Lars, that is a very good point. The slides are from a technical conference talk I delivered for the Institute of Industrial Engineers so clearly they were intended to include more detail.
1.
A Starbucks Beverage in LessThan 5 Minutes?Brandon TheissBrandon.Theiss@gmail.com
2.
The Experiment• Observe the Starbucks in New Brunswick from~07:45 AM to ~09:20 AM Monday throughFriday for 5 weeks starting on March 18th 2013until 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 inline and the total amount of time it takes for acustomer to receive a drink.
3.
Motivation• Many people elect to purchase aStarbucks Beverage prior to the start oftheir work day and therefore musteffectively approximate the total cycle timeof obtaining their beverage. If an individualallocates less than the actual amount theyare late to work. If they allocate more thanthe required time they have forgone otherusages of the time.
4.
Objective•To determine the probability of receiving a beverage fromthe Starbucks location in New Brunswick NJ between 8 and9 AM Monday –Friday in less than 5 minutes•To determine the optimal time to arrive between 8-9AM tominimize the expected time to receive a drink•To determine the optimal system configuration to makeeither 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 StarbucksCoffee 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 hasa population of 55,181 with a median household income of$36,080•Home to Rutgers University and Johnson & Johnson
7.
Starbucks in New Brunswick NJStandard Employee configuration consists of 3 Baristas.1- Barista operating the cash register1- Barista operating the espresso bar1- Barista delivering the drip coffee
10.
Measurement Procedure1. Click Start on 1 of 12 timers in the Custom Application(multiple instances of the program can be run to allow fortimers 13-24, 25-36 as needed)2. Enter Identifying characteristic for the customer intextbox3. Click „Drink Ordered‟ when a customer if first speaks tothe Starbucks Barista4. Click‟ Stop‟ when the customer receives their beverageor leaves the store. Data is automatically recorded withtimes measured in milliseconds5. Click Reset for the next customer
15.
An Anomaly in the Data CollectionRutgers was sponsoring an event for High School Students.This resulted in an anomalous measurements and it isomitted from the analysis
16.
Analysis of the Data• The data was left and right truncated toonly include arrivals into the store between8 AM and 9 AM.• The data was processed in MinitabSoftware.
17.
Characterizing the Arrivals(number oftransactions per day in hour window)
19.
The Number of Transactionsappears to vary by Week
20.
Is the Variation StatisticallySignificant?Kruskal-Wallis Test: Total versus WeekKruskal-Wallis Test on TotalWeek N Median Ave Rank ZW1 5 83.00 7.6 -1.74W2 5 90.00 11.4 -0.39W3 5 86.00 12.7 0.07W4 5 95.00 14.4 0.68W5 4 95.50 17.4 1.51Overall 24 12.5H = 4.79 DF = 4 P = 0.310H = 4.80 DF = 4 P = 0.308 (adjusted for ties)Implies there is not a statistically significantdifference in number of transactions due to week
21.
What About Day?Kruskal-Wallis Test: Total versus DayKruskal-Wallis Test on TotalDay N Median Ave Rank ZMonday 5 86.00 12.4 -0.04Tuesday 5 82.00 10.2 -0.82Wednesday 5 94.00 16.1 1.28Thursday 5 95.00 15.7 1.14Friday 4 84.00 7.0 -1.70Overall 24 12.5H = 5.27 DF = 4 P = 0.261H = 5.29 DF = 4 P = 0.259 (adjusted for ties)Implies there is not a statistically significantdifference in number of transactions due to day
22.
Conclusion about the Number ofTransactions• There is not a statistically significantdifference in the number of transactions dueto day and week.• Therefore it is reasonable to aggregate theresults.• The average number of transactions in the 1hour window is 88.83
25.
Arrival Rates and Chi-Square forPoisson for each observationEach Arrival is has a P value >0.05 whichsuggests that each days arrivals follow aPoisson Distribution
27.
Are the differences Significant?General Linear Model: Arrivals versus Week, Day, Time BucketMANOVA for Weeks = 1 m = 1.0 n = 351.5Test DFCriterion Statistic F Num Denom PWilks 0.99590 0.725 4 705 0.575Lawley-Hotelling 0.00411 0.725 4 705 0.575Pillais 0.00410 0.725 4 705 0.575Roys 0.00411MANOVA for Days = 1 m = 1.0 n = 351.5Test DFCriterion Statistic F Num Denom PWilks 0.99563 0.774 4 705 0.542Lawley-Hotelling 0.00439 0.774 4 705 0.542Pillais 0.00437 0.774 4 705 0.542Roys 0.00439MANOVA for Time Buckets = 1 m = 14.0 n = 351.5Test DFCriterion Statistic F Num Denom PWilks 0.93655 1.592 30 705 0.024Lawley-Hotelling 0.06775 1.592 30 705 0.024Pillais 0.06345 1.592 30 705 0.024Roys 0.06775The Arrival Rate is not statisticallyaffected by week and dayThe Arrival Rate butis affected by ArrivalTime
29.
