Case Study Analysis

School of Business and Governance

Ateneo de Davao University

Submitted to :

Mr. Jose Karlo Caballero

In fulfilment for the requirements on

Math

Submitted by:

Pantojan, Aillynne Mae

Patlunag, Gwenn Aries

Saligumba, Gio Dale

Sereno, Caryll Gale

August 18, 2013

I. Introduction

The Vintage Restaurant is on Captiva Island, a resort community near Fort Myers, Florida. The

restaurant, which is owned and operated by Karen Payne, has just completed its third year of operation. During

that time, Karen has sought to establish a reputation for the restaurant as a high-quality dining establishment that

specializes in fresh seafood. The efforts by Karen and her staff have proven successful, and her restaurant has

become one of the best and fastest-growing restaurants on the island. Karen has concluded that to plan for the

growth of therestaurant in the future, she needs to develop a system that will enable her to forecast food and

beverage sales by month for up to one year in advance. Karen has the following data ($1000s) on total food and

beverage sales for the three years of operation. The data can be found in an Excel spreadsheet (Lost Beverage and

Food Sales). Perform an analysis of the sales data for the Vintage Restaurant. Prepare a report for Karen that

summarizes your findings, forecasts, and recommendations.

II. Problem Statement

Perform an analysis of the sales data for the Vintage Restaurant. Prepare a report for Karen that

summarizes your findings, forecasts, and recommendations.

Include the following:

1. A graph of the time series. 

2. An analysis of the seasonality of the data. Indicate the seasonal indexes for each month,

and comment on the high and low seasonal sales months. Do the seasonal indexes make intuitive sense?

Discuss.

3. A forecast of sales for January through December of the fourth year.

4. Assume that January sales for the fourth year turn out to be $295,000. What was your forecast error? If this is a

large error, Karen may be puzzled about the difference between your forecast and the actual sales value. What can

you do to resolve her uncertainty in the forecasting procedure?

5. Recommendations as to when the system that you have developed should be updated to account for new sales

data that will occur.

6. Detailed calculations of your analysis in the appendix of your report.

III. Objective

To enable Karen to forecast food and beverage sales by month for up to one year in advance so that she

will be able to anticipate the future and develop appropriate strategies.

IV. Analysis

The time series plot is shown below:

0 5 10 15 20 25 30 35 400

50

100

150

200

250

300

Time Series

Month 1 = January for year 1;

month 2 =February for year 1;

and so on.

The time series plot indicates a linear trend and a seasonal pattern. The graph above shows a

straight line that may be a good approximation of the trend in Food and beverages sales. It has no consistent

increase or decrease over time and thus no trend.

2. Analysis of seasonality:

Month

Seasonal-Irregular

Component Values Seasonal

Index

January 1.445 1.441 1.44

February 1.301 1.297 1.30

March 1.344 1.343 1.34

April 1.047 1.034 1.04

May 1.044 1.054 1.05

June .779 .801 .80

July .882 .834 .83

August .857 .848 .85

September .618 .638 .63

October .725 .675 .70

November .843 .862 .85

December 1.137 1.180 1.16

The deseasonalized time series is shown below:

t Deseasonalized

Sales

t Deseasonalized

Sales

1 168.06 19 189.16

2 180.77 20 189.41

3 173.13 21 193.65

4 171.15 22 185.71

5 175.24 23 196.47

6 175.00 24 198.28

7 174.70 25 195.83

8 178.82 26 196.15

9 174.60 27 197.76

10 185.71 28 197.12

11 178.82 29 200.00

12 177.59 30 200.00

13 182.64 31 200.00

14 183.08 32 204.71

15 184.33 33 200.00

16 185.58 34 211.43

17 183.81 35 203.53

18 186.25 36 202.59

The trend line fitted to the deseasonalized time series is

T t = 169.499 + 1.02 t

3. Sales forecasts

Forecast for Year 4

Using T t = 169.499 + 1.02 t

Month

Trend

Forecast

Seasonal

Index

Monthly

Forecast

January 207.239 1.44 298.424

February 208.259 1.30 270.737

March 209.279 1.34 280.434

April 210.299 1.04 218.711

May 211.319 1.05 221.885

June 212.339 .80 169.871

July 213.359 .83 177.088

August 214.379 .85 182.222

September 215.399 .63 135.701

October 216.419 .70 151.493

November 217.439 .85 184.823

December 218.459 1.16 253.194

4.. Forecast error = $295,000 - $298,424 = -$3,424

The forecast we developed over predicted by $3,424; this represents a very small error.V.

Solutions

Month Seasonal Index

January 1.445+1.441/2 1.44

February 1.301+1.297/2 1.30

March 1.344+1.343/2 1.34

April 1.047+1.034/2 1.04

May 1.044+1.054/2 1.05

June .779+.801/2 .80

July .882+.834/2 .83

August .857+.848/2 .85

September .618+.638/2 .63

October .725+.675/2 .70

November .843+.862/2 .85

December 1.137+1.180/2 1.16

t Deseasonalized

Sales

t Deseasonalized

Sales

1 168.06=242/1.44 19 189.16=157/.83

2 180.77=235/1.30 20 189.41=161/.85

3 173.13=232/1.34 21 193.65=122/.63

4 171.15=178/1.04 22 185.71=130/.70

5 175.24=184/1.05 23 196.47=167/.85

6 175.00=140/.80 24 198.28=230/1.16

7 174.70=145/.83 25 195.83=282/1.44

8 178.82=152/.85 26 196.15=255/1.30

9 174.60=110/.63 27 197.76=265/1.34

10 185.71=130/.70 28 197.12=205/1.04

11 178.82=152/.85 29 200.00=210/1.05

12 177.59=206/1.16 30 200.00=160/.80

13 182.64=263/1.44 31 200.00=166/.83

14 183.08=238/1.30 32 204.71=174/.85

15 184.33=247/1.34 33 200.00=126/.63

16 185.58=193/1.04 34 211.43=148/.70

17 183.81=193/1.05 35 203.53=173/.85

18 186.25=149/.80 36 202.59=235/1.16

Month

Trend Forecast Seasonal

Index

Monthly Forecast

January 207.239=

169.499+1.02(37)

1.44 298.424= 207.239*1.44

February 208.259=

169.499+1.02(38)

1.30 270.737=208.259*1.30

March 209.279=

169.499+1.02(39)

1.34 280.434=209.279*1.34

April 210.299=

169.499+1.02(40)

1.04 218.711=210.299*1.04

May 211.319=

169.499+1.02(41)

1.05 221.885=211.319*1.05

June 212.339=

169.499+1.02(42)

.80 169.871=212.339*.80

July 213.359=

169.499+1.02(43)

.83 177.088=213.359*.83

August 214.379=

169.499+1.02(44)

.85 182.222=214.379*.85

September 215.399=

169.499+1.02(45)

.63 135.701=215.399*.63

October 216.419=

169.499+1.02(46)

.70 151.493=216.419*.70

November 217.439=

169.499+1.02(47)

.85 184.823=217.439*.85

December 218.459= 1.16 253.194=218.459*1.16

169.499+1.02(48)

Suppose the actual January sales for the fourth year turn out to be $295,000. The forecasted January sales are

$296,458.

Forecast error = $295,000 - $298,424 = -$3,424

VI. Conclusion

Karen does not have to worry about the error and she can be assured that her forecast model is

extremely good. She has to update the data monthly to have a better understanding of the pattern of past

sales, leading to better prediction of the future sales for the product. The analysis can be easily

updated each month, especially if a computer software package is used to perform the

analysis.