Red Dragon solutions.xlsx

7/30/2019 Red Dragon solutions.xlsx

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Order Deliverer PrepTime ravelTime Distance Total Speed49 1 14.6 1.9 0.6 16.5 18.9547 1 11.7 3.3 1.4 15.0 25.4573 1 9.0 3.5 1.5 12.5 25.7117 1 12.1 5.0 1.7 17.1 20.4046 1 14.0 5.3 2.5 19.3 28.3051 1 7.1 7.2 3.3 14.3 27.5075 1 11.0 11.6 3.6 22.6 18.6219 1 7.9 9.0 3.7 16.9 24.6713 1 14.9 8.7 4.2 23.6 28.9740 1 10.3 9.5 4.3 19.8 27.1674 1 13.1 11.9 4.4 25.0 22.1818 1 9.9 9.9 4.5 19.8 27.2711 1 12.0 12.9 4.5 24.9 20.93

3 1 9.2 9.2 4.7 18.4 30.6524 1 11.0 10.5 5.0 21.5 28.5710 1 14.3 13.4 5.3 27.7 23.7350 1 9.5 12.6 6.5 22.1 30.9528 1 9.2 13.4 7.0 22.6 31.3456 1 13.0 12.6 7.2 25.6 34.29

31 1 9.3 22.8 8.2 32.1 21.582 1 10.9 17.8 8.6 28.7 28.99

71 1 17.3 16.6 9.3 33.9 33.6160 1 9.5 21.6 11.6 31.1 32.2214 1 9.7 29.9 11.7 39.6 23.4833 1 11.4 26.1 12.9 37.5 29.6626 2 10.1 2.6 1.4 12.7 32.31

9 2 9.8 4.9 2.6 14.7 31.8470 2 8.7 7.0 2.9 15.7 24.8676 2 12.0 7.5 3.3 19.5 26.4020 2 17.2 6.5 3.4 23.7 31.38

6 2 9.5 8.1 3.6 17.6 26.6712 2 13.0 8.8 4.1 21.8 27.9529 2 18.7 8.9 5.6 27.6 37.7567 2 10.9 17.8 6.9 28.7 23.2632 2 10.1 14.5 7.7 24.6 31.8645 2 9.7 13.8 9.2 23.5 40.0015 2 10.0 18.2 9.5 28.2 31.3269 2 13.4 18.9 10.1 32.3 32.0636 2 15.4 21.2 10.7 36.6 30.28

7 2 7.1 31.6 11.3 38.7 21.4642 2 9.4 23.5 12.2 32.9 31.15

5 2 14.5 21.9 12.2 36.4 33.4266 2 12.9 29.5 14.0 42.4 28.4763 3 17.0 6.0 2.8 23.0 28.0052 3 8.5 7.3 3.0 15.8 24.6661 3 13.1 10.1 3.1 23.2 18.42

34 3 18.0 10.8 3.8 28.8 21.114 3 7.2 14.7 4.3 21.9 17.55

65 3 8.8 13.6 4.6 22.4 20.2962 3 8.4 24.1 5.8 32.5 14.4443 3 6.6 17.0 6.3 23.6 22.2468 3 9.7 23.8 6.4 33.5 16.1341 3 14.4 29.7 6.9 44.1 13.9427 3 8.2 19.0 7.5 27.2 23.6838 3 13.9 21.9 8.4 35.8 23.01


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72 3 7.0 31.3 8.6 38.3 16.4916 3 10.8 22.9 8.8 33.7 23.0622 3 15.0 24.0 9.8 39.0 24.50

8 3 8.5 29.0 10.3 37.5 21.311 3 13.0 30.0 13.3 43.0 26.60

48 4 12.7 0.7 0.2 13.4 17.1430 4 11.0 9.3 2.2 20.3 14.1964 4 14.2 18.6 2.4 32.8 7.7437 4 6.1 6.9 2.8 13.0 24.3521 4 10.2 29.3 3.4 39.5 6.9658 4 10.3 9.4 4.1 19.7 26.1739 4 9.5 17.8 4.6 27.3 15.5153 4 9.9 26.2 5.2 36.1 11.9123 4 12.5 19.5 5.4 32.0 16.6244 4 15.6 18.5 5.9 34.1 19.1455 4 12.0 23.1 7.7 35.1 20.0025 4 15.7 29.0 7.9 44.7 16.3457 4 16.2 28.3 8.2 44.5 17.3954 4 14.3 28.7 8.9 43.0 18.6135 4 14.0 28.8 11.7 42.8 24.38

