Gourmet Delight: Five-Star Restaurant In Melbourne

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

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.

 

PART C

 

(a) Restaurant patronage is often measured by what is termed “turns” per table (successive seatings per day) and by “covers” (seated dining per night). Sheet 4 of the
Serving Time Project file gives the patronage for Gourmet Delight for successive days in August. The patronage recorded refers to all paying customers over the entire
trading day. Write a brief report of the pattern of patronage. Provide explanation for the pattern observed. Obtain a simple exponentially smoothed series of the data.

 

(You need to plot both series – original series and the smoothed series.

 

(b) Gourmet Delight’s quarterly takings for the past few years are given in Sheet 5 of the Serving Time Project file. Using trend analysis, obtain a forecast for the four quarters of 2018. Write a brief report of your findings. In your report, you need to explain how you have used trend analysis to obtain the forecasts.

A five start restaurant known as Gourmet Delight is a fictitious restaurant. It is located in the Central Business District in the city of Melbourne. The restaurant is quite large, in terms of sitting arrangement as it has a capacity to accommodate 100 people at one particular time.  This indicates that the restaurant can provide a sitting capacity to 100 people together in one sitting. The restaurant is open for all the 7 days in a week but is not open for the whole day. The dining hours are from 12 pm – 3 pm for lunch purposes and from 6 pm – 11 pm, for dinner purposes. The Owner of the restaurant, Gourmet Delight has noticed that the number of clients who had been visiting the restaurant has reduced considerably in the last 6 months. The reason behind this is the poor service for the meals that the staffs of the restaurant has been providing to the clients. Thus, with an aim to improve the service time, the owner made a plan to provide extensive training to the staffs, so that the standard of performance for each of the staffs are uplifted. It is the belief of the owner of Gourmet delight that a service will be considered as efficient service if the serving time is within 20 minutes. The training program has been conducted on the basis of this belief of the owner.

The owner obtained information on the service times to 30 customers before the training was provided and the training was provided. A summary of the service times with comparison are provided in the following tables and figures. Table 1 shows the summary of the service times to the customers before training program and after the training program. From the summary table, it can be seen very clearly that the average service time before the training was conducted is 40.53 minutes, with a standard deviation of 9.59 minutes, which is very less. Thus, it indicates that the average service time reliable. Moreover, it can also be said that more than 50 percent of the clients have been served food in a time higher than 39.5 minutes. Thus, the clients were not at all provided with efficient services. Hence, the loss in the number of clientele. On the other hand, from the analysis of the service times after training, it can be seen that the average service time has reduced to 20 minutes, with a standard deviation of 6.65 minutes, which is less. Thus, it indicates that the average service time reliable. Moreover, it can also be said that less than 50 percent of the clients have been served food in a time less than 19 minutes and no customers have been found to be served in a time higher than 34 minutes. Thus, the clients were mostly provided with efficient services.

Table 1: Summary of Service Times before and after Training

	Serving Times prior to training (minutes)	Serving Times after Training (minutes)
Mean	40.5333	20
Standard Error	1.7517	1.2149
Median	39.5	19
Mode	35	18
Standard Deviation	9.5943	6.6540
Sample Variance	92.0506	44.2759
Kurtosis	0.5310	-0.8648
Skewness	0.6965	0.2521
Range	40	24
Minimum	25	10
Maximum	65	34
Sum	1216	600
Count	30	30

From the boxplot constructed from the given data on the service times, illustrated in figure 1, it can be seen that no outliers are present in the data on service times before the training and after the training as well. Further, by comparing the boxplots for the service times before and after the training, it can be observed clearly that all the measures such as minimum service time, first quartile (indicating the least 25 percent of the service times), third quartile (indicating the least 75 percent of the service times) and the maximum service time are higher before the training was provided than after the training.

Further, from the histograms comparing the service times to the clients before and after the training program, given in figures 2 and 3 respectively, it can be seen that the distribution of the service times before and after the training are approximately normal. The mean or average is said to be the best measure of central tendency for a normal distribution and hence, it can be said that the average serving time after the training has reduced from that before the training.

Thus, it can be said that the aim that the owner of the restaurant had, to uplift the standard of performance of the staffs has been achieved and the standard of performance of the staffs has been uplifted to satisfy the customers and provide efficient service.

