Forecasting problems in operations management

Problem 18-4

Here are the data for the past 21 months for actual sales of a particular product:

LAST YEAR

THIS YEAR

  January

365

300

  February

455

375

  March

400

375

  April

430

455

  May

432

440

  June

505

380

  July

400

385

  August

320

305

  September

395

365

  October

500

  November

590

  December

490

Develop a forecast for the fourth quarter using a three-quarter, weighted moving average. Weight the most recent quarter 0.50, the second most recent 0.25, and the third 0.25. Do the problem using quarters, as opposed to forecasting separate months. (Round your answer to 2 decimal places.)

  Forecast for the fourth quarter

Explanation:

Third most recent quarter 300 + 375 + 375 = 1,050

Second most recent quarter 455 + 440 + 380 = 1,275

Most recent quarter 385 + 305 + 365 = 1,055

WMA = (0.25 × 1,050) + (0.25 × 1,275) + (0.50 × 1,055) = 1,108.75

References

WorksheetDifficulty: Challenge

Problem 18-4Learning Objective: 18-02 Evaluate demand using quantitative forecasting models.

Problem 18-7

The following table contains the demand from the last 10 months:

MONTH

ACTUAL DEMAND

1

32

2

35

3

36

4

38

5

41

6

39

7

39

8

41

9

44

10

40

a.

Calculate the single exponential smoothing forecast for these data using an α of 0.30 and an initial forecast (F1) of 32. (Round your answers to 2 decimal places.)

Month

        Exponential Smoothing

1

2

3

4

5

6

7

8

9

10

b.

Calculate the exponential smoothing with trend forecast for these data using an α of 0.30, a δ of 0.20, an initial trend forecast (T1) of 1.00, and an initial exponentially smoothed forecast (F1) of 31. (Round your answers to 2 decimal places.)

Month

          FITt

1

2

3

4

5

6

7

8

9

10

c-1.

Calculate the mean absolute deviation (MAD) for the last nine months of forecasts. (Round your answers to 2 decimal places.)

MAD

  Single exponential smoothing forecast

  Exponential smoothing with trend forecast

c-2.

Which is best?

Exponential smoothing with trend forecast

Single exponential smoothing forecast

Explanation:

a. to c.

Month

Demand

Exponential Smoothing

Absolute Deviation

Tt

Ft

FITt

Absolute Deviation

1

32

32.00

1.00

31.00

32.00

2

35

32.00

3.00

1.00

32.00

33.00

2.00

3

36

32.90

3.10

1.12

33.60

34.72

1.28

4

38

33.83

4.17

1.20

35.10

36.30

1.70

5

41

35.08

5.92

1.30

36.81

38.11

2.89

6

39

36.86

2.14

1.47

38.98

40.45

1.45

7

39

37.50

1.50

1.38

40.02

41.40

2.40

8

41

37.95

3.05

1.24

40.68

41.92

0.92

9

44

38.87

5.13

1.18

41.64

42.82

1.18

10

40

40.41

0.41

1.25

43.17

44.42

4.42

  MAD

3.16

2.03

Based upon the MAD of each forecast, the exponential smoothing with trend is the better forecasting model.

References

WorksheetDifficulty: Challenge

Problem 18-7Learning Objective: 18-02 Evaluate demand using quantitative forecasting models.

Problem 18-10

The number of cases of merlot wine sold by the Connor Owen winery in an eight-year period is as follows:

YEAR

CASES OF MERLOT WINE

2005

291

2006

377

2007

419

2008

477

2009

379

2010

521

2011

431

2012

397

Using an exponential smoothing model with an alpha value of 0.40, estimate the smoothed value calculated as of the end of 2012. Use the average demand for 2005 through 2007 as your initial forecast for 2008, and then smooth the forecast forward to 2012. (Round your intermediate calculations and final answer to the nearest whole number.)

  Forecast for 2012

Explanation:

Year

Demand

F(t)

2005

291

2006

377

2007

419

2008

477

362

2009

379

408

2010

521

396

2011

431

446

2012

397

440

References

WorksheetDifficulty: Challenge

Problem 18-10Learning Objective: 18-02 Evaluate demand using quantitative forecasting models.

Problem 18-15

Historical demand for a product is

DEMAND

  January

16

  February

14

  March

18

  April

16

  May

19

  June

18

a.

Using a weighted moving average with weights of 0.50 (June), 0.20 (May), and 0.30 (April), find the July forecast. (Round your answer to 1 decimal place.)

  July forecast

b.

Using a simple three-month moving average, find the July forecast. (Round your answer to 1 decimal place.)

  July forecast

c.

Using single exponential smoothing with α = 0.20 and a June forecast = 12, find the July forecast. (Round your answer to 1 decimal place.)

  July forecast

d.

Using simple linear regression analysis, calculate the regression equation for the preceding demand data. (Do not round intermediate calculations. Round your intercept value to 1 decimal place and slope value to 2 decimal places.)

  Y = + t

e.

Using the regression equation in d, calculate the forecast for July. (Do not round intermediate calculations. Round your answer to 1 decimal place.)

  July forecast

Explanation:

a.

FJuly = 0.50(18) + 0.20(19) + 0.30(16) = 17.6

b.

FJuly = (18 + 19 + 16)/3 = 17.7

c.

FJuly = FJune + α(AJune – FJune) = 12 + 0.20(18 − 12) = 13.2

d.

   t

   y

   ty

    t2

  January

1

16

16

1

  February

2

14

28

4

  March

3

18

54

9

  April

4

16

64

16

  May

5

19

95

25

  June

6

18

108

36

  Total

21

101

365

91

Average

3.5

16.8

 = 3.5

 = 16.833

Y = a + bt = 14.5 + 0.66t

e.

FJuly, where July is the 7th month.

Y = a + bt = 14.5 + 0.66(7) = 19.1

References

WorksheetDifficulty: Challenge

Problem 18-15Learning Objective: 18-02 Evaluate demand using quantitative forecasting models.

Problem 18-22

Your manager is trying to determine what forecasting method to use. Based upon the following historical data, calculate the following forecast and specify what procedure you would utilize.