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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
- Underlying basis of all business decisions
- Production
- Inventory
- Personnel
- Facilities

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

- 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

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 CycleFigure 2.5

Introduction Growth Maturity Decline

OM Strategy/Issues

Product Life CycleProduct 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

- 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!

- 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

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 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

- 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 Methods

- Sales force composite
- Estimates from individual salespersons are reviewed for reasonableness, then aggregated
- Consumer Market Survey
- Ask the customer

Associative Model

Overview of Quantitative Approaches- Naive approach
- Moving averages
- Exponential smoothing
- Trend projection
- Linear regression

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

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

∑ 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

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

∑(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

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

- Increasing n smooths the forecast but makes it less sensitive to changes
- Do not forecast trends well
- Require extensive historical data

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 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

Predicted demand = 142 Ford Mustangs

Actual demand = 153

Smoothing constant a = .20

New forecast = 142 + .2(153 – 142)

Exponential Smoothing ExamplePredicted demand = 142 Ford Mustangs

Actual demand = 153

Smoothing constant a = .20

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

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

including (FITt) =

trend

exponentially exponentially

smoothed (Ft) + (Tt) smoothed

forecast trend

Exponential Smoothing with Trend AdjustmentWhen a trend is present, exponential smoothing must be modified

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

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 ExampleTable 4.1

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 ExampleStep 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

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 ExampleStep 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

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 ExampleStep 3: Calculate FIT for Month 2

FIT2 = F2 + T1

FIT2 = 12.8 + 1.92

= 14.72 units

Table 4.1

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 Example15.18 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

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 ExampleFigure 4.3

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 ProjectionsFitting 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

Deviation7

Deviation5

Deviation6

Deviation3

Values of Dependent Variable

Deviation4

Deviation1

Deviation2

^

Trend line, y = a + bx

Time period

Least Squares MethodFigure 4.4

Deviation7

Deviation5

Deviation6

Deviation3

Values of Dependent Variable

Deviation4

Deviation1

Deviation2

^

Trend line, y = a + bx

Time period

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

Figure 4.4

Sx2 - nx2

b =

^

y = a + bx

a = y - bx

Least Squares MethodEquations to calculate the regression variables

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 ExampleYear 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 Exampley = 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 ExampleSeasonal 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

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 ExampleDemand 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 Example0.957

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 ExampleDemand 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 ExampleExpected annual demand = 1,200

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