Forecasting c 12

7/31/2019 Forecasting c 12

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Chapter 12

Forecasting


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Lecture Outline

Strategic Role of Forecasting in Supply ChainManagement Components of Forecasting Demand Time Series Methods Forecast Accuracy Time Series Forecasting Using Excel Regression Methods

Copyright 2011 John Wiley & Sons, Inc. 12-2


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Forecasting

Predicting the future Qualitative forecast methods

subjective

Quantitative forecast methods based on mathematical formulas



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Supply Chain Management

Accurate forecasting determines inventory levelsin the supply chain Continuous replenishment

supplier & customer share continuously updated data typically managed by the supplier reduces inventory for the company speeds customer delivery

Variations of continuous replenishment quick response JIT (just-in-time) VMI (vendor-managed inventory) stockless inventory



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The Effect of Inaccurate Forecasting



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Forecasting

Quality Management Accurately forecasting customer demand is a key toproviding good quality service

Strategic Planning Successful strategic planning requires accurate

forecasts of future products and markets



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Types of Forecasting Methods

Depend on time frame demand behavior causes of behavior



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Time Frame

Indicates how far into the future is forecast Short- to mid-range forecast typically encompasses the immediate future daily up to two years

Long-range forecast usually encompasses a period of time longer than

two years



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Demand Behavior

Trend a gradual, long-term up or down movement of demand

Random variations movements in demand that do not follow a pattern

Cycle an up-and-down repetitive movement in demand

Seasonal pattern an up-and-down repetitive movement in demand

occurring periodically



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Forms of Forecast Movement


Time(a) Trend

Time(d) Trend with seasonal pattern

Time(c) Seasonal pattern

Time(b) Cycle

D e m a n

d

D e m a n

d

D e m a n

d

D e m a n

d

Randommovement


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Qualitative Methods

Management, marketing, purchasing, andengineering are sources for internal qualitativeforecasts

Delphi method involves soliciting forecasts about technological

advances from experts



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Forecasting Process


6. Check forecastaccuracy with one or more measures

4. Select a forecastmodel that seemsappropriate for data

5. Develop/computeforecast for period of historical data

8a. Forecast over planning horizon

9. Adjust forecast basedon additional qualitativeinformation and insight

10. Monitor resultsand measure forecastaccuracy

8b. Select newforecast model or adjust parameters of existing model

7.Is accuracy of

forecastacceptable?

1. Identify thepurpose of forecast

3. Plot data and identifypatterns

2. Collect historicaldata

No

Yes


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Time Series

Assume that what has occurred in the past willcontinue to occur in the future Relate the forecast to only one factor - time Include

moving average exponential smoothing linear trend line



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Moving Average: Nave Approach


Jan 120Feb 90Mar 100

Apr 75May 110June 50July 75

Aug 130Sept 110Oct 90

ORDERSMONTH PER MONTH

-120

90

10075110

5075

130110

90Nov -

FORECAST


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Simple Moving Average


MAn =

n

i = 1D i

n where

n = number of periods inthe moving average

D i = demand in period i


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3-month Simple Moving Average




Aug 130Sept 110Oct 90Nov -


MA3 =

3

i = 1D i

3

= 90 + 110 + 1303

= 110 orders for Nov

103.388.395.078.378.385.0

105.0110.0

MOVING AVERAGE


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5-month Simple Moving Average


MA5 =

5

i = 1D i

5

= 90 + 110 + 130+75+505

= 91 orders for Nov



Aug 130Sept 110Oct 90Nov -


99.085.082.088.095.091.0

MOVING AVERAGE


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Smoothing Effects


150

125

100

75

50

25

0 | | | | | | | | | | |Jan Feb Mar Apr May June July Aug Sept Oct Nov

Actual

O r d e r s

Month

5-month

3-month


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Weighted Moving Average


Adjusts moving average method to more closelyreflect data fluctuations

WMAn =i = 1

W i D i

where

W i = the weight for period i,between 0 and 100

percentW i = 1.00

n


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Weighted Moving Average Example


MONTH WEIGHT DATAAugust 17% 130September 33% 110October 50% 90

WMA3 =3

i = 1W i D i

= (0.50)(90) + (0.33)(110) + (0.17)(130)

= 103.4 orders

November Forecast


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Exponential Smoothing


Averaging method Weights most recent data more strongly Reacts more to recent changes Widely used, accurate method


