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Operations Management. Chapter 4 - Forecasting. PowerPoint presentation to accompany Heizer/Render Principles of Operations Management, 6e Operations Management, 8e . © 2006 Prentice Hall, Inc. ??. What is Forecasting?. Process of predicting a future event

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Slide1 l.jpg

Operations Management

Chapter 4 -

Forecasting

PowerPoint presentation to accompany

Heizer/Render

Principles of Operations Management, 6e

Operations Management, 8e

© 2006 Prentice Hall, Inc.


What is forecasting l.jpg

??

What is Forecasting?

  • Process of predicting a future event

  • Underlying basis of all business decisions

    • Production

    • Inventory

    • Personnel

    • Facilities


Forecasting time horizons l.jpg
Forecasting Time Horizons

  • Short-range forecast

    • Up to 1 year, generally less than 3 months

    • Purchasing, job scheduling, workforce levels, job assignments, production levels

  • Medium-range forecast

    • 3 months to 3 years

    • Sales and production planning, budgeting

  • Long-range forecast

    • 3+ years

    • New product planning, facility location, research and development


Influence of product life cycle l.jpg
Influence of Product Life Cycle

  • Introduction and growth require longer forecasts than maturity and decline

  • As product passes through life cycle, forecasts are useful in projecting

    • Staffing levels

    • Inventory levels

    • Factory capacity

Introduction – Growth – Maturity – Decline


Product life cycle l.jpg

Introduction Growth Maturity Decline

Best period to increase market share

R&D engineering is critical

Practical to change price or quality image

Strengthen niche

Poor time to change image, price, or quality

Competitive costs become critical

Defend market position

Cost control critical

Company Strategy/Issues

Fax machines

CD-ROM

Internet

Drive-through restaurants

Color printers

Sales

3 1/2” Floppy disks

Flat-screen monitors

DVD

Product Life Cycle

Figure 2.5


Product life cycle6 l.jpg

Introduction Growth Maturity Decline

OM Strategy/Issues

Product Life Cycle

Product design and development critical

Frequent product and process design changes

Short production runs

High production costs

Limited models

Attention to quality

Forecasting critical

Product and process reliability

Competitive product improvements and options

Increase capacity

Shift toward product focus

Enhance distribution

Standardization

Less rapid product changes – more minor changes

Optimum capacity

Increasing stability of process

Long production runs

Product improvement and cost cutting

Little product differentiation

Cost minimization

Overcapacity in the industry

Prune line to eliminate items not returning good margin

Reduce capacity

Figure 2.5


Types of forecasts l.jpg
Types of Forecasts

  • Economic forecasts

    • Address business cycle – inflation rate, money supply, housing starts, etc.

  • Technological forecasts

    • Predict rate of technological progress

    • Impacts development of new products

  • Demand forecasts

    • Predict sales of existing product


The realities l.jpg
The Realities!

  • Forecasts are seldom perfect

  • Most techniques assume an underlying stability in the system

  • Product family and aggregated forecasts are more accurate than individual product forecasts


Forecasting approaches l.jpg
Forecasting Approaches

Qualitative Methods

  • Used when situation is vague and little data exist

    • New products

    • New technology

  • Involves intuition, experience

    • e.g., forecasting sales on Internet


Forecasting approaches10 l.jpg
Forecasting Approaches

Quantitative Methods

  • Used when situation is ‘stable’ and historical data exist

    • Existing products

    • Current technology

  • Involves mathematical techniques

    • e.g., forecasting sales of color televisions


Overview of qualitative methods l.jpg
Overview of Qualitative Methods

  • Jury of executive opinion

    • Pool opinions of high-level executives, sometimes augment by statistical models

  • Delphi method

    • Panel of experts, queried iteratively


Overview of qualitative methods12 l.jpg
Overview of Qualitative Methods

  • Sales force composite

    • Estimates from individual salespersons are reviewed for reasonableness, then aggregated

  • Consumer Market Survey

    • Ask the customer


Overview of quantitative approaches l.jpg

Time-Series Models

Associative Model

Overview of Quantitative Approaches

  • Naive approach

  • Moving averages

  • Exponential smoothing

  • Trend projection

  • Linear regression


Time series forecasting l.jpg
Time Series Forecasting

  • Set of evenly spaced numerical data

    • Obtained by observing response variable at regular time periods

  • Forecast based only on past values

    • Assumes that factors influencing past and present will continue influence in future


