Gourmet Delight: Analysis Of Service Times And Revenue, And Trend Essay.

Overview of Gourmet Delight

The data analytical part of the project (75% of total project mark) is divided into 3 parts. Each part tests you on different statistical tools that you have learned in this course. As a group, you need to demonstrate that you have participated in all parts of this project. Work allocation should not be divided according to the parts shown here. The instructions that follow refer to the Data analysis component of your overall project. The other 25 marks will be allocated to the Introduction and Conclusion sections. Please refer to the marking rubrics to see how marks are allocated to the entire project. An additional 10 marks will be assigned for proper sourcing and referencing and another 10 marks for verbal presentation. Total Project will be worth 120 marks.

Part A Gourmet Delight is a fictitious five star restaurant in the Central Business District (CBD) of Melbourne. The restaurant has the capacity to sit 100 customers. The restaurant is open for lunch (12pm – 3pm) and for dinner (6 -11pm) seven days a week. The owner of Gourmet Delight has been concern that the clientele at the restaurant has been declining in the last six months due to poor service times for their meals. The owner decided to put all staff through an extensive training program in the hope of uplifting the standard of their performance. The owner of Gourmet Delight strongly believes that a serving time of no more than 20 minutes equates to efficient service.

File: Serving Times Project Sem 2 2018.xls, Sheet 1, gives the serving times (in minutes) of the restaurant prior to training and after training. Using EXCEL, obtain the following summary measures and write a report of your findings:

(a) Summary statistics

(b) Box- whiskers plots

(c) Histograms (If you need help, see Computer Exercise 3)

Six months after the training, several staff left the employment at Gourmet Delight. This caused concerns to the owner of Gourmet delight. A further random sample of service times was recorded and stored in the same file (Sheet 2). Use this information to determine if the owner of Gourmet Delight should be concern.

Part B

To increase patronage to Gourmet Delight, the owner decided to advertise in the local press, offering special discounts and other promotions such as “two for the price of one” deals. Advertising expenditure and monthly revenue for Gourmet Delight for a period of 18 months are given in Sheet 3 of the Serving Times Project file. Using regression analysis, obtain the necessary outputs, and write a report to determine if advertising expenditure has an impact on the restaurant’s revenue.

In the Central Business District in Melbourne, there is a five-star restaurant called Gourmet Delight. The restaurant has a sitting capacity of around a 100 people at a time. The dining hours in the restaurant are 12pm – 3pm for the purpose of lunch and from 6pm – 11pm for dinner. There is a not a day in week when the restaurant remains closed. The restaurant is open for all the seven days in a week, from Monday till Sunday. There has been a concern for the owner of the restaurant that there has been a decrease in the number of clientele in the restaurant in the last 6 months. According to him, the decrease in the number of clientele has been due to the service times of the meals. The clients in the restaurant has been kept waiting for a much longer time, which has been the reason for the decrease in their number. Thus, the owner has put the employees through a training program, so that the standard of the performance of the staffs serving the restaurant increases. According to the owner, less than 20 minutes of serving time can be considered as efficient service. A waiting time of more than 20 minutes might lead to the loss of clients.

This analysis has been performed to check whether the waiting time of the customers has been decreased after conducting the training program with the staffs. A comparative study of the service times before and after the training program has been conducted. It can be seen from the summary statistics provided in table 2.1 that the average serving time used to be 40.53 minutes before the training program has been conducted. However, the service has been reduced to 20 minutes after the training program.  Moreover, the median value, it can be clearly seen that before the training program, the service time has been more than 39.5 minutes in 50 percent of the cases. Moreover, after the training program has been conducted, it can be seen that that in 50 percent of the cases, the service time has been less than 19 minutes. The standard deviation of the service times has also been found to decrease after the training program. This indicates that the service time has been much more consistent than before, after the training has been conducted. The value of skewness is positive for both before and after the training program. This indicates that the service times are positively skewed, that is more of the service times are less than the average service time. The summary of the service times are shown with the help of a boxplot provided in figure 2.1, comparing the service times before and after the training program. 

Assessment of Service Times

Table 2.1: Summary Statistics of the Service Time before and after the Training Program

	Serving Times prior to training (minutes)	Serving Times after Training (minutes)
Mean	40.53	20
Standard Error	1.75	1.21
Median	39.5	19
Mode	35	18
Standard Deviation	9.59	6.65
Sample Variance	92.05	44.28
Kurtosis	0.53	-0.86
Skewness	0.70	0.25
Range	40	24
Minimum	25	10
Maximum	65	34
Sum	1216	600
Count	30	30

 

Figure 2.1: Five Point Summary Statistics of the Service Time before and after the Training Program

A comparison of the service times of the restaurant has been illustrated with the help of a histogram in figure 2.2. It can be seen from the histogram clearly that there have been 2 cases before the training has been conducted when the service time has been more than 60 minutes. But after the training has been conducted, the service time has improved a lot and it can be seen clearly that there is no service time more than 40 minutes.

 

Figure 2.2: Comparison of Service Time Before and After Training

After 6 months of the training program, there has been a situation, when several staffs left their work at Gourmet Delight. The owner of the company has been concerned on this issue as this might again affect the performance of the staffs and increase in the service time as the number of employees to serve the customers has reduced. A summary of the service times has been obtained after 6 months of the training program. From the summary given in table 2.2, it can be seen that the average service time has been increased to 22.5 minutes. It can also be said from the median value that in 50 percent of the cases, the waiting time has been higher than 23 minutes, which is more than 20 minutes. Thus, the owner must be concerned regarding this attrition issue and must immediately work on the grievances of the staffs and identify the reason behind them leaving their work in the restaurant.