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F t +1 = D t + (1 - )F t where:F t +1 = forecast for next period

D t = actual demand for present period F t = previously determined forecast for present period

= weighting factor, smoothing constant


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0.0 1.0If = 0.20, then F t +1 = 0.20 D t + 0.80 F t

If = 0, then F t +1 = 0 D t + 1 F t = F t Forecast does not reflect recent data

If = 1, then F t +1 = 1 D t + 0 F t = D t Forecast based only on most recent data

Effect of Smoothing Constant



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Exponential Smoothing ( =0.30)


F 2 = D 1 + (1 - )F 1= (0.30)(37) + (0.70)(37)

= 37

F 3 = D 2 + (1 - )F 2

= (0.30)(40) + (0.70)(37)= 37.9

F 13 = D 12 + (1 - )F 12= (0.30)(54) + (0.70)(50.84)

= 51.79

PERIOD MONTH DEMAND1 Jan 372 Feb 403 Mar 414 Apr 375 May 456 Jun 507 Jul 438 Aug 479 Sep 56

10 Oct 52

11 Nov 5512 Dec 54


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FORECAST, F t + 1 PERIOD MONTH DEMAND ( = 0.3) ( = 0.5)

1 Jan 37 2 Feb 40 37.00 37.003 Mar 41 37.90 38.504 Apr 37 38.83 39.75

5 May 45 38.28 38.376 Jun 50 40.29 41.687 Jul 43 43.20 45.848 Aug 47 43.14 44.429 Sep 56 44.30 45.71

10 Oct 52 47.81 50.8511 Nov 55 49.06 51.4212 Dec 54 50.84 53.2113 Jan 51.79 53.61


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70

60

50

40

30

20

10

0 | | | | | | | | | | | | |1 2 3 4 5 6 7 8 9 10 11 12 13

Actual

O r d e r s

Month

= 0.50

= 0.30


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Adjusted Exponential Smoothing


AF t +1 = F t +1 + T t +1 whereT = an exponentially smoothed trend factor

T t +1 = (F t +1 - F t ) + (1 - ) T t where

T t = the last period trend factor = a smoothing constant for trend

0 1


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Adjusted Exponential Smoothing ( =0.30)


PERIOD MONTH DEMAND

1 Jan 372 Feb 403 Mar 414 Apr 37

5 May 456 Jun 507 Jul 438 Aug 479 Sep 56

10 Oct 5211 Nov 5512 Dec 54

T 3 = (F 3 - F 2) + (1 - ) T 2 = (0.30)(38.5 - 37.0) + (0.70)(0)

= 0.45

AF 3 = F 3 + T 3 = 38.5 + 0.45

= 38.95

T 13 = (F 13 - F 12 ) + (1 - ) T 12

= (0.30)(53.61 - 53.21) + (0.70)(1.77)

= 1.36

AF 13 = F 13 + T 13 = 53.61 + 1.36 = 54.97


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Adjusted Exponential Smoothing


FORECAST TREND ADJUSTEDPERIOD MONTH DEMAND F t +1 Tt +1 FORECAST AF t +1

1 Jan 37 37.00 2 Feb 40 37.00 0.00 37.003 Mar 41 38.50 0.45 38.95

4 Apr 37 39.75 0.69 40.445 May 45 38.37 0.07 38.446 Jun 50 38.37 0.07 38.447 Jul 43 45.84 1.97 47.828 Aug 47 44.42 0.95 45.379 Sep 56 45.71 1.05 46.76

10 Oct 52 50.85 2.28 58.1311 Nov 55 51.42 1.76 53.1912 Dec 54 53.21 1.77 54.9813 Jan 53.61 1.36 54.96


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Adjusted Exponential SmoothingForecasts


70

60

50

40

30

20

10

0 | | | | | | | | | | | | |1 2 3 4 5 6 7 8 9 10 11 12 13

Actual

D e m a n d

Period

Forecast ( = 0.50)

Adjusted forecast ( = 0.30)


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Linear Trend Line


y = a + bx

wherea = intercept

b = slope of the line x = time period y = forecast for demand for period x

b =

a = y - b x

wheren = number of periods

x = = mean of the x values

y = = mean of the y values

xy - nxy x2 - nx2

xn y

n


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Least Squares Example


x(PERIOD) y(DEMAND) xy x2

1 73 37 12 40 80 43 41 123 94 37 148 165 45 225 256 50 300 367 43 301 498 47 376 649 56 504 81

