Forcasting (1)

Copyright 2006 John Wiley & Sons, Inc.Beni Asllani

University of Tennessee at Chattanooga

Forecasting

Operations Management - 5th EditionOperations Management - 5th Edition

Chapter 11

Roberta Russell & Bernard W. Taylor, III

Copyright 2006 John Wiley & Sons, Inc. 11-2

Lecture Outline

Strategic Role of Forecasting in Supply Chain Management and TQM

Components of Forecasting Demand Time Series Methods Forecast Accuracy Regression Methods


Forecasting

Predicting the Future Qualitative forecast methods

subjective

Quantitative forecast methods

based on mathematical formulas


Forecasting and Supply Chain Management

Accurate forecasting determines how much inventory a company must keep at various points along its supply chain

Continuous replenishment supplier and 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


Forecasting and TQM

Accurate forecasting customer demand is a key to providing good quality service

Continuous replenishment and JIT complement TQM eliminates the need for buffer inventory, which, in

turn, reduces both waste and inventory costs, a primary goal of TQM

smoothes process flow with no defective items meets expectations about on-time delivery, which is

perceived as good-quality service


Types of Forecasting Methods

Depend on time frame demand behavior causes of behavior


Time Frame

Indicates how far into the future is forecast Short- to mid-range forecast

typically encompasses the immediate futuredaily up to two years

Long-range forecastusually encompasses a period of time longer

than two years


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


Time(a) Trend

Time(d) Trend with seasonal pattern

Time(c) Seasonal pattern

Time(b) Cycle

Dem

and

Dem

and

Dem

and

Dem

and

Random movement

Forms of Forecast Movement


Forecasting Methods

Qualitative use management judgment, expertise, and opinion to

predict future demand

Time series statistical techniques that use historical demand data

to predict future demand

Regression methods attempt to develop a mathematical relationship

between demand and factors that cause its behavior


Qualitative Methods

Management, marketing, purchasing, and engineering are sources for internal qualitative forecasts

Delphi method involves soliciting forecasts about

technological advances from experts


Forecasting Process

6. Check forecast accuracy with one or more measures

4. Select a forecast model that seems appropriate for data

5. Develop/compute forecast for period of historical data

8a. Forecast over planning horizon

9. Adjust forecast based on additional qualitative information and insight

10. Monitor results and measure forecast accuracy

8b. Select new forecast model or adjust parameters of existing model

7.Is accuracy of

forecast acceptable?