Does the Aggregated Processfollow a Poisson?Per two minute time window
30.
A Very Interesting ResultGoodness-of-Fit Test for Poisson DistributionData column: Arrival RatePoisson mean for Arrivals = 2.82392N N* DF Chi-Sq P-Value744 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 DistributionData column: ArrivalsPoisson mean for Arrivals = 1.41940N N* DF Chi-Sq P-Value1464 0 5 37.3578 0.000
33.
Conclusions About Arrival Rate• The arrival rate does not depend on Week orDay• The arrival rate is influenced by arrival time• The average arrival rate is 1.42 customersper minute• Possible Violation of the assumption ofindependence for a Poisson Process
41.
A Non Parametric ApproachComparison of Survival CurvesTest StatisticsMethod Chi-Square DF P-ValueLog-Rank 121.876 4 0.000Wilcoxon 105.831 4 0.000Implies there is a statistically significantdifference in Time To Drink due to the week
42.
Is the Difference StatisticallySignificant?Kruskal-Wallis Test: To Drink versus WeekKruskal-Wallis Test on To DrinkWeek 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 1065.0H = 102.49 DF = 4 P = 0.000H = 102.49 DF = 4 P = 0.000 (adjusted for ties)Implies there is a statistically significantdifference in Time To Drink due to the week
46.
A Non Parametric ApproachComparison of Survival CurvesTest StatisticsMethod Chi-Square DF P-ValueLog-Rank 146.730 4 0.000Wilcoxon 155.155 4 0.000Implies there is a statistically significantdifference in Time To Drink due to the Day
47.
Is the difference StatisticallySignificant?Kruskal-Wallis Test: To Drink versus DayKruskal-Wallis Test on To DrinkDay 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 1065.0H = 159.03 DF = 4 P = 0.000H = 159.03 DF = 4 P = 0.000 (adjusted for ties)Implies there is a statistically significantdifference in Time To Drink due to the day
51.
How does arrival time effect thetime to drink?
52.
Is the difference Significant?Kruskal-Wallis Test: To Drink versus Time BucketKruskal-Wallis Test on To DrinkTime Bucket N Median Ave Rank Z0 49 4.913 1302.2 2.732 60 4.166 1143.3 1.004 64 3.463 940.9 -1.646 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 significantdifference in Time To Drink due to the arrivaltime
53.
Conclusions About Time to Drink• The time a customer waits for their drink is welldescribed by a 3 Parameter Gamma distribution which• The time a customer waits for a drink is influenced bythe day, week and time of arrival.• The aggregated average Time to Drink is 4.21 minutes
57.
More Detailed ProcessArriveWaitinLineOrderDrinkDrinkDeliveredIs DripCoffee?PourDripMakeDrinkDrinkDeliveredYes (45%)No (55%)
58.
Drip Coffee vs. Other Drinks• Drip Coffee is a made to stock item that is storedin large carafes with a very short cycle time forthe coffee to be poured into a cup• Other Drinks (Lattes, Cappuccinos etc) aremade to order items with a long cycle time. Theprocess is specific to the drink but often requiresmaking espresso and steaming milk. Minimumcycle time is greater than 1.5 minutes
59.
Percentage of Drip Coffees (make time<1.5 minutes)
62.
Is Difference StatisticallySignificant?Kruskal-Wallis Test: % versus WeekKruskal-Wallis Test on %Week N Median Ave Rank ZW1 5 0.3614 10.0 -0.89W2 5 0.3956 9.4 -1.10W3 5 0.5349 16.6 1.46W4 5 0.4545 13.0 0.18W5 4 0.4894 13.8 0.39Overall 24 12.5H = 3.42 DF = 4 P = 0.491Implies there is a not a statisticallysignificant difference in the mix of dripcoffees by week
64.
Is the difference Significant by DayKruskal-Wallis Test: % versus DayKruskal-Wallis Test on %Day N Median Ave Rank ZMonday 5 0.4857 14.6 0.75Tuesday 5 0.5591 17.6 1.81Wednesday 5 0.4189 9.6 -1.03Thursday 5 0.3474 5.8 -2.38Friday 4 0.5059 15.5 0.93Overall 24 12.5H = 9.09 DF = 4 P = 0.059Implies there is a may be a statisticallysignificant difference in the mix of dripcoffees by day
70.
