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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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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

  • 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


IntroductionGrowthMaturityDecline

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


IntroductionGrowthMaturityDecline

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

  • 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


Time-Series Models

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


Trend

Cyclical

Seasonal

Random

Time Series Components


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


Actual3-Month

MonthShed SalesMoving Average

January10

February12

March13

April16

May19

June23

July26

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


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


Weights AppliedPeriod

3Last month

2Two months ago

1Three months ago

6Sum of weights

Actual3-Month Weighted

MonthShed SalesMoving Average

January10

February12

March13

April16

May19

June23

July26

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)

whereFt=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 Example

Predicted 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


Mean Absolute Deviation (MAD)

MAD =

∑ |actual - forecast|

n

Common Measure of Error


Forecast

including (FITt) =

trend

exponentiallyexponentially

smoothed (Ft) +(Tt)smoothed

forecasttrend

Exponential Smoothing with Trend Adjustment

When 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


Forecast

ActualSmoothedSmoothedIncluding

Month(t)Demand (At)Forecast, FtTrend, TtTrend, FITt

11211213.00

217

320

419

524

621

731

828

936

10

Exponential Smoothing with Trend Adjustment Example

Table 4.1


Forecast

ActualSmoothedSmoothedIncluding

Month(t)Demand (At)Forecast, FtTrend, TtTrend, FITt

11211213.00

217

320

419

524

621

731

828

936

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


Forecast

ActualSmoothedSmoothedIncluding

Month(t)Demand (At)Forecast, FtTrend, TtTrend, FITt

11211213.00

21712.80

320

419

524

621

731

828

936

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


Forecast

ActualSmoothedSmoothedIncluding

Month(t)Demand (At)Forecast, FtTrend, TtTrend, FITt

11211213.00

21712.801.92

320

419

524

621

731

828

936

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


Forecast

ActualSmoothedSmoothedIncluding

Month(t)Demand (At)Forecast, FtTrend, TtTrend, FITt

11211213.00

21712.801.9214.72

320

419

524

621

731

828

936

10

Exponential Smoothing with Trend Adjustment Example

15.182.1017.28

17.822.3220.14

19.912.2322.14

22.512.3824.89

24.112.0726.18

27.142.4529.59

29.282.3231.60

32.482.6835.16

Table 4.1


35 –

30 –

25 –

20 –

15 –

10 –

5 –

0 –

Actual demand (At)

Product demand

Forecast including trend (FITt)

|||||||||

123456789

Time (month)

Exponential Smoothing with Trend Adjustment Example

Figure 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 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


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


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


Sxy - nxy

Sx2 - nx2

b =

^

y = a + bx

a = y - bx

Least Squares Method

Equations to calculate the regression variables


TimeElectrical Power

YearPeriod (x)Demandx2xy

1999174174

20002794158

20013809240

200249016360

2003510525525

2004614236852

2005712249854

∑x = 28∑y = 692∑x2 = 140∑xy = 3,063

x = 4y = 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


TimeElectrical Power

YearPeriod (x)Demandx2xy

1999174174

20002794158

20013809240

200249016360

2003510525525

2004614236852

2005712249854

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

x = 4y = 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


Trend line,

y = 56.70 + 10.54x

160 –

150 –

140 –

130 –

120 –

110 –

100 –

90 –

80 –

70 –

60 –

50 –

^

Power demand

|||||||||

199920002001200220032004200520062007

Year

Least Squares Example


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


DemandAverageAverage Seasonal

Month2003200420052003-2005MonthlyIndex

Jan80851059094

Feb7085858094

Mar8093828594

Apr909511510094

May11312513112394

Jun11011512011594

Jul10010211310594

Aug8810211010094

Sept8590959094

Oct7778858094

Nov7572838094

Dec8278808094

Seasonal Index Example


DemandAverageAverage Seasonal

Month2003200420052003-2005MonthlyIndex

Jan80851059094

Feb7085858094

Mar8093828594

Apr909511510094

May11312513112394

Jun11011512011594

Jul10010211310594

Aug8810211010094

Sept8590959094

Oct7778858094

Nov7572838094

Dec8278808094

average 2003-2005 monthly demand

average monthly demand

Seasonal index =

= 90/94 = .957

Seasonal Index Example

0.957


DemandAverageAverage Seasonal

Month2003200420052003-2005MonthlyIndex

Jan808510590940.957

Feb70858580940.851

Mar80938285940.904

Apr9095115100941.064

May113125131123941.309

Jun110115120115941.223

Jul100102113105941.117

Aug88102110100941.064

Sept85909590940.957

Oct77788580940.851

Nov75728380940.851

Dec82788080940.851

Seasonal Index Example


DemandAverageAverage Seasonal

Month2003200420052003-2005MonthlyIndex

Jan808510590940.957

Feb70858580940.851

Mar80938285940.904

Apr9095115100941.064

May113125131123941.309

Jun110115120115941.223

Jul100102113105941.117

Aug88102110100941.064

Sept85909590940.957

Oct77788580940.851

Nov75728380940.851

Dec82788080940.851

Forecast for 2006

1,200

12

1,200

12

Janx .957 = 96

Febx .851 = 85

Seasonal Index Example

Expected annual demand = 1,200


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