Time series components l.jpg

Trend

Cyclical

Seasonal

Random

Time Series Components


Naive approach l.jpg
Naive Approach

  • Assumes demand in next period is the same as demand in most recent period

    • e.g., If May sales were 48, then June sales will be 48

  • Sometimes cost effective and efficient


Moving average method l.jpg

demand in previous n periods

n

Moving average =

Moving Average Method

  • MA is a series of arithmetic means

  • Used if little or no trend

  • Used often for smoothing

    • Provides overall impression of data over time


Moving average example l.jpg

Actual 3-Month

Month Shed Sales Moving Average

January 10

February 12

March 13

April 16

May 19

June 23

July 26

10

12

13

(10 + 12 + 13)/3 = 11 2/3

Moving Average Example

(12 + 13 + 16)/3 = 13 2/3

(13 + 16 + 19)/3 = 16

(16 + 19 + 23)/3 = 19 1/3


Weighted moving average l.jpg

Weightedmoving average

∑(weight for period n) x (demand in period n)

∑ weights

=

Weighted Moving Average

  • Used when trend is present

    • Older data usually less important

  • Weights based on experience and intuition


Weighted moving average20 l.jpg

Weights Applied Period

3 Last month

2 Two months ago

1 Three months ago

6 Sum of weights

Actual 3-Month Weighted

Month Shed Sales Moving Average

January 10

February 12

March 13

April 16

May 19

June 23

July 26

10

12

13

[(3 x 13) + (2 x 12) + (10)]/6 = 121/6

Weighted Moving Average

[(3 x 16) + (2 x 13) + (12)]/6 = 141/3

[(3 x 19) + (2 x 16) + (13)]/6 = 17

[(3 x 23) + (2 x 19) + (16)]/6 = 201/2


Potential problems with moving average l.jpg
Potential Problems With Moving Average

  • Increasing n smooths the forecast but makes it less sensitive to changes

  • Do not forecast trends well

  • Require extensive historical data


Exponential smoothing l.jpg
Exponential Smoothing

  • Form of weighted moving average

    • Weights decline exponentially

    • Most recent data weighted most

  • Requires smoothing constant ()

    • Ranges from 0 to 1

    • Subjectively chosen

  • Involves little record keeping of past data


Exponential smoothing23 l.jpg
Exponential Smoothing

New forecast = last period’s forecast

+ a(last period’s actual demand

– last period’s forecast)

Ft = Ft – 1 +a(At – 1 - Ft – 1)

where Ft = new forecast

Ft – 1 = previous forecast

a = smoothing (or weighting) constant (0  a  1)


Exponential smoothing example l.jpg
Exponential Smoothing Example

Predicted demand = 142 Ford Mustangs

Actual demand = 153

Smoothing constant a = .20


Exponential smoothing example25 l.jpg

New forecast = 142 + .2(153 – 142)

Exponential Smoothing Example

Predicted demand = 142 Ford Mustangs

Actual demand = 153

Smoothing constant a = .20


Exponential smoothing example26 l.jpg
Exponential Smoothing Example

Predicted demand = 142 Ford Mustangs

Actual demand = 153

Smoothing constant a = .20

New forecast = 142 + .2(153 – 142)

= 142 + 2.2

= 144.2 ≈ 144 cars


Choosing l.jpg
Choosing

The objective is to obtain the most accurate forecast no matter the technique

We generally do this by selecting the model that gives us the lowest forecast error

Forecast error = Actual demand - Forecast value

= At - Ft


Common measure of error l.jpg

Mean Absolute Deviation (MAD)

MAD =

∑ |actual - forecast|

n

Common Measure of Error


Exponential smoothing with trend adjustment l.jpg

Forecast

including (FITt) =

trend

exponentially exponentially

smoothed (Ft) + (Tt) smoothed

forecast trend

Exponential Smoothing with Trend Adjustment

When a trend is present, exponential smoothing must be modified


Exponential smoothing with trend adjustment30 l.jpg
Exponential Smoothing with Trend Adjustment