Is the difference Significant?Kruskal-Wallis Test on MakeWeek N Median Ave Rank ZW1 410 1.744 1089.2 0.89W2 441 2.089 1136.8 2.76W3 439 1.495 982.4 -3.16W4 461 1.803 1062.7 -0.09W5 378 1.633 1053.7 -0.39Overall 2129 1065.0H = 14.72 DF = 4 P = 0.005H = 14.72 DF = 4 P = 0.005 (adjusted forties) Implies there is a statistically significantdifference in time to make a drink by week
72.
Is the difference Significant?Kruskal-Wallis Test: Make versus DayKruskal-Wallis Test on MakeDay N Median Ave Rank ZMonday 443 1.618 1017.0 -1.85Tuesday 437 1.432 944.9 -4.58Wednesday 462 1.850 1096.7 1.25Thursday 463 2.125 1211.0 5.78Friday 324 1.554 1038.8 -0.83Overall 2129 1065.0H = 47.33 DF = 4 P = 0.000H = 47.33 DF = 4 P = 0.000 (adjusted for ties)Implies there is a statistically significantdifference in time to make a drink by day
74.
Conclusions About the Processto Make a Drink• There are actually two processes being observed. The process to make a drip coffee and theprocess 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)
77.
Looking at the Problem Differently• A failure occurs when a drink is received ingreater than 5 minutes.• So let us look at the failure rates to see ifthere is a statistically significant differenceby day and week.
80.
Is the difference Significant?General Linear Model: % >5 versus Week, DayMANOVA for Weeks = 1 m = 1.0 n = 6.5Test DFCriterion Statistic F Num Denom PWilks 0.68284 1.742 4 15 0.193Lawley-Hotelling 0.46447 1.742 4 15 0.193Pillais 0.31716 1.742 4 15 0.193Roys 0.46447MANOVA for Days = 1 m = 1.0 n = 6.5Test DFCriterion Statistic F Num Denom PWilks 0.60502 2.448 4 15 0.091Lawley-Hotelling 0.65285 2.448 4 15 0.091Pillais 0.39498 2.448 4 15 0.091Roys 0.65285 Implies there does not appear to be astatistically significant difference in failuresrates 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 receivinga drink in a less than 5 minutes is from67.41% to 71.37% with a mean of 69.42%
83.
Answering Research Questions (Whattime should you arrive to minimize the expected to receive your drink)
88.
Demonstrating that 8:08 is anExtreme ValueTesting Homogeneity of Survival Curves for To_Drink over Strata
89.
Transforming the dataRequired since we established earlier that the time to drink isnot normally distributed
90.
Using the Transformed DataThe Point at 8:08 isshowing specialcause variation
91.
About Control Charts• The Control Limit on a Shewhart Control chartrepresents a +/- 3 Sigma Confidence Interval.• This implies that there is a 99.7% chance that arandomly fluctuating observation will beobserved within the control limits.• Or conversely there is only a 0.3% chance ofobserving a more extreme observation than thecontrol limits.• As the limits are symmetric 0.15% of theobservation being below the mean
92.
Answering Research Questions (Whattime should you arrive to minimize the expected to receive your drink)• An individual should arrive at 8:08 tominimize the expected time they will waitto receive their drink.
93.
ConclusionTime Wasted•4.21 minutes that a customer spends in Starbucks each day• 4.21 min* 5 working days = 21.05 minutes in a workweek• 21.05 min * 50 weeks = 1,052.5 minutes in a work year• 1,052.5 minutes = 17.54 hours/yr spent in waiting inStarbucksIF THE AVERAGE CUSTOMER SPENDS 4 MINUTES INSTARBUCKS, 5 DAYS WEEK, THEN THEY LOSE 2 FULL8.5 HOUR WORK DAYS IN A YEAR BY GOING TOSTARBUCKS.
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 everystore.88.9* 6,075= 540,067 customers spend their time in Starbucks from 8AM - 9 AMWhich means 2,273,684 minutes (37,895 hours) are wasted each dayat Starbucks!At an average wage of $25/hr that is $236,842,101.56 nationally in lostproductivity
95.
Overall Conclusions• The best time to arrive at the New BrunswickStarbucks between 8AM and 9AM is 08:08• The probability of receiving a drink under 5minutes is roughly 70%
96.
Further ResearchUsing the Collected DataBased upon the observed data, the taskwas then to develop a computer simulationfor the system that would allow forevaluation of• Optimal Number of Employees• Optimal Queue Configuration• Optimal Employee Allocation
99.
