a 3 forecasting final

8/6/2019 A 3 Forecasting Final

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1. (a)Three months weighted moving average method to forecast the sales for the months April

December:

Given weights are W1= 3/6, W2= 2/6 and W3= 1/6. We are giving more weight to more recent data.

Formula Used:

Ft = [W1 * A (t-1) + W2 * A (t-2) + W3 * A (t-3)] / (W1 + W2 + W3)

FArpil = (W1 * A March + W2 * A February + W3 * A January) / (W1 + W2 + W3)

= (3/6 * 27 + 2/6 * 24 + 1/6 * 20) / (3/6 + 2/6 + 1/6)

= (13.5 + 8 + 3.33) / (6/6)

= $ 24.8332 Million

*** The formula has been used in the same way using the relevant data for forecasting sales for other

months.

MonthsActual Sales, At

(Million)

ForecastSales, Ft(Million)

Error (et)At - Ft

Absolute Value ofError | et |

{Error(et)}

2

January 20 - - - -

February 24 - - - -March 27 - - - -

April 31 24.83 6.17 6.17 38.07

May 37 28.50 8.50 8.50 72.25

June 47 33.33 13.67 13.67 186.87

July 53 41 12 12 144

August 52 48.33 3.67 3.67 13.47

September 54 51.50 2.5 2.56.25

October 36 53.17 -17.17 17.17 294.81

November 32 44.67 -12.67 12.67 160.53

December 29 37 -8 8 64


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1. (b)Simple Exponential Smoothing ( = 0.6) Method to forecast the sales for the months April

December:

Given that, = 0.6 and the initial forecast for January was $22 million.

Formula used:

Ft= F (t-1) + [A (t-1) - F (t-1)] = F (t-1) + 0.6*[A (t-1) - F (t-1)]

F April= F March + (A March - F March)

= 22.72 + 0.6*(27 22.72) = $ 25.2880 Million

*** The formula has been used in the same way using the relevant data for forecasting sales for other

months.

MonthsActual Sales,At (Million)


Error (et)At - Ft


{Error(et)}

2

January 20 22.00 -2 2 4

February 24 20.80 3.2 3.2 10.24

March 27 22.72 4.28 4.28 18.32

April 31 25.29 5.71 5.71 32.6

May 37 28.72 8.28 8.28 68.56

June 47 33.69 13.31 13.31 177.16

July 53 41.67 11.33 11.33 128.37

August 52 48.47 3.53 3.53 12.46

September 54 50.59 3.41 3.41 11.63

October 36 52.64 -16.64 16.64 276.89

November 32 42.65 -10.65 10.65 113.42

December 29 36.27 -7.27 7.27 52.85

Mean Absolute Deviation of Simple Exponential Smoothing (=0.6):


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MonthsActual Sales,

At (Million)

Forecast

Sales, Ft

(Million)

Error (et)

At - Ft

Absolute Value

of Error | et |

April 31 25.29 5.71 5.71

May 37 28.72 8.28 8.28

June 47 33.69 13.31 13.31

July 53 41.67 11.33 11.33

August 52 48.47 3.53 3.53

September 54 50.59 3.41 3.41

October 36 52.64 -16.64 16.64

November 32 42.65 -10.65 10.65

December 29 36.27 -7.27 7.27

et = 11.01 | et | = 80.13

MAD SES (=0.6) = ( | et |) / n = 80.13 / 9 = 8.90

Running Sum Forecasting Error (RSFE) = et = 11.01

Tracking Signal (TS) = RSFE / MAD SES (=0.6)

= 11.01 / 8.90 = 1.24

Here Tracking Signal forSimple Exponential Smoothing (=0.6) is 1.24 which is between -3 and 3. So

we can say that Simple Exponential Smoothing (=0.6) forForecasting is Unbiased.