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

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

Step 1: Compute Ft

Step 2: Compute Tt

Step 3: Calculate the forecast FITt= Ft+ Tt


Exponential smoothing with trend adjustment example l.jpg

Forecast

Actual Smoothed Smoothed Including

Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt

1 12 11 2 13.00

2 17

3 20

4 19

5 24

6 21

7 31

8 28

9 36

10

Exponential Smoothing with Trend Adjustment Example

Table 4.1


Exponential smoothing with trend adjustment example32 l.jpg

Forecast

Actual Smoothed Smoothed Including

Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt

1 12 11 2 13.00

2 17

3 20

4 19

5 24

6 21

7 31

8 28

9 36

10

Exponential Smoothing with Trend Adjustment Example

Step 1: Forecast for Month 2

F2 = aA1 + (1 - a)(F1 + T1)

F2 = (.2)(12) + (1 - .2)(11 + 2)

= 2.4 + 10.4 = 12.8 units

Table 4.1


Exponential smoothing with trend adjustment example33 l.jpg

Forecast

Actual Smoothed Smoothed Including

Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt

1 12 11 2 13.00

2 17 12.80

3 20

4 19

5 24

6 21

7 31

8 28

9 36

10

Exponential Smoothing with Trend Adjustment Example

Step 2: Trend for Month 2

T2 = b(F2 - F1) + (1 - b)T1

T2 = (.4)(12.8 - 11) + (1 - .4)(2)

= .72 + 1.2 = 1.92 units

Table 4.1


Exponential smoothing with trend adjustment example34 l.jpg

Forecast

Actual Smoothed Smoothed Including

Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt

1 12 11 2 13.00

2 17 12.80 1.92

3 20

4 19

5 24

6 21

7 31

8 28

9 36

10

Exponential Smoothing with Trend Adjustment Example

Step 3: Calculate FIT for Month 2

FIT2 = F2 + T1

FIT2 = 12.8 + 1.92

= 14.72 units

Table 4.1


Exponential smoothing with trend adjustment example35 l.jpg

Forecast

Actual Smoothed Smoothed Including

Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt

1 12 11 2 13.00

2 17 12.80 1.92 14.72

3 20

4 19

5 24

6 21

7 31

8 28

9 36

10

Exponential Smoothing with Trend Adjustment Example

15.18 2.10 17.28

17.82 2.32 20.14

19.91 2.23 22.14

22.51 2.38 24.89

24.11 2.07 26.18

27.14 2.45 29.59

29.28 2.32 31.60

32.48 2.68 35.16

Table 4.1


Exponential smoothing with trend adjustment example36 l.jpg

35

30 –

25 –

20 –

15 –

10 –

5 –

0 –

Actual demand (At)

Product demand

Forecast including trend (FITt)

| | | | | | | | |

1 2 3 4 5 6 7 8 9

Time (month)

Exponential Smoothing with Trend Adjustment Example

Figure 4.3


Trend projections l.jpg

^

y = a + bx

^

where y = computed value of the variable to be predicted (dependent variable)

a = y-axis intercept

b = slope of the regression line

x = the independent variable

Trend Projections

Fitting a trend line to historical data points to project into the medium-to-long-range

Linear trends can be found using the least squares technique


Least squares method l.jpg

Actual observation (y value)

Deviation7

Deviation5

Deviation6

Deviation3

Values of Dependent Variable

Deviation4

Deviation1

Deviation2

^

Trend line, y = a + bx

Time period

Least Squares Method

Figure 4.4


Least squares method39 l.jpg

Actual observation (y value)

Deviation7

Deviation5

Deviation6

Deviation3

Values of Dependent Variable

Deviation4

Deviation1

Deviation2

^

Trend line, y = a + bx

Time period

Least Squares Method

Least squares method minimizes the sum of the squared errors (deviations)

Figure 4.4


Least squares method40 l.jpg

Sxy - nxy

Sx2 - nx2

b =

^

y = a + bx

a = y - bx

Least Squares Method

Equations to calculate the regression variables


Least squares example l.jpg

Time Electrical Power

Year Period (x) Demand x2 xy

1999 1 74 1 74

2000 2 79 4 158

2001 3 80 9 240

2002 4 90 16 360

2003 5 105 25 525

2004 6 142 36 852

2005 7 122 49 854

∑x = 28 ∑y = 692 ∑x2 = 140 ∑xy = 3,063

x = 4 y = 98.86

3,063 - (7)(4)(98.86)