Table 2.2: Serving Time (6 months Late)
Mean	22.5
Standard Error	1.175406
Median	23
Mode	20
Standard Deviation	5.256575
Sample Variance	27.63158
Kurtosis	-1.14532
Skewness	-0.10388
Range	17
Minimum	14
Maximum	31
Sum	450
Count	20

 

Figure 2.2: Comparison of Service Time after training and 6 months after Training

Thus, in order to have an increase in the patronage of the restaurant Gourmet Delight, advertisement to the local press was decided to be given. The advertisement would include special offers and deals such as “Two for the Price of One”. The expenditures involved for advertisements in the past 18 months has been provided by the owner. It can be seen from the regression analysis that the significance value is less than 0.05, and thus it can be said that the regression model is significant. Thus, it can be said that advertising expenditure has a significant impact on the revenue of the restaurant. The impact of the expenditure on revenue is positive, thus, with each dollar increase in the advertisement expenditure of the restaurant, the revenue of the restaurant increases by $7.45.

Table 3.1: Regression Results of Advertising Expenditures and Revenues of Gourmet Delight
Regression Statistics
Multiple R	0.92
R Square	0.84
Adjusted R Square	0.83
Standard Error	916.47
Observations	18
ANOVA
	df	SS	MS	F	Significance F
Regression	1	71361888.58	71361888.58	84.964	0.000
Residual	16	13438585.04	839911.5647
Total	17	84800473.61
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	717.75	405.94	1.768	0.096	-142.79	1578.29
Advertising Expenditure($)	7.45	0.81	9.218	0.000	5.74	9.16

Impact of Training Program on Service Times

Analysis of pattern on patronage 

Table 4.1: Number of customers served in different days of a week

Row Labels	Sum of Number of people who were served a meal
Sun	304
Mon	250
Wed	290
Fri	447
Sat	426
Thur	360
Tues	308
Grand Total	2385

Patronage in the restaurant is measured by considering successive seating per day and successive seating per night on different days for the month of August. In the given month, maximum number of people served on Friday with number of people being 447. The second most populated day for the restaurant is Saturday. The number of people served during the entire month summed up to 426. Thursday, Friday and Sunday are moderately populated day with total number of people being served are 360, 308 and 304 respectively. The least populated day is Monday. Lowest number of people served on that day.

 

Figure 4.1: People served in each day of a week

As observed from the pattern of the visitors, people mostly visit the restaurant at weekends especially on Friday and Saturday. It might be possible that people have relatively less pressure of work on weekends and get time to visit the restaurant. While on Monday, which is the first working day of the week least number of people visit there.

Figure 4.2: Original and Smoothed series for number of patronage

The figure above presents shows comparison between original and smooth series for number of patronage for the restaurant. The original series s more fluctuating compared to the smoothed series. For the original series, number of people on Friday and Saturday deviates largely in comparison to other days of the week. After smoothing, the deviations get smaller indicating a relatively stable trend for number of customers’ visits in the restaurant.

Trend analysis of restaurant’s takings 

The method of trend analysis is used as a technical tool for predicting future value of a data series by observing trend in the previous period. Past values of a series gives an idea regarding the future.

The quarterly data for the restaurant undertakings are given until 2017. A trend analysis is conducted to predict undertakings for the next four quarters. The general trend for the past years is first observed and then a regression analysis is conducted for predicting the future values.

Figure 4.3: Restaurant takings over time

The figure above summarizes the trend in restaurant’s takings over different quarters of the past four years. Following the trend, it has been observed that there is a general upward trend in taking until the first quarter of 2017. The takings however shows a gradual declining trend for the last three quarters of 2017.

After observing the trend, following trend equation is set to predict the values of restaurant takings in 2018.

a is the intercept which indicates the value of restaurant takings with no change in time. b is the slope coefficient of t. It captures magnitude of changes in restaurant’s takings following unit change in time.

Result of the time series regression is given in the following table

Table 4.2: Summary of regression output

Regression Statistics
Multiple R	0.79
R Square	0.63
Adjusted R Square	0.60
Standard Error	5.04
Observations	16

ANOVA
	df	SS	MS	F	Significance F
Regression	1	597.191	597.191	23.483	0.000
Residual	14	356.027	25.430
Total	15	953.217

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	31.59	2.64	11.946	0.000	25.92	37.26
Time	1.33	0.27	4.846	0.000	0.74	1.91

Using the regression result, the estimated regression equation is

Value of the intercept is obtained as 31.59. That means with no change in time, value of restaurant takings’ is 31.59 thousand dollar. The time coefficient from the regression is obtained as 1.33. This means time has a positive influence on restaurant takings. With passes of time, the restaurant takings increases. The coefficient value is greater than 1. This means change in restaurant takings is greater than the unit change in time. The p value associated with the time coefficient is 0.000. The p value is lesser than significance value of 0.05. Hence, the null hypothesis stressing no significant influence of time on takings’ is rejected.  There is thus a positive significant change in takings with passes of time. 

Given the fact that, time has a significant influence on takings’ the estimated equation has been used to predict the future takings of the restaurant for the year 2018. Predicted value obtained from the trend analysis is given in the following table

Table 3: Predicted value of restaurant’s takings

Year	Quarter	Restaurant takings ($'000s)(yi)
2018	1	54.12
	2	55.45
	3	56.77
	4	58.10