59 4 8.5 29.8 13.0 38.3 26.17


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Deliverer 1TravelTime TotalTime Speed

Mean 12.248 23.524 26.60763351Standard Error 1.410923102 1.436666048 0.901911893 Deliverer 1Median 11.6 22.6 27.27272727 Deliverer 2Mode 13.4 22.6 #N/A Deliverer 3Standard Deviation 7.05461551 7.18333024 4.509559463 Deliverer 4Sample Variance 49.7676 51.60023333 20.33612655Kurtosis 0.587031829 -0.177503025 -0.901690944Skewness 0.892993951 0.650202141 -0.178943293Range 28 27.1 15.66502463Minimum 1.9 12.5 18.62068966Maximum 29.9 39.6 34.28571429Sum 306.2 588.1 665.1908378Count 25 25 25Confidence Level(95.0%) 2.912001562 2.96513238 1.861454275

Confidence Interval 9.34 20.56 24.7515.16 26.49 28.47

Deliverer 2

TravelTime TotalTime Speed

Mean 14.73333333 26.53333333 30.13609782Standard Error 2.02059656 2.062947317 1.097332355Median 14.15 26.1 31.23380874Mode #N/A #N/A #N/AStandard Deviation 8.572665177 8.752344224 4.655586896Sample Variance 73.49058824 76.60352941 21.67448935Kurtosis -0.73233619 -0.937011048 0.325378021Skewness 0.487086577 0.142293166 0.153385263Range 29 29.7 18.5443038Minimum 2.6 12.7 21.4556962Maximum 31.6 42.4 40Sum 265.2 477.6 542.4497607Count 18 18 18Confidence Level(95.0%) 4.263092052 4.352444465 2.31517213


Deliverer 3


Mean 19.71764706 30.78235294 20.90760273Standard Error 1.992342608 2.010875491 1.01274957Median 21.9 32.5 21.31034483Mode #N/A #N/A #N/AStandard Deviation 8.214639013 8.291052051 4.175673448Sample Variance 67.48029412 68.74154412 17.43624874Kurtosis -1.1813084 -1.042563113 -0.89441226


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Skewness -0.22513287 -0.042181458 -0.169517395Range 25.3 28.3 14.06060606Minimum 6 15.8 13.93939394Maximum 31.3 44.1 28Sum 335.2 523.3 355.4292464Count 17 17 17Confidence Level(95.0%) 4.223576698 4.262864648 2.146932695


Deliverer 4


Mean 20.24375 32.2875 17.66307043Standard Error 2.338891631 2.66027685 1.456298681Median 21.3 34.6 17.26400808Mode #N/A #N/A #N/A

Standard Deviation 9.355566525 10.6411074 5.825194724Sample Variance 87.526625 113.2331667 33.93289357Kurtosis -0.551398 -0.69620224 -0.367517939Skewness -0.76072745 -0.692576889 -0.23034761Range 29.1 31.7 19.21203931Minimum 0.7 13 6.962457338Maximum 29.8 44.7 26.17449664Sum 323.9 516.6 282.6091269Count 16 16 16Confidence Level(95.0%) 4.985232569 5.670249368 3.10402907



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24.75 28.4727.82 32.4518.76 23.0514.56 20.77

CI for speed

Interpretation: Total time is not a good measure of the efficiency oas it includes food preparation time which is out of t

Travel time is not a reliable measure of driver efficiit does not take into account the distance travelled

Average speed is the best indicator as it normalisetime to distance. i.e. how many miles each driver cin one hour.