10 52 520 10011 55 605 12112 54 648 144

78 557 3867 650


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Least Squares Example


x = = 6.5

y = = 46.42

b = = =1.72

a = y - bx = 46.42 - (1.72)(6.5) = 35.2

3867 - (12)(6.5)(46.42)650 - 12(6.5) 2

xy - nxy x2 - nx2

781255712


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Linear trend line y = 35.2 + 1.72 x Forecast for period 13 y = 35.2 + 1.72(13) = 57.56 units

70

60

50

40

30

20

10 | | | | | | | | | | | | |1 2 3 4 5 6 7 8 9 10 11 12 13

Actual

D e m a n d

Period

Linear trend line


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Seasonal Adjustment


2002 12.6 8.6 6.3 17.5 45.02003 14.1 10.3 7.5 18.2 50.12004 15.3 10.6 8.1 19.6 53.6

Total 42.0 29.5 21.9 55.3 148.7

DEMAND (1000S PER QUARTER) YEAR 1 2 3 4 Total

S 1 = = = 0.28D 1

D 42.0

148.7

S 2 = = = 0.20D 2

D 29.5

148.7 S 4 = = = 0.37D 4

D 55.3

148.7

S 3 = = = 0.15D 3

D 21.9

148.7


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Seasonal Adjustment


SF 1 = (S 1) (F 5) = (0.28)(58.17) = 16.28SF 2 = (S 2) (F 5) = (0.20)(58.17) = 11.63 SF 3 = (S 3) (F 5) = (0.15)(58.17) = 8.73SF 4 = (S 4) (F 5) = (0.37)(58.17) = 21.53

y = 40.97 + 4.30 x = 40.97 + 4.30(4) = 58.17

For 2005


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Forecast Accuracy

Forecast error difference between forecast and actual demand MAD

mean absolute deviation

MAPD mean absolute percent deviation

Cumulative error

Average error or bias



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Mean Absolute Deviation (MAD)


where

t = period number D t = demand in period t F t = forecast for period t n = total number of periods

= absolute value

D t - F t n MAD =


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MAD Example

1 37 37.00 2 40 37.00 3.00 3.003 41 37.90 3.10 3.104 37 38.83 -1.83 1.835 45 38.28 6.72 6.726 50 40.29 9.69 9.697 43 43.20 -0.20 0.208 47 43.14 3.86 3.869 56 44.30 11.70 11.70

10 52 47.81 4.19 4.1911 55 49.06 5.94 5.9412 54 50.84 3.15 3.15

557 49.31 53.39

PERIOD DEMAND, D t F

t ( =0.3) ( D

t - F

t ) | D

t - F

t |


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MAD Calculation


D t - F t n MAD =

=

= 4.85

53.3911


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Other Accuracy Measures


Mean absolute percent deviation (MAPD)

MAPD = |D t - F t |

D t

Cumulative error E = e t

Average error

E = e t

n


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Comparison of Forecasts


FORECAST MAD MAPD E (E )Exponential smoothing ( = 0.30) 4.85 9.6% 49.31 4.48Exponential smoothing ( = 0.50) 4.04 8.5% 33.21 3.02

Adjusted exponential smoothing 3.81 7.5% 21.14 1.92

( = 0.50, = 0.30)Linear trend line 2.29 4.9%


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Forecast Control

Tracking signal monitors the forecast to see if it is biased high or low

1 MAD 0.8 Control limits of 2 to 5 MADs are used most frequently


Tracking signal = =(D t - F t )MAD

E MAD


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Tracking Signal Values


1 37 37.00 2 40 37.00 3.00 3.00 3.003 41 37.90 3.10 6.10 3.054 37 38.83 -1.83 4.27 2.645 45 38.28 6.72 10.99 3.666 50 40.29 9.69 20.68 4.877 43 43.20 -0.20 20.48 4.098 47 43.14 3.86 24.34 4.069 56 44.30 11.70 36.04 5.01

10 52 47.81 4.19 40.23 4.9211 55 49.06 5.94 46.17 5.0212 54 50.84 3.15 49.32 4.85

