# Pronto Pizza problem submission

July 10, 2017 | Author: Vikas Vimal | Category: Standard Deviation, Confidence Interval, Normal Distribution, Mean, Statistical Analysis

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This is the solution to pronto pizza case study, if you know what that is...

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Statistics Assignment 3

Pronto Pizza GROUP 8

Team Members Pia Bakshi Shruti Shukla Sri Lakshmi Anumolu Vikas Vimal

Introduction Pronto Pizza is a startup company which was established by Antonio Scapelli and his wife in Vinemont about 30 years ago. The restaurant’s business is basically based on its pizza delivery service. Recently, a new fast food pizza delivery chain started competing with Pronto with its 30 minutes guaranteed service or free pizza delivery scheme. Tony, Mr. Antonio’s son now wants to deliver Pronto pizza in 29 minutes or less to eliminate competition. His scheme wants to limit the percentage of free pizza under guarantee to about 5% of all the deliveries. The delivery time for Pronto spanned from 4 p.m. to 12 midnight. The major issues to be monitored in formulating a new delivery strategy were preparation time for pizzas, waiting time to get a delivery driver and travel time to deliver the pizza. To devise a plan for efficient delivery with a target of 29 minutes, Tony did a small random sampling experiment. He collected the data to check how the issues stated above effect Pronto’s delivery, for a month and figured if Pronto could meet the 29 minute requirement or not. After a through initial analysis, Tony concluded that currently Pronto cannot promote the 29 minute delivery system to its customers. Although, increasing the number of delivery boys on Friday and Saturday would decrease the variability in the wait time hence help in attaining the 29 minute cut off. As a result, after altering the waiting period, Tony again performs the sampling of the pizza delivery. This time he samples every 10th pizza and provides discounts to its customers while figuring the strategy to score the 29 minute delivery cut off.

Objectives 1) Calculate the number of deliveries going beyond the break-even point of 5% 2) Effect of preparation time, waiting time and travel time on the delivery service 3) Effect of day and hour of delivery 4) If feasible device a strategy to score the 29 minutes delivery time

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Executive Summary We attempted to resolve the issue at hand on two basic premisesFirst Premise- From the initial data Second premise- From the second set of revisited data, which is collected after implementing the suggestions given after analysing the first data set To ensure 29 minutes delivery time, as expressed by the Owner of Pizza Pronto, it is imperative that the average time for delivery is less than or equal to 25 as the breakeven point is 5%. The distinction between the preparation time and the time for arrival of delivery boy (wait time), preparation time and Travel time are the major determining factors of our recommendations.

First Premise: The mean obtained from the initial data was 25.3 which is basically the average time taken to deliver the pizza. However, considering 95% confidence interval, the value of 25 minutes is contained in the interval (24.82, 25.82). If we had just assumed this observation as our premise, we would have gone ahead with the 29 minutes delivery target. However, the variance in the wait time was very high which suggests that the mean obtained earlier is not true in every case. Also, in the sample given, percentage of late deliveries is 13.75% which is far greater than the 5% break even point. Considering the 95% confidence interval for the true proportion of free pizzas due to late deliveries, does not contain the 5% target Due to inadequacy of available data, we could not ascertain the day with the highest number of deliveries and the hour of the day with highest number of deliveries. Looking at the data we saw that the highest percentage of free deliveries were on Friday and Saturday (23% and 30% of the total deliveries). We learnt through examination that on reducing the preparation time by 3.72 minutes, there was a decrease in the number of free deliveries by nearly 40%. Also as we see that the increase in Total time for delivery is varying proportionally to Wait time. Therefore Tony should employ more people for Delivery especially on Friday and Saturday, the two days of week when the wait time is high

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Thus, we recommend•

An increase in the number of delivery boys on Fri and Saturday in specific

Optimization of machinery used for making Pizza or increase the number of cooks to reduce the preperation time by 5 minutes

Collect data at regular intervals, as it will give information on the Delivery Density at any particular hour of the day and also reduce the sampling bias The book recommendations are similar with few exceptions:

Employ two extra employees to deliver on Fri & Sat, to decrease the wait time

Collect data for every 10th Delivery

Second Premise: As per the recommendations, Tony appointed two additional delivery boys on Friday and Saturday. Analyzing the second set of data, we estimated the mean time of deliveries and number of free deliveries on a daily and hourly basis. Correlating the wait time with the number of free deliveries and delivery time, we learnt that they were deeply related. Thus, to decrease the number of free deliveries it is imperative to decrease the variation in the wait time. Also, the correlation between travel time and sales was also significant. However, the speed is independent of the number of free deliveries. We observed that 1. The change in Total time of delivery is highly dependent on ‘wait time’ followed by the ‘Travel time’ 2. We cannot compare both the data sets and come to conclusion that, the wait time has not decreased on Saturday despite employing two employees, as the initial data set is biased 3. On Mondays, the reason for Late delivery happens to be, low travel speed and high preperation time 4. On Friday and Saturday, the hours for which the Late Delivery is high, The Travel distance is very high

