are the Curves?
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
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
Time to Drink By Day
Distribution By Day
How Different Are the Curves?
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
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
Week and Day Both Matter
Distributions by Week and Day
Interaction of Week/Day
How does arrival time effect the
time to drink?
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
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
Time to Make the Drink
What Distribution Does the Time to
Make Follow?
What does the data look like?
The “Drip” peak
More Detailed Process
Arrive
Wait
in
Line
Order
Drink
Drink
Delivere
d
Is Drip
Coffee?
Pour
Drip
Make
Drink
Drink
Delivere
d
Yes (45%)
No (55%)
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
Percentage of Drip Coffees (make time
<1.5 minutes)
Does the % Depend on Week and
Day?
Effect of Week on Drip Ratio
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
Difference By Day
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
Summary of Non Drip Process
Summary of Drip Process
Time to Make Drink for Both
Processes
How is time to make effected by
week and day?
Change in Make times due to
Week
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
Time to Make by Day
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
Both Week and Day are Significant
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
Answering Research Question
(What is the probability of receiving a drink in > 5 Minutes)
But there is a day and week
dependency!
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.
Failure Rates
Interaction of Failure Rate by
Week, Day
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
Process Capability based upon
Binomial
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%
Answering Research Questions (What
time should you arrive to minimize the expected to receive your drink)
Number of observations in each time period
Kaplan-Meier Plots of Time to Drink by Arrival Time
The 8:08 Time Bucket appears to be the Outermost!
Parameter Standard Hazard
Estimate Error Ratio
0 1 -0.7072 0.18287 14.9559 0.0001 0.493
2 1 -0.42027 0.17189 5.9779 0.0145 0.657
4 1 -0.07753 0.16879 0.211 0.646 0.925
6 1 -0.05707 0.17622 0.1049 0.7461 0.945
10 1 -0.33439 0.1681 3.9569 0.0467 0.716
12 1 -0.14799 0.16602 0.7946 0.3727 0.862
14 1 -0.30676 0.15789 3.7747 0.052 0.736
16 1 -0.31975 0.1636 3.8199 0.0506 0.726
18 1 -0.60671 0.16256 13.9303 0.0002 0.545
20 1 -0.54465 0.16443 10.9721 0.0009 0.58
22 1 -0.54313 0.15702 11.9642 0.0005 0.581
24 1 -0.73163 0.16463 19.7504 <.0001 0.481
26 1 -0.37543 0.15735 5.6931 0.017 0.687
28 1 -0.42767 0.16295 6.8884 0.0087 0.652
30 1 -0.35601 0.17266 4.2516 0.0392 0.7
32 1 -0.19665 0.17914 1.2051 0.2723 0.821
34 1 -0.12916 0.17266 0.5597 0.4544 0.879
36 1 -0.07839 0.1647 0.2266 0.6341 0.925
38 1 -0.32529 0.16815 3.7426 0.053 0.722
40 1 -0.15968 0.16355 0.9533 0.3289 0.852
42 1 -0.41828 0.15691 7.1063 0.0077 0.658
44 1 -0.3835 0.16539 5.3766 0.0204 0.681
46 1 -0.2805 0.18867 2.2102 0.1371 0.755
48 1 -0.16627 0.16481 1.0178 0.313 0.847
50 1 -0.44875 0.17297 6.731 0.0095 0.638
52 1 -0.465 0.16807 7.6545 0.0057 0.628
54 1 -0.32921 0.15671 4.4131 0.0357 0.719
56 1 -0.11747 0.16667 0.4967 0.4809 0.889
58 1 -0.28259 0.16236 3.0294 0.0818 0.754
60 1 -0.17944 0.18601 0.9306 0.3347 0.836
62 1 0.05145 0.21007 0.06 0.8065 1.053
Analysis of Maximum Likelihood Estimates Ref=8
DF Chi-
Square
Pr > Chi
Sq
Are the differeces
Significant in terms
of their hazard
ratios?
Demonstrating that 8:08 is an
Extreme Value
Testing Homogeneity of Survival Curves for To_Drink over Strata
Transforming the data
Required since we established earlier that the time to drink is
not normally distributed
Using the Transformed Data
The Point at 8:08 is
showing special
cause variation
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
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.
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.
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
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%
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
Questions?
Brandon Theiss
Brandon.Theiss@gmail.com
Starbucks Wait Time Analysis
Scenario 1 - Base Line
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
Comparison of Measured Values
with Simulated
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
Measured Values vs Simulated
Test Statistics
Method P-Value
Log-Rank 0.365
Wilcoxon
0.510
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.
Scenario 2 - Two baristas spec drinks;
1 Register/Drip
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.
Scenario 3 - Faster Drip
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!
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
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
Scenario 4 - One Barista Spec Drink;
One Register/Drip w/ faster drip
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%)
Scenario 5 - Base line w/ extra barista spec
drinks
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
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%)
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
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?
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

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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
  • 8. Starbucks New Brunswick Store Layout
  • 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
  • 12. The Measurements of the Process Arrive Wait in Line Order Drink Drink Delivered Wait For Drink To Order To Make To Drink Time Stamp
  • 13. The Measurement Process in the Space
  • 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.
  • 17. Characterizing the Arrivals(number of transactions per day in hour window)
  • 18. Is the Number of transactions constant?