1. (c) Comparison of the performances of Three Months Weighted Moving Average and Simple

Exponential Smoothing Method (=0.6) using Mean Absolute Deviation (MAD):

Mean Absolute Deviation (MAD) of Three Months Weighted Moving Average:


(Million)


Error (et)At - Ft



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April 31 24.83 6.17 6.17

May 37 28.50 8.50 8.50

June 47 33.33 13.67 13.67

July 53 41 12 12

August 52 48.33 3.67 3.67

September 54 51.50 2.5 2.5

October 36 53.17 -17.17 17.17

November 32 44.67 -12.67 12.67

December 29 37 -8 8

| et | = 84.35

MAD3 Months WMA = ( | et |) / n = 84.35 / 9 = 9.372

Mean Absolute Deviation of Simple Exponential Smoothing (=0.6):


(Million)


Error (et)At - Ft


April 31 25.29 5.71 5.71

May 37 28.72 8.28 8.28

June 47 33.69 13.31 13.31

July 53 41.67 11.33 11.33

August 52 48.47 3.53 3.53

September 54 50.59 3.41 3.41

October 36 52.64 -16.64 16.64

November 32 42.65 -10.65 10.65

December 29 36.27 -7.27 7.27

| et | = 80.13

MAD SES (=0.6) = ( | et |) / n = 80.13 / 9 = 8.90

Recommendation:


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Mean Absolute Deviation (MAD) for Simple Exponential Smoothing (=0.6) 8.90 is less than

Mean Absolute Deviation (MAD) for Three Months Weighted Moving Average 9.372. As Simple

Exponential Smoothing forecasts the sales for Dalworth Company with less error, we recommend

Simple Exponential Smoothing (=0.6) over the Three Months Weighted Moving Average

Method.

1. (d) Comparison of the performances of Three Months Weighted Moving Average and Simple

Exponential Smoothing Method (=0.6) using Root Mean Squared Error (RMSE):

Root Mean Squared Error (RMSE) of Three Months Weighted Moving Average:


(Million)


Error (et)At - Ft

AbsoluteValue ofError | et |

{Error (et)}2

April 31 24.83 6.17 6.17 38.07

May 37 28.50 8.50 8.50 72.25

June 47 33.33 13.67 13.67 186.87

July 53 41 12 12 144

August 52 48.33 3.67 3.67 13.47

September 54 51.50 2.5 2.5 6.25

October 36 53.17 -17.17 17.17 294.81

November 32 44.67 -12.67 12.67 160.53

December 29 37 -8 8 64

(et)2= 980.25Mean Squared Error (MSE) 3 months WMA = (et)2 / n = 980.25 / 9 = 108.92

Root Mean Squared Error (RMSE) 3 months WMA = MSE = (108.92) = 10.44

Root Mean Squared Error (RMSE) of Simple Exponential Smoothing (=0.6):

Months Actual Sales,At (Million)

ForecastSales, Ft

Error (et)At - Ft

Absolute Valueof Error | et |

{Error (et)}2


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(Million)

April 31 25.29 5.71 5.71 32.6

May 37 28.72 8.28 8.28 68.56

June 47 33.69 13.31 13.31 177.16

July 53 41.67 11.33 11.33 128.37

August 52 48.47 3.53 3.53 12.46

September 54 50.59 3.41 3.41 11.63

October 36 52.64 -16.64 16.64 276.89

November 32 42.65 -10.65 10.65 113.42

December 29 36.27 -7.27 7.27 52.85

(et)2= 873.94

Mean Squared Error (MSE) SES (=0.6) = (et)2 / n = 873.94 / 9 = 97.10

Root Mean Squared Error (RMSE) SES (=0.6) = MSE = (873.94) = 9.85

Recommendation:

Root Mean Squared Error (RMSE) for Simple Exponential Smoothing (=0.6) 9.85 is less thanRoot Mean Squared Error (RMSE) for Three Months Weighted Moving Average 10.44. As

Simple Exponential smoothing forecasts the sales for Dalworth Company with less error, we

recommend it over the Three Months Weighted Moving Average Method.

2. Simple Exponential Smoothing ( = 0.25) Method to forecast the calls for the week of August 7:

Given that, = 0.25 and the forecast for the week of July 3 = 23 calls

Formula Used:

Ft= F (t-1) + [A (t-1) - F (t-1)] = F (t-1) + 0.25*[A (t-1) - F (t-1)]

Week of Actual Service Calls Forecast Service Calls

July 3 27 23

July 10 36 24


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July 17 31 27

July 24 24 28

July 31 23 27

August 7 26

F July 10 = F July 3 + (A July 3 F July 3) = 23 + 0.25*(27 23) = 24 calls




F August 7 = F July 31 + (A July 31 F July 31) = 27 + 0.25*(23 27) = 26 calls

Using Simple Exponential Smoothing Method with = 0.25, the forecasted number of calls for the

week of August 7th is26 calls.

3. (a) Forecast demand with Simple Exponential Smoothing with = 0.6

Given that, = 0.6 and the initial forecast for Year 1993 was 41.