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Recommendations: a.) The restaurant hires two more delivery boys for Friday and Saturday, bringing the total of recently employed delivery boys to 4 or greater based on the requirement b.) Optimize the preperation time. By reducing the Preperation time by 4.57 minutes, we can reduce the Late deliveries by 70% c.) Do not give Free Delivery on Late Delivery on Friday and Saturday if the distance if greater than 4kms and instead give a fixed discount within the limit of cost of break even Post initiating the recommended changes, it is advised that the restaurant management repeat the examination exercise.

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Procedure Observation for Pronto Initial Data: We plot the Histogram of Total time to check for normality:

Time taken for delivery vs frequency 70 60

Frequncy

50 40 30 20 10 0 -10 0

5

10

15

20

25

30

35

40

45

50

Time taken to deliver Pizza Time taken for delivery vs frequency

Graph for time taken for deliver vs. frequency for the initial data. The graph follows a normal distribution with a positive skew.

Assuming that the distribution is close to Normal, we have the summary statistics for the sample as: N

Mean 240

Std Dev 25.32

Std Dev of sample Dist

3.92

95% CI

0.25 (24.82, 25.82)

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Test and Confidence Interval of Event: Late Day

Mon

Tue

Wed

Thu

Fri

Sat

Sun

Overall

X

2

5

1

0

9

12

4

33

N

32

32

32

32

40

40

32

240

0.06

0.16

0.03

0.00

0.23

0.30

0.13

0.14

p>0.05

0.05

0.05

0.05

0.05

0.05

0.05

0.05

0.05

Standard error

0.04

0.04

0.04

0.04

0.03

0.03

0.04

0.01

Z

0.32

2.76

-0.49

-1.30

5.08

7.25

1.95

6.22

0.3728

0.0029

0.3132

0.0972

0.0000

0.0000

0.0258

0.0000

sample p' Test p=0.05 vs

P value

From the above graph we can infer that the number of free deliveries is i highest for the days Friday and Saturday.. Also from the previous table, we see that p test 0.05

0.05

0.05

Standard error

0.02

0.02

Z

1.45

8.72

P value

0.07

0.00

sample p' Test p=0.05 vs

In the above graph we can see a compiled representation of number of free deliveries for the two high risks days (Friday and Saturday) w.r.t. other days of the week. week From the table above we can say that, days other than Fri & Sat when put together are well within with the breakeven point

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Comparing the Data by Day of the week: Day

Mon

Tue

Wed

Thu

Fri

Sat

Sun

Overall

Mean Time Prep Time

14.71 14.82 14.90 15.19 14.92 15.05 15.07

14.95

Std Dev

1.00

1.20

0.94

0.90

0.93

1.24

1.11

1.05

Variance

0.99

1.45

0.89

0.81

0.86

1.53

1.24

1.11

Time

2.12

1.99

1.46

1.02

3.66

4.68

1.93

2.53

Std Dev

2.77

2.98

1.68

1.03

3.24

4.79

2.68

3.26

Variance

7.67

8.86

2.83

1.07 10.52 22.98

7.18

10.60

Mean Wait Time

Mean Travel

Time

7.06

8.25

8.09

7.72

7.96

8.08

7.64

7.84

Time

Std Dev

2.08

1.67

1.83

1.73

1.99

1.88

1.95

1.90

Variance

4.32

2.80

3.34

3.00

3.96

3.52

3.82

3.59

23.89 25.05 24.45 23.93 26.54 27.82 24.64

25.32

Mean Time Total Time

Std Dev Variance

3.40

3.13

2.56

2.26

3.76

5.65

3.52

3.92

11.54

9.77

6.54

5.09 14.17 31.96 12.39

15.40

The above table gives the summary statistics of the sample data set for each day of the week. Comparing the data with the overall data, we have identified (marked in red) the Days of the week with higher average Time of Delivery or High variance of Time of Deliver

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Observation for Pronto Revisited Data: We plot the Histogram of Total time to check for normality:

Graph for time taken for deliver vs. frequency for the revisited data. The data follows a positive skewed normal distribution.

