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Case Analysis: Forecasting Food and Beverage Sales

Extracts from this document...

Introduction

Case Analysis:  Forecasting Food and Beverage Sales

CASE ANALYSIS:

FORECASTING FOOD AND BEVERAGE SALES

Suzanne Michelle Gager

QNT 531:  Advanced Problems in Statistics and Research Methods

Terrance C. Feravich

March 20, 2006


Case Analysis: Forecasting Food and Beverage Sales

Problem Definition

        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 of 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 the restaurant 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 foodand beverage sales for the three years of operation.

Lost Beverage and Food Sales Case

Vintage Restaurant Sales

MONTH

First Year

Second Year

Third Year

January

242

263

282

February

235

238

255

March

232

247

265

April

178

193

205

May

184

193

210

June

140

149

160

July

145

157

166

August

152

161

174

September

110

122

126

October

130

130

148

November

152

167

173

December

206

230

235


The statistical Summary of the data is shown below:

Year

January

February

March

April

May

June

July

August

September

October

November

December

Total Sales

1

242

235

232

178

184

140

145

152

110

130

152

206

2106

2

263

238

247

193

193

149

157

161

122

130

167

230

2250

3

282

255

265

205

210

160

166

174

126

148

173

235

2399

Total:

787

728

744

576

587

449

468

487

358

408

492

671

6755

Mean:

262.3333333

242.66667

248

192

195.6667

149.6667

156

162.3333

119.33333

136

164

223.6667

2251.666667

Variance:

400.3333333

116.33333

273

183

174.3333

100.3333

111

122.3333

69.333333

108

117

240.3333

21464.33333

StDev:

20.0083316

10.785793

16.52271

13.52775

13.20353

10.01665

10.53565

11.06044

8.326664

10.3923

10.81665

15.5026 ...read more.

Middle

2394

199.5

199.25

105.40%

June

160

2399

199.92

199.71

80.12%

July

166

August

174

September

126

October

148

November

173

December

235


llustration

176.38

=(175.5+177.25)/2

82.21%

=145/176.38

2106

=242+235+232+178+184+140+145+152+110+130+152+206

2127

=235+232+178+184+140+145+152+110+130+152+206+263


Step 2

Calculate Seasonal index (Index picked up from above table)

Year

January

February

March

April

May

June

July

August

September

October

November

December

1

82.21%

85.69%

61.75%

72.47%

84.27%

113.73%

2

144.51%

130.14%

134.42%

104.75%

104.39%

79.89%

83.38%

84.83%

63.79%

67.53%

86.21%

118.02%

3

144.09%

129.69%

134.29%

103.40%

105.40%

80.12%

Total

Mean=

144.30%

129.91%

134.35%

104.08%

104.89%

80.00%

82.80%

85.26%

62.77%

70.00%

85.24%

115.88%

1199.48%

Adjusted mean=

144.36%

129.97%

134.41%

104.12%

104.94%

80.04%

82.83%

85.30%

62.80%

70.03%

85.28%

115.93%

1200.00%

Illustration

Total of means=

1199.4850%

144.36%

=1.0004*144.3%

This total is to be adjusted to

1200.00%

(for 12 months)

Adjusting factor=

1.0004

=1200%/1199.485%


Step 3

Deseasonalize data

Deseasonalzed Attendance

Year

Months

Sales

Seasonal index

Deseasonalized Attendance= Attendance/ Seasonal index

1

January

242

144.36%

168

=242/144.36%

February

235

129.97%

181

=235/129.97%

March

232

134.41%

173

=232/134.41%

April

178

104.12%

171

=178/104.12%

May

184

104.94%

175

June

140

80.04%

175

July

145

82.83%

175

August

152

85.30%

178

September

110

62.80%

175

October

130

70.03%

186

November

152

85.28%

178

December

206

115.93%

178

2

January

263

144.36%

182

February

238

129.97%

183

March

247

134.41%

184

April

193

104.12%

185

May

193

104.94%

184

June

149

80.04%

186

July

157

82.83%

190

August

161

85.30%

189

September

122

62.80%

194

October

130

70.03%

186

November

167

85.28%

196

December

230

115.93%

198

3

January

282

144.36%

195

February

255

129.97%

196

March

265

134.41%

197

April

205

104.12%

197

May

210

104.94%

200

June

160

80.04%

200

July

166

82.83%

200

August

174

85.30%

204

September

126

62.80%

201

October

148

70.03%

211

November

173

85.28%

203

December

235

115.93%

203

Step 4

Use Deseasonalize data to predict trend sales for the next 12 months by first calculating the regression equation and then using the equation to predict sales for the next 12 months

Year

Month

Sales

1

January

168

February

181

March

173

April

171

May

175

June

175

July

175

August

178

September

175

October

186

November

178

December

178

2

January

182

February

183

March

184

April

185

May

184

June

186

July

190

August

189

September

194

October

186

November

196

December

198

3

January

195

February

196

March

197

April

197

May

200

June

200

July

200

August

204

September

201

October

211

...read more.

