Pronto Pizza problem submission

Statistics Assignment 3

Pronto Pizza

GROUP 8

Team Members

Pia Bakshi

Shruti Shukla

Sri Lakshmi Anumolu

Vikas Vimal

2

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 premises-

First 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:

Assuming that the distribution is close to Normal, we have the summary statistics for

the sample as:

N Mean Std Dev Std Dev of sample Dist 95% CI

240 25.32 3.92 0.25 (24.82, 25.82)

-10

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30 35 40 45 50

Fre

qu

ncy

Time taken to deliver Pizza

Time taken for delivery vs frequency

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.

Test and Confidence Interval of Event: Late

Day Mon Tue

X 2

N 32

sample p' 0.06 0.16

Test p=0.05 vs

p>0.05 0.05 0.05

Standard error 0.04 0.04

Z 0.32 2.76

P value 0.3728 0.0029

From the above graph we can infer that the

days Friday and Saturday. Also from the previous table, we see that p test <0.05 holds

for Monday, Wednesday and Thursday. But we see

5% break even.

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Test and Confidence Interval of Event: Late

Tue Wed Thu Fri Sat

5 1 0 9

32 32 32 40

0.16 0.03 0.00 0.23 0.30

0.05 0.05 0.05 0.05 0.05

0.04 0.04 0.04 0.03 0.03

2.76 -0.49 -1.30 5.08 7.25

0.0029 0.3132 0.0972 0.0000 0.0000

From the above graph we can infer that the number of free deliveries i

. Also from the previous table, we see that p test <0.05 holds

for Monday, Wednesday and Thursday. But we see that Tue and Sun and close to the

Sat Sun Overall

12 4 33

40 32 240

0.30 0.13 0.14

0.05 0.05 0.05

0.03 0.04 0.01

7.25 1.95 6.22

0.0000 0.0258 0.0000

number of free deliveries is highest for the

. Also from the previous table, we see that p test <0.05 holds

d Sun and close to the

Therefore, combining all the days other than Friday and Saturday:

Non Fri &

Sat

X

N

sample p'

Test p=0.05 vs

p>0.05

Standard error

Z

P value

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

table above we can say that, days other than Fri & Sat when

the breakeven point

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Therefore, combining all the days other than Friday and Saturday:

Non Fri &

Fri & Sat

12 21

160 80

0.075 0.2625

0.05 0.05

0.02 0.02

1.45 8.72

0.07 0.00


the two high risks days (Friday and Saturday) w.r.t. other days of the week

table above we can say that, days other than Fri & Sat when put together are well with


the two high risks days (Friday and Saturday) w.r.t. other days of the week. From the

put together are well within

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Comparing the Data by Day of the week:

Day Mon Tue Wed Thu Fri Sat Sun Overall

Prep Time

Mean

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

Wait Time

Mean

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

Travel

Time

Mean

Time 7.06 8.25 8.09 7.72 7.96 8.08 7.64 7.84

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

Total Time

Mean

Time 23.89 25.05 24.45 23.93 26.54 27.82 24.64 25.32

Std Dev 3.40 3.13 2.56 2.26 3.76 5.65 3.52 3.92

Variance 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

Observation for Pronto Revisited Data:

We plot the Histogram of Total time to check for normality:

Assuming that the distribution is close to Normal, we have the summar

the sample as:

N Mean

240 25.899

In the above two graphs we can observe the number and percentage of free deliveries on

each day after the recommendations we enforced.

Graph for time taken for deliver vs. frequency for the revisited data. The data follows a

10

Observation for Pronto Revisited Data:

the Histogram of Total time to check for normality:

Assuming that the distribution is close to Normal, we have the summar

Std Dev Std Dev of sample Dist

4.081 0.25


each day after the recommendations we enforced. We can conclude that the percentage


positive skewed normal distribution.