Assuming that the distribution is close to Normal, we have the summary summar statistics for the sample as: N

Mean

Std Dev

Std Dev of sample Dist

95% CI (25.399,

240

25.899

4.081

0.25 26.399)

In the above two graphs we can observe the number and percentage of free deliveries on each day after the recommendations we enforced. We can conclude that the percentage 10

of free deliveries is highest on Friday Friday,with 16% and Saturday,, with 30% as compared to other days of the week. Non Fri & Sat Fri & Sat X 7 38 N 155 169 sample p' 0.05 0.22 Test p=0.05 vs p>0.05 0.05 0.05 Standard error 0.02 0.02 Z -0.28 10.43 P value 0.391 0.000

After looking at the graph, we compare the statistical values for Non Fri and Sat and Fri and Sat. We observe that the t late deliveries is less than 5% for rest of week other than Fri and Sat

In the above two graphs we can observe the compiled total number of free deliveries on Friday and Saturday after the recommendations we enforced. We can conclude that the percentage of free deliveries is highest on Friday and Saturday, whereas, days other than Fri & Sat when put together are well within the breakeven point.

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Tables on Analysis Comparing the data by hours in a day

Prep Time

Wait Time

Travel Time

Total Time

Hour Mean Standard Dev Variance Mean Standard Dev Variance Mean Standard Dev Variance Mean Standard Dev Variance

4 14.97 1.05 1.10 2.78 3.37 11.39 7.26 1.53 2.34 25.01 3.34 11.18

5 15.07 0.95 0.90 2.73 3.11 9.64 7.40 2.20 4.82 25.20 3.64 13.28

6 15.36 1.17 1.38 1.98 2.14 4.57 8.77 2.07 4.27 26.11 2.64 6.98

7 14.93 0.92 0.85 4.22 3.26 10.64 7.70 1.45 2.11 26.85 4.21 17.73

8 15.54 0.92 0.84 2.86 5.74 32.96 7.62 1.54 2.37 26.03 6.41 41.05

9 15.05 1.29 1.66 2.71 3.60 12.93 7.77 1.55 2.39 25.53 4.51 20.36

10 14.84 0.99 0.97 1.69 1.84 3.40 8.46 1.72 2.95 24.98 2.55 6.51

11 Overall 14.84 15.11 1.12 1.11 1.26 1.22 4.17 2.71 3.51 3.44 12.30 11.86 8.57 8.08 1.68 1.80 2.82 3.24 27.59 25.90 4.56 4.08 20.78 16.65

In the above table we compare the hourly statistics of different events that effect the delivery time. We observe that total time for Delivery is high at 5, 6 ,7 and 11th hour driven strongly by wait time for 7,8 and 11 hr and travel time for 6th hour. These values are highlighted with red. Another observation is that Variance of Total Delivery time is very high for 7, 8, 9, 11 hr driven by variance in wait time. Hence, we can conclude that Pronto’s key problem area lies between 6 p.m. to 7 p.m. and 8 p.m. to 11 p.m. especially of Friday and Saturday. Thus, we recommended to hire two more delivery boys on these two days.

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Comparing the data by days in a week

Prep Time

Wait Time

Travel Time

Total Time

Day Mean Time Std Dev Variance Mean Time Std Dev Variance Mean Time Std Dev Variance Mean Time Std Dev Variance

Mon Tue Wed Thur Fri Sat Sun Overall 15.20 15.22 15.43 14.65 14.69 14.76 15.10 1.68 1.28 0.99 1.15 0.82 1.20 1.08 2.81 1.63 0.98 1.33 0.67 1.44 1.16 4.51 1.84 1.61 0.82 2.82 4.90 1.52 3.97 2.79 1.62 0.58 2.37 5.22 1.76 15.73 7.78 2.64 0.33 5.60 27.27 3.09 7.55 8.02 8.21 7.78 8.41 8.13 7.68 2.36 1.57 1.75 1.58 1.85 1.86 1.83 5.57 2.45 3.05 2.50 3.43 3.45 3.36 26.70 24.54 24.58 23.70 26.43 28.24 24.63 4.15 2.63 2.90 2.07 3.14 5.84 2.70 17.24 6.93 8.44 4.30 9.84 34.12 7.28

15.11 1.11 1.22 2.71 3.44 11.86 8.08 1.80 3.24 25.90 4.08 16.65

In the above table we compare the daily statistics of different events that effect the delivery time. We observe that the total time for delivery is high on Mon, Fri and Sat driven by Wait time. But on Friday, Travel time is also an issue to a large extent. These values are highlighted in red. Variance of total time for delivery is also very high on Saturday, Mon and Friday compared to other days of the week which is driven by variance in Wait time. Thus, based on this data we recommended not to give Free Delivery on Late Delivery on Friday and Saturday if the distance if greater than 4 kms and instead give a fixed discount within the limit of cost of break-even point.

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