Conclusion

/td>

168

1

168

1

181

2

362

4

173

3

519

9

171

4

684

16

175

5

875

25

175

6

1050

36

175

7

1225

49

178

8

1424

64

175

9

1575

81

186

10

1860

100

178

11

1958

121

178

12

2136

144

182

13

2366

169

183

14

2562

196

184

15

2760

225

185

16

2960

256

184

17

3128

289

186

18

3348

324

190

19

3610

361

189

20

3780

400

194

21

4074

441

186

22

4092

484

196

23

4508

529

198

24

4752

576

195

25

4875

625

196

26

5096

676

197

27

5319

729

197

28

5516

784

200

29

5800

841

200

30

6000

900

200

31

6200

961

204

32

6528

1024

201

33

6633

1089

211

34

7174

1156

203

35

7105

1225

203

36

7308

1296

Σ=

6777

666

129330

16206

n=

36

 Calculation of regression coefficients using the equations

ΣY=na+b1ΣX

6777

=

36

a

+

666

b1

ΣXY=aΣX1+b1ΣX2

129330

=

666

a

+

16206

b1

36

666

a

=

6777

666

16206

b1

=

129330

Use matrix and inverse of matrix to calculate the coefficients

Inverse of the matrix

0.115873016

-0.0047619

6777

a

-0.004761905

0.0002574

X

129330

=

b1

Solving

a=

169.4143

b1=

1.0181

Hence  regression equation= Y=

169.4143 + 1.0181 X  


2 ) Predict Trend Sales for the next 12 months using the regression equation

(x=37 to 48 corresponding to Jan of year 4 to Dec of year 4)

Year

Month

Predicted Trend Sales

X

Y

4

January

37

207.08

=169.4143+1.0181*37

February

38

208.1

=169.4143+1.0181*38

March

39

209.12

=169.4143+1.0181*39

April

40

210.14

May

41

211.16

June

42

212.17

July

43

213.19

August

44

214.21

September

45

215.23

October

46

216.25

November

47

217.27

December

48

218.28

Step 5

Multiply the predicted trend sales by the seasonal index to get the Predicted Sales value for the next 12 months

Year

Month

Seasonal index

Predicted Trend Sales

Predicted sales= Seasonal index * Trend sales

4

January

144.36%

207.08

299

=207.08*144.36%

February

129.97%

208.1

270

=208.1*129.97%

March

134.41%

209.12

281

=209.12*134.41%

April

104.12%

210.14

219

=210.14*104.12%

May

104.94%

211.16

222

=211.16*104.94%

June

80.04%

212.17

170

=212.17*80.04%

July

82.83%

213.19

177

August

85.30%

214.21

183

September

62.80%

215.23

135

October

70.03%

216.25

151

November

85.28%

217.27

185

December

115.93%

218.28

253


The monthly forecasts for the 12 months of the fourth year are as shown below:

Month (yr.4)

January

February

March

April

May

June

July

August

September

October

November

December

S. Index

1.398

1.293

1.322

1.023

1.043

0.798

0.831

0.865

0.636

0.725

0.874

1.192

Forecast

296.45755

274.19143

280.3411

216.9357

221.1768

169.2226

176.2205

183.4305

134.8691

153.7423

185.339

252.7735

Suppose the actual January sales for the fourth year turn out to be $295,000. The forecasted January sales are $296,458.

Error between actual and forecasted sales = $296,458 - $295,000 = $1458

Percentage Error = image04.png

This is an extremely small percentage error. Karen does not have to worry about this error and she can be assured that her forecast model is extremely good.


REFERENCES

Bowerman, B. L., & O'Connell, R. T. (2003). Business Statistics in Practice (3rd). : McGraw Hill.

Cooper, D. & Schindler, S. (2003). Business Research Methods. Boston: McGraw-Hill Irwin.

...read more.

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