1. Identify the purpose of forecast

3. Plot data and identify patterns

2. Collect historical data

No

Yes


Time Series

Assume that what has occurred in the past will continue to occur in the future

Relate the forecast to only one factor - time Include

moving average exponential smoothing linear trend line


Moving Average

Naive forecast demand the current period is used as next

period’s forecast Simple moving average

stable demand with no pronounced behavioral patterns

Weighted moving average weights are assigned to most recent data


Moving Average:Naïve Approach

Jan 120Feb 90Mar 100Apr 75May 110June 50July 75Aug 130Sept 110Oct 90

ORDERSMONTH PER MONTH

-120

90100

751105075

13011090Nov -

FORECAST


Simple Moving Average

MAn =

n

i = 1 Di

nwhere

n = number of periods in the

moving averageDi = demand in

period i


3-month Simple Moving Average

Jan 120

Feb 90

Mar 100

Apr 75

May 110

June 50

July 75

Aug 130

Sept 110

Oct 90Nov -

ORDERS

MONTH PER MONTH

MA3 =

3

i = 1 Di

3

=90 + 110 + 130

3

= 110 ordersfor Nov

–––

103.388.395.078.378.385.0

105.0110.0

MOVING AVERAGE


5-month Simple Moving Average

Jan 120

Feb 90

Mar 100

Apr 75

May 110

June 50

July 75

Aug 130

Sept 110

Oct 90Nov -

ORDERS

MONTH PER MONTH MA5 =

5

i = 1 Di

5

=90 + 110 + 130+75+50

5

= 91 ordersfor Nov

––

– –

– 99.085.082.088.095.091.0

MOVING AVERAGE


Smoothing Effects

150 –

125 –

100 –

75 –

50 –

25 –

0 –| | | | | | | | | | |

Jan Feb Mar Apr May June July Aug Sept Oct Nov

Actual

Ord

ers

Month

5-month

3-month


Weighted Moving Average

WMAn = i = 1 Wi Di

where

Wi = the weight for period i,

between 0 and 100 percent

Wi = 1.00

Adjusts moving average method to more closely reflect data fluctuations


Weighted Moving Average Example

MONTH WEIGHT DATA

August 17% 130September 33% 110October 50% 90

WMA3 = 3

i = 1 Wi Di

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

= 103.4 orders

November Forecast


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

Exponential Smoothing


Ft +1 = Dt + (1 - )Ft

where:

Ft +1 = forecast for next period

Dt = actual demand for present period

Ft = previously determined forecast for present period

= weighting factor, smoothing constant

Exponential Smoothing (cont.)


Effect of Smoothing Constant

0.0 1.0

If = 0.20, then Ft +1 = 0.20Dt + 0.80 Ft

If = 0, then Ft +1 = 0Dt + 1 Ft 0 = Ft

Forecast does not reflect recent data

If = 1, then Ft +1 = 1Dt + 0 Ft =Dt Forecast based only on most recent data


F2 = D1 + (1 - )F1

= (0.30)(37) + (0.70)(37)

= 37

F3 = D2 + (1 - )F2

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

= 37.9

F13 = D12 + (1 - )F12

= (0.30)(54) + (0.70)(50.84)

= 51.79

Exponential Smoothing (α=0.30)

PERIOD MONTHDEMAND

1 Jan 37

2 Feb 40

3 Mar 41

4 Apr 37

5 May 45

6 Jun 50

7 Jul 43

8 Aug 47

9 Sep 56

10 Oct 52

11 Nov 55

12 Dec 54


FORECAST, Ft + 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 39.755 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



70 –

60 –

50 –

40 –

30 –

20 –

10 –

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

Actual

Ord

ers

Month


= 0.50

= 0.30


AFt +1 = Ft +1 + Tt +1

whereT = an exponentially smoothed trend factor

Tt +1 = (Ft +1 - Ft) + (1 - ) Tt

whereTt = the last period trend factor= a smoothing constant for trend

Adjusted Exponential Smoothing


Adjusted Exponential Smoothing (β=0.30)

PERIOD MONTHDEMAND

1 Jan 37

2 Feb 40

3 Mar 41

4 Apr 37

5 May 45

6 Jun 50

7 Jul 43

8 Aug 47

9 Sep 56

10 Oct 52

11 Nov 55

12 Dec 54

T3 = (F3 - F2) + (1 - ) T2

= (0.30)(38.5 - 37.0) + (0.70)(0)

= 0.45

AF3 = F3 + T3 = 38.5 + 0.45

= 38.95

T13 = (F13 - F12) + (1 - ) T12

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

= 1.36

AF13 = F13 + T13 = 53.61 + 1.36 = 54.96


Adjusted Exponential Smoothing: Example

FORECAST TREND ADJUSTEDPERIOD MONTH DEMAND Ft +1 Tt +1 FORECAST AFt +1

1 Jan 37 37.00 – –2 Feb 40 37.00 0.00 37.003 Mar 41 38.50 0.45 38.954 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


Adjusted Exponential Smoothing Forecasts

70 –

60 –

50 –

40 –

30 –

20 –

10 –

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

Actual

Dem

and

Period

Forecast ( = 0.50)

Adjusted forecast ( = 0.30)


y = a + bx

wherea = interceptb = slope of the linex = time periody = forecast for demand for period x

Linear Trend Line

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

xnyn


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


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 - nxyx2 - nx2

781255712

Least Squares Example (cont.)


Linear trend line y = 35.2 + 1.72x

Forecast for period 13 y = 35.2 + 1.72(13) = 57.56 units

70 –

60 –

50 –

40 –

30 –

20 –

10 –

0 –

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

Actual

Dem

and

Period

Linear trend line


Seasonal Adjustments

Repetitive increase/ decrease in demand Use seasonal factor to adjust forecast

Seasonal factor = Si =Di

D


Seasonal Adjustment (cont.)