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f the driverstheir control.

ency becauseby each driver.

s the travellingan complete


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Order Deliverer PrepTime ravelTime Distance Total73 1 9.0 3.5 1.5 12.526 2 10.1 2.6 1.4 12.737 4 6.1 6.9 2.8 13.048 4 12.7 0.7 0.2 13.451 1 7.1 7.2 3.3 14.3

9 2 9.8 4.9 2.6 14.7

47 1 11.7 3.3 1.4 15.0 Deliveries within 10 mile radius (n) 6370 2 8.7 7.0 2.9 15.752 3 8.5 7.3 3.0 15.8 Deliveries that took 25 mins or less 36 0.5749 1 14.6 1.9 0.6 16.519 1 7.9 9.0 3.7 16.9 Deliveries that took 30 mins or less 45 0.7117 1 12.1 5.0 1.7 17.1

6 2 9.5 8.1 3.6 17.6 Deliveries that took 35 mins or less 53 0.843 1 9.2 9.2 4.7 18.4

46 1 14.0 5.3 2.5 19.3 Z = 276 2 12.0 7.5 3.3 19.558 4 10.3 9.4 4.1 19.740 1 10.3 9.5 4.3 19.818 1 9.9 9.9 4.5 19.8

30 4 11.0 9.3 2.2 20.3 95% Confidence interval of the expected vouchers a24 1 11.0 10.5 5.0 21.512 2 13.0 8.8 4.1 21.8 Delivery promise Upper level Lower level

4 3 7.2 14.7 4.3 21.950 1 9.5 12.6 6.5 22.1 Not over 25 minutes 5,533 3,03965 3 8.8 13.6 4.6 22.475 1 11.0 11.6 3.6 22.6 Not over 30 minutes 3,995 1,71928 1 9.2 13.4 7.0 22.663 3 17.0 6.0 2.8 23.0 Not over 35 minutes 2,508 66761 3 13.1 10.1 3.1 23.245 2 9.7 13.8 9.2 23.513 1 14.9 8.7 4.2 23.6

ZProportion

(p)


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43 3 6.6 17.0 6.3 23.620 2 17.2 6.5 3.4 23.732 2 10.1 14.5 7.7 24.611 1 12.0 12.9 4.5 24.974 1 13.1 11.9 4.4 25.056 1 13.0 12.6 7.2 25.6

27 3 8.2 19.0 7.5 27.239 4 9.5 17.8 4.6 27.329 2 18.7 8.9 5.6 27.610 1 14.3 13.4 5.3 27.715 2 10.0 18.2 9.5 28.2 Bins Frequency 67 2 10.9 17.8 6.9 28.7 10.00 0

2 1 10.9 17.8 8.6 28.7 15.00 734 3 18.0 10.8 3.8 28.8 20.00 1223 4 12.5 19.5 5.4 32.0 25.00 1731 1 9.3 22.8 8.2 32.1 30.00 962 3 8.4 24.1 5.8 32.5 35.00 864 4 14.2 18.6 2.4 32.8 40.00 668 3 9.7 23.8 6.4 33.5 45.00 416 3 10.8 22.9 8.8 33.7 More 071 1 17.3 16.6 9.3 33.9

44 4 15.6 18.5 5.9 34.155 4 12.0 23.1 7.7 35.138 3 13.9 21.9 8.4 35.853 4 9.9 26.2 5.2 36.172 3 7.0 31.3 8.6 38.322 3 15.0 24.0 9.8 39.021 4 10.2 29.3 3.4 39.554 4 14.3 28.7 8.9 43.041 3 14.4 29.7 6.9 44.157 4 16.2 28.3 8.2 44.525 4 15.7 29.0 7.9 44.7

05

101520

F r e q u e n c y

Total tim

Histo


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0.12 44.7% 69.6%

0.11 60.0% 82.8%

0.09 74.9% 93.3%

ount

CI = p Z x p(1-p)

nx p(1-p)

n


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Frequency


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Order Deliverer PrepTime ravelTime Distance Total Speed49 1 14.6 1.9 0.6 16.5 18.9547 1 11.7 3.3 1.4 15.0 25.4573 1 9.0 3.5 1.5 12.5 25.7117 1 12.1 5.0 1.7 17.1 20.4046 1 14.0 5.3 2.5 19.3 28.3051 1 7.1 7.2 3.3 14.3 27.5075 1 11.0 11.6 3.6 22.6 18.6219 1 7.9 9.0 3.7 16.9 24.6713 1 14.9 8.7 4.2 23.6 28.9740 1 10.3 9.5 4.3 19.8 27.1674 1 13.1 11.9 4.4 25.0 22.1818 1 9.9 9.9 4.5 19.8 27.2711 1 12.0 12.9 4.5 24.9 20.93