 

After 6 months of the training, it has been observed that several staffs have been leaving their employment at Gourmet Delight. The owner of the restaurant had thus become a lot concerned regarding the issue. If the serving time if affected due to this issue, the whole investment of the owner on the extensive training program will be a waste as that would not have improved the condition of the restaurant. Thus, the owner again wanted to understand whether the service time has been affected or not. In order to do that, serving times to 20 randomly selected clients has further been recorded by the owner. From the analysis, it can be seen that the average serving time is 22.5 minutes with a standard deviation of 5.26 minutes, which is also very less. Thus, the mean can be said to be reliable measure. Further, it can be said that 50 percent of the clients were served within 23 minutes, which is higher than the serving time after the training was conducted. Moreover, from the histogram, it can be seen that the data is approximately normal. Hence, here also it can be said that the 22.5 is the average waiting time of all the clients in the restaurant. The summary is provided in table 2.

Table 2: Summary of 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 4: Histogram showing the serving times to the Clients 6 Months after Training

Next, in order to increase the number of clients, the owner of the restaurant went forward with advertisement in the local press. He introduced some special discounts and promotional deals such as “two for the price of one”. For 18 months, the expenditure on advertisement and monthly revenue has been provided by the owner. The regression outcomes are provided in the following table 3.

The regression has been performed to predict the monthly revenue on the basis of the advertising expenditures. The equation that will be used to predict the average monthly revenue is given as follows:

Monthly revenue = 717.75 + 7.45 * Advertising Expenditure ($)

This indicates that, with $1 increase in advertising expenditure, the monthly revenue is increased by $7.45. The initial monthly revenue is $717 when the amount spent on advertising is $0.

The null hypothesis and alternate hypothesis for the regression analysis can be given as follows:

Null Hypothesis: Advertising expenditure does not have significant impact on Monthly Revenue.

Alternate Hypothesis: Advertising expenditure has significant impact on Monthly Revenue.

From the analysis, it can be seen that the F value is 84.96, with a p-value which is less than 0.05. Thus, it can be said the model so developed is significant and the null hypothesis can be rejected. From the coefficient of determination (R Square), it can be determined that there is 84 % variation in monthly revenue which is explained by advertising expenditure. 

Table 3: Regression Output Table

Table 3.1: Regression Statistics
Multiple R	0.91734781
R Square	0.841527005
Adjusted R Square	0.831622443
Standard Error	916.4668923
Observations	18

 

Table 3.2: ANOVA
	df	SS	MS	F	Significance F
Regression	1	71361889	71361889	84.96357	8.42876E-08
Residual	16	13438585	839911.6
Total	17	84800474

 

Table 3.3: Regression Coefficients

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	717.7498437	405.9354	1.768138	0.096098	-142.79473	1578.294
Advertising Expenditure($)	7.449183908	0.808151	9.217569	8.43E-08	5.735981	9.162387

The exponential smoothing to a given data series can be estimated with the help of the following equation:

Exponential Smoothing (ES):

Considering a = 0.5, the exponential smoothing series is along with the original series is given in the following figure 5. From the figure, it can be seen clearly that the smoothed series is less fluctuating that the original series. But there is still instability present in the data. This is because of the seasonality that is present in the data.

 

The trend equation with the help of which the restaurant takings can be forecasted is given as follows:

Restaurant takings (in ‘000s) = 31.59 + 1.33 * t

From the equation, it can be said that with one-unit increase in time, the restaurant takings will increase by 1330 units. In order to predict the restaurant takings for the next four quarters in 2018, the value of t is substituted in the trend equation. The result obtained will be the predicted restaurant takings (in ‘000s) for that particular time. The predicted values are provided in the following table and the original and the predicted series is illustrated with the help of a line graph in figure 6. 

Table 4: Original and Forecasted Restaurant takings

Year	Quarters	Time (t)	Restaurant takings ($'000s)(yi)	Forecast
2014	1	1	$                                                36.77	$    32.92
	2	2	$                                                31.85	$    34.24
	3	3	$                                                33.84	$    35.57
	4	4	$                                                36.56	$    36.89
2015	1	5	$                                                38.12	$    38.22
	2	6	$                                                34.41	$    39.54
	3	7	$                                                38.00	$    40.87
	4	8	$                                                41.13	$    42.19
2016	1	9	$                                                47.90	$    43.52
	2	10	$                                                42.00	$    44.84
	3	11	$                                                50.30	$    46.17
	4	12	$                                                55.69	$    47.50
2017	1	13	$                                                58.83	$    48.82
	2	14	$                                                48.81	$    50.15
	3	15	$                                                46.00	$    51.47
	4	16	$                                                45.50	$    52.80
2018	1	17		$    54.12
	2	18		$    55.45
	3	19		$    56.77
	4	20		$    58.10

Figure 6: Actual and Forecasted trend for Restaurant Takings of Gourmet Delight