140 - (7)(42)

a = y - bx = 98.86 - 10.54(4) = 56.70

∑xy - nxy

∑x2 - nx2

b = = = 10.54

Least Squares Example


Least squares example42 l.jpg

Time Electrical Power

Year Period (x) Demand x2 xy

1999 1 74 1 74

2000 2 79 4 158

2001 3 80 9 240

2002 4 90 16 360

2003 5 105 25 525

2004 6 142 36 852

2005 7 122 49 854

Sx = 28 Sy = 692 Sx2 = 140 Sxy = 3,063

x = 4 y = 98.86

The trend line is

^

y = 56.70 + 10.54x

3,063 - (7)(4)(98.86)

140 - (7)(42)

a = y - bx = 98.86 - 10.54(4) = 56.70

Sxy - nxy

Sx2 - nx2

b = = = 10.54

Least Squares Example


Least squares example43 l.jpg

Trend line,

y = 56.70 + 10.54x

160 –

150 –

140 –

130 –

120 –

110 –

100 –

90 –

80 –

70 –

60 –

50 –

^

Power demand

| | | | | | | | |

1999 2000 2001 2002 2003 2004 2005 2006 2007

Year

Least Squares Example


Seasonal variations in data l.jpg
Seasonal Variations In Data

The multiplicative seasonal model can modify trend data to accommodate seasonal variations in demand

Find average historical demand for each season

Compute the average demand over all seasons

Compute a seasonal index for each season

Estimate next year’s total demand

Divide this estimate of total demand by the number of seasons, then multiply it by the seasonal index for that season


Seasonal index example l.jpg

Demand Average Average Seasonal

Month 2003 2004 2005 2003-2005 Monthly Index

Jan 80 85 105 90 94

Feb 70 85 85 80 94

Mar 80 93 82 85 94

Apr 90 95 115 100 94

May 113 125 131 123 94

Jun 110 115 120 115 94

Jul 100 102 113 105 94

Aug 88 102 110 100 94

Sept 85 90 95 90 94

Oct 77 78 85 80 94

Nov 75 72 83 80 94

Dec 82 78 80 80 94

Seasonal Index Example


Seasonal index example46 l.jpg

Demand Average Average Seasonal

Month 2003 2004 2005 2003-2005 Monthly Index

Jan 80 85 105 90 94

Feb 70 85 85 80 94

Mar 80 93 82 85 94

Apr 90 95 115 100 94

May 113 125 131 123 94

Jun 110 115 120 115 94

Jul 100 102 113 105 94

Aug 88 102 110 100 94

Sept 85 90 95 90 94

Oct 77 78 85 80 94

Nov 75 72 83 80 94

Dec 82 78 80 80 94

average 2003-2005 monthly demand

average monthly demand

Seasonal index =

= 90/94 = .957

Seasonal Index Example

0.957


Seasonal index example47 l.jpg

Demand Average Average Seasonal

Month 2003 2004 2005 2003-2005 Monthly Index

Jan 80 85 105 90 94 0.957

Feb 70 85 85 80 94 0.851

Mar 80 93 82 85 94 0.904

Apr 90 95 115 100 94 1.064

May 113 125 131 123 94 1.309

Jun 110 115 120 115 94 1.223

Jul 100 102 113 105 94 1.117

Aug 88 102 110 100 94 1.064

Sept 85 90 95 90 94 0.957

Oct 77 78 85 80 94 0.851

Nov 75 72 83 80 94 0.851

Dec 82 78 80 80 94 0.851

Seasonal Index Example


Seasonal index example48 l.jpg

Demand Average Average Seasonal

Month 2003 2004 2005 2003-2005 Monthly Index

Jan 80 85 105 90 94 0.957

Feb 70 85 85 80 94 0.851

Mar 80 93 82 85 94 0.904

Apr 90 95 115 100 94 1.064

May 113 125 131 123 94 1.309

Jun 110 115 120 115 94 1.223

Jul 100 102 113 105 94 1.117

Aug 88 102 110 100 94 1.064

Sept 85 90 95 90 94 0.957

Oct 77 78 85 80 94 0.851

Nov 75 72 83 80 94 0.851

Dec 82 78 80 80 94 0.851

Forecast for 2006

1,200

12

1,200

12

Jan x .957 = 96

Feb x .851 = 85

Seasonal Index Example

Expected annual demand = 1,200


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