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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

Operations Management

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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.

??

- Process of predicting a future event
- Underlying basis of all business decisions
- Production
- Inventory
- Personnel
- Facilities

- 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

- 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

Figure 2.5

IntroductionGrowthMaturityDecline

OM Strategy/Issues

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

- 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

- 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

Qualitative Methods

- Used when situation is vague and little data exist
- New products
- New technology

- Involves intuition, experience
- e.g., forecasting sales on Internet

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

- Jury of executive opinion
- Pool opinions of high-level executives, sometimes augment by statistical models

- Delphi method
- Panel of experts, queried iteratively

- Sales force composite
- Estimates from individual salespersons are reviewed for reasonableness, then aggregated

- Consumer Market Survey
- Ask the customer

Time-Series Models

Associative Model

- Naive approach
- Moving averages
- Exponential smoothing
- Trend projection
- Linear regression

- 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

- 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 =

- 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

(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

=

- 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

[(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

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

- 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

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)

Predicted demand = 142 Ford Mustangs

Actual demand = 153

Smoothing constant a = .20

New forecast= 142 + .2(153 – 142)

Predicted demand = 142 Ford Mustangs

Actual demand = 153

Smoothing constant a = .20

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

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

Forecast

including (FITt) =

trend

exponentiallyexponentially

smoothed (Ft) +(Tt)smoothed

forecasttrend

When a trend is present, exponential smoothing must be modified

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

Table 4.1

Forecast

ActualSmoothedSmoothedIncluding

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

11211213.00

217

320

419

524

621

731

828

936

10

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

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

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

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)

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

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

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 minimizes the sum of the squared errors (deviations)

Figure 4.4

Sxy - nxy

Sx2 - nx2

b =

^

y = a + bx

a = y - bx

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

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

Trend line,

y = 56.70 + 10.54x

160 –

150 –

140 –

130 –

120 –

110 –

100 –

90 –

80 –

70 –

60 –

50 –

^

Power demand

|||||||||

199920002001200220032004200520062007

Year

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

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

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

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

Expected annual demand = 1,200