Assuming that the distribution is close to Normal, we have the summary statistics for

Std Dev of sample Dist 95% CI

0.25

(25.399,

26.399)


We can conclude that the percentage


of free deliveries is highest on Friday

other days of the week.

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

percentage of free deliveries is

Fri & Sat when put together are well within the breakeven point.

Non Fri & Sat

X

N 155

sample p' 0.05

Test p=0.05 vs p>0.05 0.05

Standard error 0.02

Z -0.28

P value 0.391

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highest on Friday,with 16% and Saturday, with 30%


Friday and Saturday after the recommendations we enforced. We can conclude

highest on Friday and Saturday, whereas, days other than

Fri & Sat when put together are well within the breakeven point.

Non Fri & Sat Fri & Sat

7 38

155 169

0.05 0.22

0.05 0.05

0.02 0.02

-0.28 10.43

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 t

is less than 5% for rest of week other than Fri

and Sat

, with 30% as compared to


Friday and Saturday after the recommendations we enforced. We can conclude that the

highest on Friday and Saturday, whereas, days other than

After looking at the graph, we compare the

statistical values for Non Fri and Sat and Fri

observe that the late deliveries

is less than 5% for rest of week other than Fri

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Tables on Analysis

Comparing the data by hours in a day

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.

Hour 4 5 6 7 8 9 10 11 Overall

Mean 14.97 15.07 15.36 14.93 15.54 15.05 14.84 14.84 15.11

Standard Dev 1.05 0.95 1.17 0.92 0.92 1.29 0.99 1.12 1.11

Variance 1.10 0.90 1.38 0.85 0.84 1.66 0.97 1.26 1.22

Mean 2.78 2.73 1.98 4.22 2.86 2.71 1.69 4.17 2.71

Standard Dev 3.37 3.11 2.14 3.26 5.74 3.60 1.84 3.51 3.44

Variance 11.39 9.64 4.57 10.64 32.96 12.93 3.40 12.30 11.86

Mean 7.26 7.40 8.77 7.70 7.62 7.77 8.46 8.57 8.08

Standard Dev 1.53 2.20 2.07 1.45 1.54 1.55 1.72 1.68 1.80

Variance 2.34 4.82 4.27 2.11 2.37 2.39 2.95 2.82 3.24

Mean 25.01 25.20 26.11 26.85 26.03 25.53 24.98 27.59 25.90

Standard Dev 3.34 3.64 2.64 4.21 6.41 4.51 2.55 4.56 4.08

Variance 11.18 13.28 6.98 17.73 41.05 20.36 6.51 20.78 16.65

Prep Time

Wait Time

Travel Time

Total Time

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Comparing the data by days in a week

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.

Day Mon Tue Wed Thur Fri Sat Sun Overall

Mean Time 14.65 14.69 14.76 15.10 15.20 15.22 15.43 15.11

Std Dev 1.68 1.28 0.99 1.15 0.82 1.20 1.08 1.11

Variance 2.81 1.63 0.98 1.33 0.67 1.44 1.16 1.22

Mean Time 4.51 1.84 1.61 0.82 2.82 4.90 1.52 2.71

Std Dev 3.97 2.79 1.62 0.58 2.37 5.22 1.76 3.44

Variance 15.73 7.78 2.64 0.33 5.60 27.27 3.09 11.86

Mean Time 7.55 8.02 8.21 7.78 8.41 8.13 7.68 8.08

Std Dev 2.36 1.57 1.75 1.58 1.85 1.86 1.83 1.80

Variance 5.57 2.45 3.05 2.50 3.43 3.45 3.36 3.24

Mean Time 26.70 24.54 24.58 23.70 26.43 28.24 24.63 25.90

Std Dev 4.15 2.63 2.90 2.07 3.14 5.84 2.70 4.08

Variance 17.24 6.93 8.44 4.30 9.84 34.12 7.28 16.65

Wait Time

Travel Time

Total Time

Prep Time

Pronto Pizza problem submission

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