  • 19. The Number of Transactions appears to vary by Week
  • 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
  • 23. Arrival Rates ( Per Every 2 Minutes)
  • 24. Is the Arrival Rate Constant?
  • 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
  • 26. Which Factors Matter to the Arrival Rate?
  • 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
  • 28. Arrival Rates by Arrival Time
  • 29. Does the Aggregated Process follow a Poisson? Per two minute time window
  • 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
  • 35. What Distribution Characterizes the Data? 3 Parameter Gamma and Johnson Transformation adequately describe the observed data
  • 36. 3 Parameter Gamma Fit to the Data
  • 37. Which Factors Influence the Time to Drink?
  • 38. Time to Drink By Week
  • 39. Distribution of Time to Drink By Week
  • 40. How different are the Curves?
  • 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
  • 43. Time to Drink By Day
  • 45. How Different Are the Curves?
  • 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
  • 48. Week and Day Both Matter
  • 51. How does arrival time effect the time to drink?
  • 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
  • 54. Time to Make the Drink
  • 55. What Distribution Does the Time to Make Follow?
  • 56. What does the data look like? The “Drip” peak
  • 57. More Detailed Process Arrive Wait in Line Order Drink Drink Delivere d Is Drip Coffee? Pour Drip Make Drink Drink Delivere d Yes (45%) No (55%)
  • 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
  • 59. Percentage of Drip Coffees (make time <1.5 minutes)
  • 60. Does the % Depend on Week and Day?
  • 61. Effect of Week on Drip Ratio
  • 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
  • 65. Summary of Non Drip Process
  • 66. Summary of Drip Process
  • 67. Time to Make Drink for Both Processes
  • 68. How is time to make effected by week and day?
  • 69. Change in Make times due to Week
  • 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
  • 71. Time to Make by Day
  • 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
  • 73. Both Week and Day are Significant
  • 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
  • 75. Answering Research Question (What is the probability of receiving a drink in > 5 Minutes)
  • 76. But there is a day and week dependency!
  • 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.
  • 79. Interaction of Failure Rate by Week, Day
  • 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
  • 81. Process Capability based upon Binomial
  • 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%
  • 83. Answering Research Questions (What time should you arrive to minimize the expected to receive your drink)
  • 84. Number of observations in each time period
  • 85. Kaplan-Meier Plots of Time to Drink by Arrival Time
  • 86. The 8:08 Time Bucket appears to be the Outermost!
  • 87. Parameter Standard Hazard Estimate Error Ratio 0 1 -0.7072 0.18287 14.9559 0.0001 0.493 2 1 -0.42027 0.17189 5.9779 0.0145 0.657 4 1 -0.07753 0.16879 0.211 0.646 0.925 6 1 -0.05707 0.17622 0.1049 0.7461 0.945 10 1 -0.33439 0.1681 3.9569 0.0467 0.716 12 1 -0.14799 0.16602 0.7946 0.3727 0.862 14 1 -0.30676 0.15789 3.7747 0.052 0.736 16 1 -0.31975 0.1636 3.8199 0.0506 0.726 18 1 -0.60671 0.16256 13.9303 0.0002 0.545 20 1 -0.54465 0.16443 10.9721 0.0009 0.58 22 1 -0.54313 0.15702 11.9642 0.0005 0.581 24 1 -0.73163 0.16463 19.7504 <.0001 0.481 26 1 -0.37543 0.15735 5.6931 0.017 0.687 28 1 -0.42767 0.16295 6.8884 0.0087 0.652 30 1 -0.35601 0.17266 4.2516 0.0392 0.7 32 1 -0.19665 0.17914 1.2051 0.2723 0.821 34 1 -0.12916 0.17266 0.5597 0.4544 0.879 36 1 -0.07839 0.1647 0.2266 0.6341 0.925 38 1 -0.32529 0.16815 3.7426 0.053 0.722 40 1 -0.15968 0.16355 0.9533 0.3289 0.852 42 1 -0.41828 0.15691 7.1063 0.0077 0.658 44 1 -0.3835 0.16539 5.3766 0.0204 0.681 46 1 -0.2805 0.18867 2.2102 0.1371 0.755 48 1 -0.16627 0.16481 1.0178 0.313 0.847 50 1 -0.44875 0.17297 6.731 0.0095 0.638 52 1 -0.465 0.16807 7.6545 0.0057 0.628 54 1 -0.32921 0.15671 4.4131 0.0357 0.719 56 1 -0.11747 0.16667 0.4967 0.4809 0.889 58 1 -0.28259 0.16236 3.0294 0.0818 0.754 60 1 -0.17944 0.18601 0.9306 0.3347 0.836 62 1 0.05145 0.21007 0.06 0.8065 1.053 Analysis of Maximum Likelihood Estimates Ref=8 DF Chi- Square Pr > Chi Sq Are the differeces Significant in terms of their hazard ratios?
  • 88. Demonstrating that 8:08 is an Extreme Value Testing Homogeneity of Survival Curves for To_Drink over Strata
  • 89. Transforming the data Required since we established earlier that the time to drink is not normally distributed
  • 90. Using the Transformed Data The Point at 8:08 is showing special cause variation
  • 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
  • 99. Scenario 1 - Base Line
  • 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
  • 101. Comparison of Measured Values with Simulated
  • 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.
  • 107. Scenario 3 - Faster Drip
  • 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