2002 12.6 8.6 6.3 17.5 45.0

2003 14.1 10.3 7.5 18.2 50.1

2004 15.3 10.6 8.1 19.6 53.6

Total 42.0 29.5 21.9 55.3 148.7

DEMAND (1000’S PER QUARTER)

YEAR 1 2 3 4 Total

S1 = = = 0.28 D1

D42.0

148.7

S2 = = = 0.20 D2

D29.5

148.7S4 = = = 0.37

D4

D55.3

148.7

S3 = = = 0.15 D3

D21.9

148.7


Seasonal Adjustment (cont.)

SF1 = (S1) (F5) = (0.28)(58.17) = 16.28

SF2 = (S2) (F5) = (0.20)(58.17) = 11.63

SF3 = (S3) (F5) = (0.15)(58.17) = 8.73

SF4 = (S4) (F5) = (0.37)(58.17) = 21.53

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

For 2005


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


Mean Absolute Deviation (MAD)

where t = period number

Dt = demand in period t

Ft = forecast for period t

n = total number of periods = absolute value

S Dt - Ft nMAD =


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, Dt Ft ( =0.3) (Dt - Ft) |Dt - Ft|

S Dt - Ft nMAD =

=

= 4.85

53.3911


Other Accuracy Measures

Mean absolute percent deviation (MAPD)

MAPD =|Dt - Ft|

Dt

Cumulative error

E = et

Average error

E =et

n


Comparison of Forecasts

FORECAST MAD MAPD E (E)

Exponential smoothing (= 0.30) 4.85 9.6% 49.31 4.48

Exponential 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% – –


Forecast Control

Tracking signal monitors the forecast to see if it is biased

high or low

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

frequently

Tracking signal = =(Dt - Ft)

MAD

E

MAD


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 Dt Ft Dt - Ft (Dt - Ft) MAD

TS3 = = 2.006.103.05

Tracking signal for period 3

–1.002.001.623.004.255.016.007.198.189.2010.17

TRACKINGSIGNAL


Tracking Signal Plot

3 –

2 –

1 –

0 –

-1 –

-2 –

-3 –

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

Trac

kin

g s

ign

al (

MA

D)

Period

Exponential smoothing ( = 0.30)

Linear trend line


Statistical Control Charts

=(Dt - Ft)2

n - 1

Using we can calculate statistical control limits for the forecast error

Control limits are typically set at 3


Statistical Control ChartsE

rro

rs

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


Regression Methods

Linear regression a mathematical technique that relates a

dependent variable to an independent variable in the form of a linear equation

Correlation a measure of the strength of the relationship

between independent and dependent variables


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 - nxyx2 - nx2

xnyn


Linear Regression Example

x y(WINS) (ATTENDANCE) xy x2

4 36.3 145.2 166 40.1 240.6 366 41.2 247.2 368 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


Linear Regression Example (cont.)

x = = 6.125

y = = 43.36

b =

=

= 4.06

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

498

346.98

xy - nxy2

x2 - nx2

(2,167.7) - (8)(6.125)(43.36)(311) - (8)(6.125)2


| | | | | | | | | | |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 + 4.06x

Wins, x

Att

end

ance

, y

Linear Regression Example (cont.)

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

Regression equation Attendance forecast for 7 wins


Correlation and Coefficient of Determination

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

Coefficient of determination, r2

Percentage of variation in dependent variable resulting from changes in the independent variable


Computing Correlation

n xy - x y

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

Coefficient of determination r2 = (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


Multiple Regression

Study the relationship of demand to two or more independent variables

y = 0 + 1x1 + 2x2 … + kxk

where0 = the intercept

1, … , k = parameters for the

independent variablesx1, … , xk = independent variables


Copyright 2006 John Wiley & Sons, Inc.All rights reserved. Reproduction or translation of this work beyond that permitted in section 117 of the 1976 United States Copyright Act without express permission of the copyright owner is unlawful. Request for further information should be addressed to the Permission Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages caused by the use of these programs or from the use of the information herein.

Forcasting (1)

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