Simulation Model vs ObservedSim ModelDescription Value UnitAvg time in syst (W) 2.71(+6.2%)minObserved SituationDescription Value UnitAvg time in syst (W) 2.89 minRegular coffeeDescription Value UnitAvg time in syst (W) 5.94(+12.5%)minDescription Value UnitAvg time in syst (W) 5.28 minOther drinksDescription Value UnitAvg time in syst (W) 4.42(+5%)minDescription Value UnitAvg time in syst (W) 4.21 minCombined drinks
101.
Comparison of Measured Valueswith SimulatedKruskal-Wallis Test: Avg versus FactorFactor 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 = 0.853Not significant. Simulated = Measured
102.
Measured Values vs SimulatedTest StatisticsMethod P-ValueLog-Rank 0.365Wilcoxon0.510
103.
Measured Values vs SimulatedConclusion• Krushall Wallis test is not significant• Log Rank and Wilcoxon tests are not significantSimulation Model can be used to reproduceobserved situation for further analysis.
104.
Scenario 2 - Two baristas spec drinks;1 Register/Drip
105.
Queuing PerformanceBase Line SimulationAvg CT systemRegular 2.71 minSpecial 5.94 minCombined 4.42 minCost / unit (regular) $0.27Cost / unit (special) $0.33Total Cost (1 hr) $24Extra Barista; Reg/DripAvg CT systemRegular 8.84 min (+226%)Special 9.60 min (+62%)Combined 9.26 min (+109%)Cost / unit (regular) $0.27Cost / unit (special) $0.33Total Cost (1 hr) $24Avg CT significantly increased. Cost remains the same.This scenario is not a valid option.
107.
Scenario 3 - Speeding Up the DripCoffee ProcessCurrently the barista must walk a minimum of 17.9 feet to complete a drip coffeetransaction.This barista is walking 2/3 of a mile per week during the 08:00-09:00window to make the drip coffees!
108.
Move the Drip Coffee to DirectlyBeyond the RegisterBy locating the drip coffee directly behind the cash register the total distancetraveled for the process is reduced to 8 feet. A 61.2% reduction in the distancetraveled.The 15th percentile for mixed gender walkers is 1.15 ft/s. Which means the dripcoffee cycle time could be reduced by 8.6 seconds
109.
Queuing PerformanceBase Line SimulationAvg CT systemRegular 2.71 minSpecial 5.94 minCombined 4.42 minCost / unit (regular) $0.27Cost / unit (special) $0.33Total Cost (1 hr) $24Speeding up drip processAvg CT systemRegular 2.45 min (-9.6%)Special 5.82 min (-2%)Combined 4.30 min (-2.7%)Cost / unit (regular) $0.27Cost / unit (special) $0.33Total Cost (1 hr) $24Only improvement from Base Line is the Avg CT.Cost remains the same.This scenario is a valid option
111.
Queuing PerformanceBase Line SimulationAvg CT systemRegular 2.71 minSpecial 5.94 minCombined 4.42 minCost / unit (regular) $0.27Cost / unit (special) $0.33Total Cost (1 hr) $24Register/DripAvg CT systemRegular 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%)
112.
Scenario 5 - Base line w/ extra barista specdrinks
113.
Queuing PerformanceBase Line SimulationAvg time in queueSpecial 3.70 minAvg CT systemSpecial 5.94 minCost / unit (regular) $0.27Cost / unit (special) $0.33Total Cost (1 hr) $24Base Line (extra barista)Avg time in queueSpecial 0.18 min (-95%)Avg CT systemSpecial 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
114.
Queuing PerformanceBase SimulationResource UtilizationRegister 70.7%Barista Reg 53.4%Barista Special 81.7%Cost Used ResBarista Special $6.54Cost Unused ResBarista Special $1.46Base with extra baristaResource UtilizationRegister 70.7%Barista Reg 53.4%Barista Special 43.9% (-46%)Cost Used ResBarista Special $7.02 (+7%)Cost Unused ResBarista Special $8.98 (+515%)
115.
Queuing PerformanceConclusionTwo valid optionsBaseline with Faster Drip• Avg CT Drip (9.6%)• Total CostBaseline with Extra Barista• Avg CT (58%)• Total Cost (33%)• Cost Unused Res (515%)• Queue Specialty Drink
116.
How many more customers wouldbe required?• Starbucks Gross Operating Margin is 15.4%with an average drink cost of $3.00.• To justify the additional baristas anadditional $8/ (3*15.4%) = ~18 customersper hourCan the system handle the additional 18customers per hour?
117.
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) - 3.63Drip Coffee is now longer! And itscycle time has increased by a minute!But the overall cycle time is stillimproved from 4.42 min