3 1 9.2 9.2 4.7 18.4 30.6524 1 11.0 10.5 5.0 21.5 28.5710 1 14.3 13.4 5.3 27.7 23.7350 1 9.5 12.6 6.5 22.1 30.95

28 1 9.2 13.4 7.0 22.6 31.3456 1 13.0 12.6 7.2 25.6 34.2931 1 9.3 22.8 8.2 32.1 21.58

2 1 10.9 17.8 8.6 28.7 28.9971 1 17.3 16.6 9.3 33.9 33.6160 1 9.5 21.6 11.6 31.1 32.2214 1 9.7 29.9 11.7 39.6 23.4833 1 11.4 26.1 12.9 37.5 29.6626 2 10.1 2.6 1.4 12.7 32.31

9 2 9.8 4.9 2.6 14.7 31.8470 2 8.7 7.0 2.9 15.7 24.8676 2 12.0 7.5 3.3 19.5 26.40

20 2 17.2 6.5 3.4 23.7 31.386 2 9.5 8.1 3.6 17.6 26.6712 2 13.0 8.8 4.1 21.8 27.9529 2 18.7 8.9 5.6 27.6 37.7567 2 10.9 17.8 6.9 28.7 23.2632 2 10.1 14.5 7.7 24.6 31.8645 2 9.7 13.8 9.2 23.5 40.0015 2 10.0 18.2 9.5 28.2 31.3269 2 13.4 18.9 10.1 32.3 32.0636 2 15.4 21.2 10.7 36.6 30.28

7 2 7.1 31.6 11.3 38.7 21.4642 2 9.4 23.5 12.2 32.9 31.15

5 2 14.5 21.9 12.2 36.4 33.4266 2 12.9 29.5 14.0 42.4 28.4763 3 17.0 6.0 2.8 23.0 28.0052 3 8.5 7.3 3.0 15.8 24.6661 3 13.1 10.1 3.1 23.2 18.4234 3 18.0 10.8 3.8 28.8 21.11

4 3 7.2 14.7 4.3 21.9 17.5565 3 8.8 13.6 4.6 22.4 20.2962 3 8.4 24.1 5.8 32.5 14.44


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43 3 6.6 17.0 6.3 23.6 22.2468 3 9.7 23.8 6.4 33.5 16.1341 3 14.4 29.7 6.9 44.1 13.9427 3 8.2 19.0 7.5 27.2 23.6838 3 13.9 21.9 8.4 35.8 23.0172 3 7.0 31.3 8.6 38.3 16.49

16 3 10.8 22.9 8.8 33.7 23.0622 3 15.0 24.0 9.8 39.0 24.50

8 3 8.5 29.0 10.3 37.5 21.311 3 13.0 30.0 13.3 43.0 26.60

48 4 12.7 0.7 0.2 13.4 17.1430 4 11.0 9.3 2.2 20.3 14.1964 4 14.2 18.6 2.4 32.8 7.7437 4 6.1 6.9 2.8 13.0 24.3521 4 10.2 29.3 3.4 39.5 6.9658 4 10.3 9.4 4.1 19.7 26.1739 4 9.5 17.8 4.6 27.3 15.5153 4 9.9 26.2 5.2 36.1 11.91

23 4 12.5 19.5 5.4 32.0 16.6244 4 15.6 18.5 5.9 34.1 19.1455 4 12.0 23.1 7.7 35.1 20.0025 4 15.7 29.0 7.9 44.7 16.3457 4 16.2 28.3 8.2 44.5 17.3954 4 14.3 28.7 8.9 43.0 18.6135 4 14.0 28.8 11.7 42.8 24.3859 4 8.5 29.8 13.0 38.3 26.17


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Comparison of Deliverers

Comparison of Deliverer 1 and 2

t-Test: Two-Sample Assuming Unequal Variances

Deliverer 1 Deliverer 2 Mean 26.60763 30.1361Variance 20.33613 21.67449Observations 25 18Hypothesized Mean Difference 0df 36t Stat -2.48411P(T