Formula used:

Ft= F (t-1) + [A (t-1) - F (t-1)] = F (t-1) + 0.6*[A (t-1) - F (t-1)]

F 1994= F 1993 + (A 1993 - F 1993)

= 41 + 0.6*(45 41)


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= 43.4 Surgeries

*** The formula has been used in the same way using the relevant data for forecasting surgeries for

other years.

Year Actual Demand, At Forecast Demand, Ft

1993 45 41.0000

1994 50 43.4000

1995 52 47.3600

1996 56 50.1440

1997 58 53.6576

1998 56.2630

(b) Forecast demand with Simple Exponential Smoothing with = 0.9

Given that, = 0.6 and the initial forecast for Year 1993 was 41.

Formula used:

Ft= F (t-1) + [A (t-1) - F (t-1)] = F (t-1) + 0.6*[A (t-1) - F (t-1)]

F 1994= F 1993 + (A 1993 - F 1993)

= 41 + 0.9*(45 41)

= 44.6 Surgeries


other years.

Year Actual Demand, At Forecast Demand, Ft

1993 45 41.00001994 50 44.6000

1995 52 49.4600

1996 56 51.7460

1997 58 55.5746

1998 57.7575


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(c) Three Year Moving average method to forecast :

Formula Used:

Ft = ( A t-1 + A t-2 + A t-3 ) / 3

F1996 = ( A 1995 + A 1994 + A 1993 ) / 3

= ( 52 + 50 + 45 ) / 3

= 49 Surgeries

*** The formula has been used in the same way using the relevant data for forecasting surgeries

for other years.

Year Actual Demand, AtForecast Demand,

Ft

1993 45 -

1994 50 -

1995 52 -

1996 56 49.0000

1997 58 52.6667

1998 55.3333

(d) Three Year weighted moving average method to Forecast:

Given weights are W1= 3/6, W2= 2/6 and W3= 1/6. We are giving more weight to more recent data.

Formula Used:

Ft = [W1 * A (t-1) + W2 * A (t-2) + W3 * A (t-3)] / (W1 + W2 + W3)

F1996 = (W1 * A 1995 + W2 * A 1994 + W3 * A 1993) / (W1 + W2 + W3)

= (3/6 * 52 + 2/6 * 50 + 1/6 * 45) / (3/6 + 2/6 + 1/6)

= 50.17 Surgeries


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other years.


Ft

1993 45 -

1994 50 -

1995 52 -

1996 56 50.17

1997 58 53.67

1998 56.33

(e) Forecasting using Regression Model (Y=42.6+3.2X) :

By putting value of Independent Variable X we can forecast the value of dependent Variable Y.

Here X is the Index for the Year and Y is the number of Surgeries.

Formula:

Y = 42.6+3.2X

Y1993 = 42.6 + 3.2 * 1 = 45.8


other years.


Ft1993 45 45.8

1994 50 49

1995 52 52.2

1996 56 55.4

1997 58 58.6


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1998 61.8

(f) Comparison of the performances of Simple Exponential Smoothing with = 0.6, Simple

Exponential Smoothing with = 0.9, Three Year Moving Average (MA), Three Year WeightedMoving Average (WMA) and Regression Model (Y=42.6+3.2X) by using Mean Absolute Deviation

(MAD).

(i) Mean Absolute Deviation of Simple Exponential Smoothing with = 0.6

YearActual

Demand, At

ForecastDemand, Ft

Error (et),At - Ft

Absolute Value ofError, | et |

1993 45 41.0000 4.0000 4.0000

1994 50 43.4000 6.6000 6.6000

1995 52 47.3600 4.6400 4.6400

1996 56 50.1440 5.8560 5.8560

1997 58 53.6576 4.3424 4.3424

1998 56.2630 | et | = 25.4384

MAD SES (=0.6) = ( | et |) / n = 25.4384 / 5 = 5.0877

(ii) Mean Absolute Deviation of Simple Exponential Smoothing with = 0.9

YearActual

Demand, At

ForecastDemand, Ft

Error (et),At - Ft

Absolute Value ofError, | et |

1993 45 41.0000 4.0000 4.0000

1994 50 44.6000 5.4000 5.40001995 52 49.4600 2.5400 2.5400

1996 56 51.7460 4.2540 4.2540

1997 58 55.5746 2.4254 2.4254

1998 57.7575 | et | = 18.6194


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MAD SES (=0.9) = ( | et |) / n = 18.6194 / 5 = 3.7239

