Question

In: Operations Management

A pharmacist has been monitoring sales of a certain over-the-counter pain reliever. Monthly sales during the...

A pharmacist has been monitoring sales of a certain over-the-counter pain reliever. Monthly sales during the last 15 months were:

Month

Number sold

Month

Number sold

Month

Number sold

1

36

6

49

11

52

2

38

7

50

12

55

3

42

8

49

13

54

4

44

9

52

14

56

5

48

10

48

15

57
  1. Using 3-Month Weighted Moving Average using 0.2, 0.3, and 0.5 with the heaviest weights applied to the most recent months, develop forecasts for months from 11 to 16.
  2. Using Exponential Smoothing using an α = 0.4 and the 10th Month forecast of 50, develop forecasts for months from 11 to 16.  
  3. Using Trend Projection, develop forecasts for months from 11 to 16.
  4. Justify which method you would suggest using to predict future sales.

Solutions

Expert Solution

a. 3-Month Weighted Moving Average using 0.2, 0.3, and 0.5 with the heaviest weights applied to the most recent months, the forecasts for months 11 to 16 are

Month Number

Sold

3 month weighted moving average

1

36

2

38

3

42

4

44

5

48

6

49

7

50

8

49

9

52

10

48

11

52

49.4

12

55

50.8

13

54

52.7

14

56

53.9

15

57

55.2

16

56.1

Forecast for month 11 = 0.2*49+0.3*52+0.5*48 = 49.4

Similarly the forecast for months 12 to 16 are calculated

Calculating Error (Mean Absolute Deviation)

Month Number

Sold

3 month weighted moving average

|D-F| for moving average

1

36

2

38

3

42

4

44

5

48

6

49

7

50

8

49

9

52

10

48

11

52

49.4

2.6

12

55

50.8

4.2

13

54

52.7

1.3

14

56

53.9

2.1

15

57

55.2

1.8

16

56.1

Total

12

The absolute value of Demand - Forecast is calculated. The sum is 12 as shown in the above table.

MAD = ∑|D-F| / n = 12/5 = 2.4

The demand for 16th month is not available, hence n = 5.

Excel Formulae

b. Exponential Smoothing using an α = 0.4 and the 10th Month forecast of 50, the forecasts for months 11 to 16 are

Month Number

Sold

Exponential Smoothing Using α =0.4

1

36

2

38

3

42

4

44

5

48

6

49

7

50

8

49

9

52

10

48

50

11

52

49

12

55

50

13

54

52

14

56

53

15

57

54

16

55

Forecast for 11th Month = Demand for Month 10 * α + Forecast for Month 10 * (1- α)

= 48*0.4+50*(1-0.4) = 49

Similarly the values for other months can be calculated.

Calculating MAD:

Month Number

Sold

Exponential Smoothing Using α =0.4

|D-F| for exponential smoothing

1

36

2

38

3

42

4

44

5

48

6

49

7

50

8

49

9

52

10

48

50.0

11

52

49.2

2.8

12

55

50.3

4.7

13

54

52.2

1.8

14

56

52.9

3.1

15

57

54.1

2.9

16

55.3

Total

15.2

MAD = ∑|D-F| / n = 15.2/5 = 3.04

Excel Formulae

c. Trend Projection:

Month Number (x)

Sold (y)

xy

x^2

1

36

36

1296

2

38

76

1444

3

42

126

1764

4

44

176

1936

5

48

240

2304

6

49

294

2401

7

50

350

2500

8

49

392

2401

9

52

468

2704

10

48

480

2304

11

52

572

2704

12

55

660

3025

13

54

702

2916

14

56

784

3136

15

57

855

3249

120

730

6211

36084

The xy and x^2 are calculated to help in finding the trend equation

Trend Equation:

Y = a + bX

b = (∑xy – nx̄ȳ) / (∑(x^2)-n (x̄^2))

a = ȳ - b x̄

x̄ = ∑x /n = 120/15 = 8

ȳ = ∑y/n = 730/15 = 48.66

b = (6211-15*8*48.66)/(36084-15*8^2) = 0.0106

a = 48.66-0.0106*8 = 48.57

Equation is

y = 48.57+0.0106x

replacing values of x in the equation

Month Number (x)

Sold (y)

xy

x^2

Forecast

|D-F|

1

36

36

1296

2

38

76

1444

3

42

126

1764

4

44

176

1936

5

48

240

2304

6

49

294

2401

7

50
keosha answered 5 months ago
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