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Deliverer 1 Deliverer 4Mean 26.60763 17.66307Variance 20.33613 33.93289Observations 25 16

Hypothesized Mean Difference 0df 26t Stat 5.221683P(T


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Hypothesized Mean Difference 0df 27t Stat 1.829113P(T


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ntervals overlap we conclude that there is noticant difference. If you are interested in more

e and interpretation of the hypothesis testinge assume the variances (standard deviation

al. Both tests can be found in Data...Data

liverer 2 or not") and one tailed test ("Is deliverer 1for the first test below.

nificant difference between the mean speed of deliverer 1 and deliverer 2. We set up

ple mean difference is from the hypothesized mean difference (here 0). We can see thatthe left of 0. In order to reject the null hypothesis in the two tailed test above, the sampleerrors ("t Critical two-tail") away from the mean. Hence, we reject the null hypothesiserer 2 at 5% significance level. We can come to the same conclusion by considering thewo-tail test (the area in the tails beyond +/-2.48 standard errors from 0). Since 0.018 ispothesis.

significantly faster that 1. We set up the following one-tailed hypothesis test (we putis):

ence is many standard errors to the left of 0 (then we would believe del2 is faster thanerrors to the left of 0. In order to reject H 0 we need to be 1.69 ("t Critical one-tail")e is 0.009, which is quite low and lower than 0.05, our significance level. Hence, we can

ay from 0 (the hypothesized value) and the smaller the p value is, the more convinced

in the one-tail test. In the two-tail test it is trivial since the rejection area is in both tails (if zed mean we reject). In the one-tail test we need to determine from the test we set up inejection region is the left tail (if the mean of del1 is much smaller then of del2 we rejecter away to the left of 0 that "t Critical one-tail" = 1.69.

e 5% significance level.


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5% significance level.


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% significance level.s not very low, about 4%.

level. However, we can, but the thing to keepases we are on thene-tail hypothesis tests.


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Comparison of Deliverer 1 and 2

t-Test: Two-Sample Assuming Equal Variances

Deliverer 1 Deliverer 2 Mean 26.60763 30.1361Variance 20.33613 21.67449Observations 25 18Pooled Variance 20.89106Hypothesized Mean Difference 0df 41t Stat -2.49734P(T


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Pooled Variance 25.56565Hypothesized Mean Difference 0df 39t Stat 5.525464P(T


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Pooled Variance 25.4185Hypothesized Mean Difference 0df 31t Stat 1.847586P(T


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An example of a r


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commendation

Red Dragon - Recommendations to Management

Efficiency of Delivery People

people because (i) includes food preparation time while (ii) does not take into account thedifferent route lengths. From the Mean Speed of Delivery we can infer that there aresignificant differences in efficiency between delivery people. The significance tests

performed for each pair of delivery people provide further evidence in favour of this

(iii) Management could use these statistical tools to measure performance of delivery peopleand set incentives and take appropriate action. One way to reduce efficiency gaps is to share

best practice between delivery people. Further, Management could invest in the training of new hires, i.e. familiarity with destinations within the 10 mile radius. To increase overallefficiency, Management should develop a tool for the planning of delivery routes, so that onedeliverer can take care of multiple orders for destinations close to each other.

Certificates,

than 50% and more than 30% of deliveries would be late in the case of the 25 minutes planand the 30 minutes plan respectively. Hence, assuming an average purchase value of 10 per delivery, on average these plans would cost more than 50% and 30% of revenuesrespectively. Therefore, Management should refrain from introducing these plans. The risk associated with the 35 minutes plan is limited. We could state with 95% confidence that the35 minutes plan would cost between 5% and 22% of revenues on average. Management couldfurther reduce this risk by measuring and improving the performance of the delivery people

Notes on the Data

1) The data samples for each deliverer are relatively small. To enable a more reliableapproximation to the Normal Distribution it would be helpful to have a larger sample size approximately 30 data points for each deliverer.

2) The data does not include other important information such as rush hours. For example,, .

need to investigate the causes for these data points and exclude them from the analyses to

Red Dragon solutions.xlsx

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