(iii) Mean Absolute Deviation of Three Year Moving Average (MA):

Year ActualDemand, At

Forecast

Demand,Ft

Error

(et),At - Ft

Absolute Value of

Error,| et |

1993 45 - - -

1994 50 - - -

1995 52 - - -

1996 56 49.0000 7.0000 7.0000

1997 58 52.6667 5.3333 5.3333

1998 55.3333 | et | = 12.3333

MAD 3 year MA = ( | et |) / n = 12.3333 / 2 = 6.1667

(iv) Mean Absolute Deviation of Three Year Weighted Moving Average (WMA):

YearActual

Demand, At

ForecastDemand,

Ft

Error(et),

At - Ft

Absolute Value ofError,

| et |

1993 45 - - -

1994 50 - - -

1995 52 - - -

1996 56 50.1665 5.8335 5.8335

1997 58 53.6666 4.3334 4.3334

1998 56.3332 | et | = 10.1669MAD 3 year WMA = ( | et |) / n = 10.1669 / 2 = 5.0835

(v) Mean Absolute Deviation of Regression Model (Y=42.6+3.2X):

YearActual

Demand, At

ForecastDemand,

Ft

Error(et),

At - Ft

Absolute Value ofError,

| et |

1993 45 45.8 -0.8 0.8

1994 50 49 1 1

1995 52 52.2 -0.2 0.2

1996 56 55.4 0.6 0.6

1997 58 58.6 -0.6 0.6

1998 61.8 | et | = 3.2


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MAD RM(Y=42.6+3.2X) = ( | et |) / n = 3.2 / 5 = 0.64

Recommendation:

From our calculation, we have found that,

MAD 3 year MA (6.1667) > MAD SES (=0.6) (5.0877) > MAD 3 year WMA (5.0835) > MAD SES (=0.9) (3.7239) >

MAD RM(Y=42.6+3.2X) (0.64)

Therefore, we recommend the Regression Model (Y=42.6+3.2X) Method to be used to forecast the

surgeries for the year 1998 as it has the least error.

(g) Comparison of the performances of Simple Exponential Smoothing with = 0.6, Simple

Exponential Smoothing with = 0.9, Three Year Moving Average (MA), Three Year Weighted

Moving Average (WMA) and Regression Model (Y=42.6+3.2X) by using Root Mean Squared Error

(RMSE).

(i)Root Mean Squared Error (RMSE) of Simple Exponential Smoothing (=0.6):

YearActual

Demand, At

ForecastDemand,

Ft

Error (et),At - Ft

Absolute Valueof Error,

| et |{Error (et)}

2

1993 45 41.0000 4.0000 4.0000 16.0000

1994 50 43.4000 6.6000 6.6000 43.56001995 52 47.3600 4.6400 4.6400 21.5296

1996 56 50.1440 5.8560 5.8560 34.2927

1997 58 53.6576 4.3424 4.3424 18.8564

1998 56.2630 (et)2 = 134.2388


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Mean Squared Error (MSE) 3 Year MA = (et)2 / n = 77.4444 / 2 = 38.7772

Root Mean Squared Error (RMSE) 3 Year MA = MSE = (38.7772) = 6.2227

(iv)Root Mean Squared Error (RMSE) of Three Year Weighted Moving Average (WMA):

YearActual

Demand, At

ForecastDemand,

Ft

Error (et),At - Ft


| et |{Error (et)}

2

1993 45 - - - -

1994 50 - - - -

1995 52 - - - -

1996 56 50.1665 5.8335 5.8335 34.0297

1997 58 53.6666 4.3334 4.3334 18.7784

1998 56.3332 (et)2 = 52.8081

Mean Squared Error (MSE) 3 Year WMA = (et)2 / n = 52.8081 / 2 = 26.4040

Root Mean Squared Error (RMSE) 3 Year WMA = MSE = (26.4040) = 5.1385

(v)Root Mean Squared Error (RMSE) of Regression Model (Y=42.6+3.2X):

YearActual

Demand, At

ForecastDemand,

Ft

Error(et),

At - Ft


| et |{Error (et)}

2

1993 45 45.8 -0.8 0.8 0.64

1994 50 49 1 1 11995 52 52.2 -0.2 0.2 0.04

1996 56 55.4 0.6 0.6 0.36

1997 58 58.6 -0.6 0.6 0.36

1998 61.8 (et)2 = 2.4


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a 3 forecasting final

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