starbucks wait time analysis

A Starbucks Beverage in Less Than 5 Minutes?

Brandon [email protected]

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 register1- Barista operating the espresso bar1- 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

ArriveWait

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


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


Wilks' 0.99563 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


Wilks' 0.93655 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-Value1464 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 CurvesTest StatisticsMethod Chi-Square DF P-ValueLog-Rank 121.876 4 0.000Wilcoxon 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 ZW1 410 3.680 1009.4 -2.04W2 441 3.958 1092.5 1.05W3 439 3.236 857.0 -7.96W4 461 3.932 1111.7 1.84W5 378 4.691 1277.9 7.42Overall 2129 1065.0

H = 102.49 DF = 4 P = 0.000H = 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 CurvesTest StatisticsMethod Chi-Square DF P-ValueLog-Rank 146.730 40.000Wilcoxon 155.155 40.000

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


Day N Median Ave Rank ZMonday 443 3.273 865.4 -7.68Tuesday 437 3.481 989.4 -2.88Wednesday 462 4.096 1142.4 3.06Thursday 463 4.840 1331.3 10.54Friday 324 3.365 949.1 -3.69Overall 2129 1065.0

H = 159.03 DF = 4 P = 0.000H = 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


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 -0.4956 67 3.625 1014.1 -0.6958 74 3.988 1070.6 0.0860 46 3.884 1069.9 0.0562 32 3.193 864.5 -1.86Overall 2129 1065.0H = 66.39 DF = 31 P = 0.000H = 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

ArriveWait

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 %


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 = 0.491Implies there is a not a statistically significant difference in the mix of drip coffees by week

Difference By Day

Is the difference Significant by DayKruskal-Wallis Test: % versus Day

Kruskal-Wallis Test on %


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 = 0.059Implies 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


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


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


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 HazardEstimate Error Ratio

0 1 -0.7072 0.18287 14.9559 0.0001 0.4932 1 -0.42027 0.17189 5.9779 0.0145 0.6574 1 -0.07753 0.16879 0.211 0.646 0.9256 1 -0.05707 0.17622 0.1049 0.7461 0.94510 1 -0.33439 0.1681 3.9569 0.0467 0.71612 1 -0.14799 0.16602 0.7946 0.3727 0.86214 1 -0.30676 0.15789 3.7747 0.052 0.73616 1 -0.31975 0.1636 3.8199 0.0506 0.72618 1 -0.60671 0.16256 13.9303 0.0002 0.54520 1 -0.54465 0.16443 10.9721 0.0009 0.5822 1 -0.54313 0.15702 11.9642 0.0005 0.58124 1 -0.73163 0.16463 19.7504 <.0001 0.48126 1 -0.37543 0.15735 5.6931 0.017 0.68728 1 -0.42767 0.16295 6.8884 0.0087 0.65230 1 -0.35601 0.17266 4.2516 0.0392 0.732 1 -0.19665 0.17914 1.2051 0.2723 0.82134 1 -0.12916 0.17266 0.5597 0.4544 0.87936 1 -0.07839 0.1647 0.2266 0.6341 0.92538 1 -0.32529 0.16815 3.7426 0.053 0.72240 1 -0.15968 0.16355 0.9533 0.3289 0.85242 1 -0.41828 0.15691 7.1063 0.0077 0.65844 1 -0.3835 0.16539 5.3766 0.0204 0.68146 1 -0.2805 0.18867 2.2102 0.1371 0.75548 1 -0.16627 0.16481 1.0178 0.313 0.84750 1 -0.44875 0.17297 6.731 0.0095 0.63852 1 -0.465 0.16807 7.6545 0.0057 0.62854 1 -0.32921 0.15671 4.4131 0.0357 0.71956 1 -0.11747 0.16667 0.4967 0.4809 0.88958 1 -0.28259 0.16236 3.0294 0.0818 0.75460 1 -0.17944 0.18601 0.9306 0.3347 0.83662 1 0.05145 0.21007 0.06 0.8065 1.053

Analysis of Maximum Likelihood Estimates Ref=8DF Chi-

SquarePr > 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.

ConclusionTime 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 [email protected]

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


Avg time in syst (W) 2.89 min

Regular coffee


Avg time in syst (W) 5.94 (+12.5%)

min



Other drinks


Avg time in syst (W) 4.42(+5%)

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 ZObserved 24 3.848 24.1 -0.19Simulation 24 4.112 24.9 0.19Overall 48 24.5H = 0.03 DF = 1 P = 0.853

Not significant. Simulated = Measured

Measured Values vs Simulated

Test StatisticsMethod P-ValueLog-Rank 0.365Wilcoxon 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 PerformanceBase Line Simulation

Avg CT system

Regular 2.71 minSpecial 5.94 min

Combined 4.42 minCost / unit (regular) $0.27Cost / unit (special) $0.33Total 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


Avg CT system

Regular 2.71 minSpecial 5.94 minCombined 4.42 min

Cost / unit (regular) $0.27Cost / unit (special) $0.33Total 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


Avg CT system

Regular 2.71 minSpecial 5.94 minCombined 4.42 min

Cost / unit (regular) $0.27Cost / unit (special) $0.33Total 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


Avg time in queue

Special 3.70 minAvg CT system

Special 5.94 minCost / unit (regular) $0.27Cost / unit (special) $0.33Total 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 PerformanceBase Simulation

Resource Utilization

Register 70.7%Barista Reg 53.4%Barista Special 81.7%

Cost Used Res

Barista Special $6.54Cost 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 PerformanceConclusion

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 • TH can increase (Extra capacity)

Is Option 2 worth it ???

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 ino Drip Coffee Time to Drink - 3.9o Non Drip Time to Drink- 3.3o 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

starbucks wait time analysis

Education