Forecasting

Lecture Outline

• Strategic Role of Forecasting in Supply Chain Management

• Components of Forecasting Demand• Time Series Methods• Forecast Accuracy• Time Series Forecasting Using Excel• Regression Methods

12-2

Forecasting

• Predicting the future

• Qualitative forecast methods• subjective

• Quantitative forecast methods• based on mathematical formulas

12-3

Supply Chain Management

• Accurate forecasting determines inventory levels in 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

12-4

The Effect of Inaccurate Forecasting

12-5

Forecasting

• Quality Management• Accurately forecasting customer demand is a key

to providing good quality service

• Strategic Planning• Successful strategic planning requires accurate

forecasts of future products and markets

12-6

Types of Forecasting Methods

• Depend on• time frame

• demand behavior

• causes of behavior

12-7

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

12-8

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

12-9

Forms of Forecast Movement

12-10

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

Forecasting Methods

• 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• use management judgment, expertise, and opinion to

predict future demand

12-11

Qualitative Methods

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

• Delphi method• involves soliciting forecasts about technological

advances from experts

12-12

Forecasting Process

12-13

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

12-14

Moving Average

• Naive forecast• demand in current period is used as next period’s forecast

• Simple moving average• uses average demand for a fixed sequence of periods• stable demand with no pronounced behavioral patterns

• Weighted moving average• weights are assigned to most recent data

12-15

Moving Average: Naïve Approach

12-16

Jan 120

Feb 90

Mar 100

Apr 75

May 110

June 50

July 75

Aug 130

Sept 110

Oct 90

ORDERSMONTH PER MONTH

-120

90100

75110

5075

130110

90Nov -

FORECAST

Simple Moving Average

12-17

MAn =

n

i = 1 Di

nwhere

n =number of periods in the moving average

Di =demand in period i

3-month Simple Moving Average

12-18

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 orders for Nov

–––

103.388.395.078.378.385.0

105.0110.0

MOVING AVERAGE

5-month Simple Moving Average

12-19

MA5 =

5

i = 1 Di

5

=90 + 110 + 130+75+50

5

= 91 orders for Nov

Jan 120

Feb 90

Mar 100

Apr 75

May 110

June 50

July 75

Aug 130

Sept 110

Oct 90Nov -

ORDERS

MONTH PER MONTH –

–– –

– 99.085.082.088.095.091.0

MOVING AVERAGE

Smoothing Effects

12-20

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

12-21

• Adjusts moving average method to more closely reflect data fluctuations

WMAn = i = 1 Wi Di

where

Wi = the weight for period i,

between 0 and 100 percent

Wi = 1.00

n

Weighted Moving Average Example

12-22

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

Exponential Smoothing

12-23

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

Exponential Smoothing

12-24

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

0.0 1.0

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

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

Forecast does not reflect recent data

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

Effect of Smoothing Constant

12-25

Exponential Smoothing (α=0.30)

12-26

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

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

Exponential Smoothing

12-27

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

Exponential Smoothing

12-28

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

Adjusted Exponential Smoothing

12-29

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 trend0 ≤ ≤

Adjusted Exponential Smoothing (β=0.30)

12-30

PERIOD MONTH DEMAND

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 = 54.97

Adjusted Exponential Smoothing

12-31

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 SmoothingForecasts

12-32

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)

Linear Trend Line

12-33

y = a + bx

wherea = interceptb = slope of the linex = time periody = 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

yn

Least Squares Example

12-34

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

Least Squares Example

12-35

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

12-36

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

Actual

Dem

and

Period

Linear trend line

Seasonal Adjustments

12-37

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

Seasonal factor = Si =Di

D

Seasonal Adjustment

12-38

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

D

42.0148.7

S2 = = = 0.20 D2

D

29.5148.7

S4 = = = 0.37 D4

D

55.3148.7

S3 = = = 0.15 D3

D

21.9148.7

Seasonal Adjustment

12-39

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

12-40

Mean Absolute Deviation (MAD)

12-41

where t= period number

Dt= demand in period t

Ft= forecast for period t

n= total number of periods= absolute value

Dt - Ft nMAD =

12-42

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|

MAD Calculation

12-43

Dt - Ft nMAD =

=

= 4.85

53.3911

Other Accuracy Measures

12-44

Mean absolute percent deviation (MAPD)

MAPD =|Dt - Ft|

Dt

Cumulative error

E = et

Average error

E =et

n

Comparison of Forecasts

12-45

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

12-46

Tracking signal = =(Dt - Ft)

MAD

E

MAD

Tracking Signal Values

12-47

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

–1.002.001.623.004.255.016.007.198.189.2010.17

TRACKINGSIGNAL

TS3 = = 2.006.103.05

Tracking Signal Plot

12-48

3 –

2 –

1 –

0 –

-1 –

-2 –

-3 –

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

Tra

ckin

g si

gnal

(M

AD

)

Period

Exponential smoothing ( = 0.30)

Linear trend line

Statistical Control Charts

12-49

=(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 Charts

12-50

Err

ors

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

Time Series Forecasting Using Excel

• Excel can be used to develop forecasts:• Moving average

• Exponential smoothing

• Adjusted exponential smoothing

• Linear trend line

12-51

Exponentially Smoothed and Adjusted Exponentially Smoothed Forecasts

12-52

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

=C10+D10

=ABS(B10-E10)

=SUM(F10:F20)

=G22/11

Demand and Exponentially Smoothed Forecast

12-53

Click on “Insert” then “Line”

Data Analysis Option

12-54

Forecasting With Seasonal Adjustment

12-55

Forecasting With OM Tools

12-56

Regression Methods

• Linear regression• 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

12-57

Linear Regression

12-58

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

Linear Regression Example

12-59

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

12-60

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

Linear Regression Example

12-61

| | | | | | | | | | |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

Atte

ndan

ce, y

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

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

12-62

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

Computing Correlation

Copyright 2011 John Wiley & Sons, Inc. 12-63

Regression Analysis With Excel

12-64

=INTERCEPT(B5:B12,A5:A12)

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

Regression Analysis with Excel

12-65

Regression Analysis With Excel

12-66

Multiple Regression

12-67

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

Multiple Regression With Excel

12-68

r2, the coefficientof determination

Regression equationcoefficients for x1 and x2

Multiple Regression Example

12-69

y = 19,094.42 + 3560.99 x1 + .0368 x2

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

= 46,229.35