DEMAND FORECAST, ERROR E =PERIOD D t F t D t - F t (D t - F t ) MAD

1.002.001.623.004.255.016.007.198.189.2010.17

TRACKINGSIGNAL

TS 3 = = 2.006.103.05

ki l


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Tracking Signal Plot


3

2

1

0

-1

-2

-3

| | | | | | | | | | | | |0 1 2 3 4 5 6 7 8 9 10 11 12

T r a c

k i n g s i g n a

l ( M A D )

Period

Exponential smoothing ( = 0.30)

Linear trend line


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Statistical Control Charts


=(D t - F t )2

n - 1

Using we can calculate statisticalcontrol limits for the forecast error Control limits are typically set at 3

l l h


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Statistical Control Charts


E r r o r s

18.39

12.24

6.12

0

-6.12

-12.24

-18.39

| | | | | | | | | | | | |0 1 2 3 4 5 6 7 8 9 10 11 12

Period

UCL = +3

LCL = -3

l


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Time Series Forecasting Using Excel

Excel can be used to develop forecasts: Moving average Exponential smoothing Adjusted exponential smoothing

Linear trend line


Exponentially Smoothed and Adjusted


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Exponentially Smoothed and AdjustedExponentially Smoothed Forecasts


=B5*(C11-C10)+(1-B5)*D10

=C10+D10

=ABS(B10-E10)

=SUM(F10:F20)

=G22/11

D d d E i ll S h d


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Demand and Exponentially SmoothedForecast


Click on Insert then Line

D A l i O i


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Data Analysis Option


F i Wi h S l Adj


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Forecasting With Seasonal Adjustment


F i Wi h OM T l


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Forecasting With OM Tools


R i M th d


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Regression Methods

Linear regression mathematical technique that relates a dependent

variable to an independent variable in the form of alinear equation

Correlation a measure of the strength of the relationship between

independent and dependent variables


Li R i


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Linear Regression


y = a + bx a = y - b x b =

wherea = interceptb = slope of the line

x = = mean of the x data

y = = mean of the y data

xy - nxy x2 - nx2

xn yn

Li R g i E l


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Linear Regression Example


x y (WINS) (ATTENDANCE) xy x2

4 36.3 145.2 166 40.1 240.6 366 41.2 247.2 36

8 53.0 424.0 646 44.0 264.0 367 45.6 319.2 495 39.0 195.0 257 47.5 332.5 49

49 346.7 2167.7 311

Li R i E l


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x = = 6.125

y = = 43.36

b =

=

= 4.06

a = y - bx = 43.36 - (4.06)(6.125)= 18.46

49

8346.98

xy - nxy2

x2

- nx2

(2,167.7) - (8)(6.125)(43.36)

(311) - (8)(6.125) 2

Li R g i E l


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| | | | | | | | | | |0 1 2 3 4 5 6 7 8 9 10

60,000

50,000

40,000

30,000

20,000

10,000

Linear regression line, y = 18.46 + 4.06 x

Wins, x

A t t e n

d a n c e , y

y = 18.46 + 4.06(7)= 46.88, or 46,880

Attendance forecast for 7 wins

Correlation and Coefficient of


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Correlation and Coefficient of Determination

Correlation, r Measure of strength of relationship Varies between -1.00 and +1.00

Coefficient of determination, r 2 Percentage of variation in dependent variable

resulting from changes in the independent variable


Computing Correlation


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n xy

- x

y

[n x2 - ( x)2] [n y2 - ( y)2]

r =

Coefficient of determinationr 2 = (0.947) 2 = 0.897

r =(8)(2,167.7) - (49)(346.9)

[(8)(311) - (49 )2] [(8)(15,224.7) - (346.9) 2]

r = 0.947

Computing Correlation


Regression Analysis With Excel


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=INTERCEPT(B5:B12,A5:A12)

=CORREL(B5:B12,A5:A12)=SUM(B5:B12)

Regression Analysis with Excel


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Regression Analysis with Excel




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Multiple Regression


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Multiple Regression


Study the relationship of demand to two or moreindependent variables

y = 0 + 1x 1 + 2x 2 + kx k

where0 = the intercept

1, , k = parameters for theindependent variables

x 1, , x k = independent variables

Multiple Regression With Excel


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Multiple Regression With Excel


r 2, the coefficientof determination

Regression equationcoefficients for x 1 and x 2

Multiple Regression Example


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Multiple Regression Example


y = 19,094.42 + 3560.99 x 1 + .0368 x 2

y = 19,094.42 + 3560.99 (7) + .0368 (60,000)= 46,229.35


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