Unit08 - Demand Forecasting

7/31/2019 Unit08 - Demand Forecasting

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Dr. Rameez Khalid, PMPAssociate Professor

NED University of Engineering and Technology

What is Forecasting? Process of predicting a future

event

Underlying basis ofall business decisions

Production

Inventory

Personnel

Facilities

Timely

AccurateReliable

Written

I see that you willget an A this semester.


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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 anddevelopment

Forecasting Time Horizons

Influence of Product Life Cycle

Introduction and growth require longer forecaststhan maturity and decline

As product passes through life cycle, forecasts

are useful in projecting

Staffing levels Inventory levels

Factory capacity

Introduction Growth Maturity Decline


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Product Life Cycle

Best period toincrease marketshare

R&D engineering iscritical

Practical to changeprice or qualityimage

Strengthen niche

Poor time to changeimage, price, orquality

Competitive costsbecome criticalDefend marketposition

Cost controlcritical

Introduction Growth Maturity Decline

CompanyStrategy/Issues

Internet search engines

Sales

Xbox 360

Drive-throughrestaurants

CD-ROMs

3 1/2Floppydisks

LCD & plasma TVsAnalog TVs

iPods

Types of Forecasts

Economic forecasts

Address business cycle inflation rate, moneysupply, housing starts, etc.

Technological forecasts

Predict rate of technological progress

Impacts development of new products

Demand forecasts Predict sales of existing products and services


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Seven Steps in Forecasting

Determine the use of the forecast

Select the items to be forecasted

Determine the time horizon of the forecast

Select the forecasting model(s)

Gather the data

Make the forecast

Validate and implement results

Forecasting Approaches

Used when situation is vague andlittle data exist

New products

New technology

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

Qualitative Methods


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Forecasting Approaches

Used when situation is stable andhistorical data exist

Existing products

Current technology

Involves mathematical techniques e.g., forecasting sales of color

televisions

Quantitative Methods

Overview of Qualitative Methods Jury of executive opinion

Pool opinions of high-level experts, 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


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Overview of Quantitative Approaches

1. Naive approach

2. Moving averages

3. Exponentialsmoothing

4. Trend projection

5. Linear regression

Time-SeriesModels

AssociativeModel

Set of evenly spaced numerical data

Obtained by observing response variable at

regular time periods

Forecast based only on past values, no other

variables important

Assumes that factors influencing past and

present will continue influence in future

Time Series Forecasting


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Trend

Seasonal

Cyclical

Random

Time Series Components

Components of Demand

Demandforproductorservice

| | | |1 2 3 4

Year

Average

demand overfour years

Seasonal peaks

Trendcomponent

Actualdemand

Randomvariation


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Nave Approach

Assumes demand in nextperiod is the same asdemand in most recent period

e.g., If January sales were 68, thenFebruary sales will be 68

Sometimes cost effective andefficient

Can be good starting point


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Stable t ime series data

F(t) = A(t-1)

Seasonal variations

F(t) = A(t-n)

Data with trends

F(t) = A(t-1) + (A(t-1) A(t-2))

Uses for Nave Forecasts


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MA is a series of arithmetic means

Used if lit tle or no trend

Used often for smoothing

Provides overall impression of data over t ime

Moving Average Method

Moving average = demand in previous nperiods

n

January 10February 12March 13April 16May 19

June 23July 26

Actual 3-MonthMonth Shed Sales Moving Average

(12 + 13 + 16)/3 = 13 2/3(13 + 16 + 19)/3 = 16(16 + 19 + 23)/3 = 19 1/3

Moving Average

101213

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


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Used when trend is present

Older data usually less important

Weights based on experience and intuition

Weighted Moving Average

Weightedmoving average =

(weight for period n)

x (demand in period n) weights

January 10February 12March 13

April 16May 19June 23July 26

Actual 3-Month WeightedMonth Shed Sales 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


101213

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

1

/6

Weights Applied Period

3 Last month2 Two months ago1 Three months ago

6 Sum of weights


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Moving Average And


30

25

20

15

10

5

Salesdemand

| | | | | | | | | | | |

J F M A M J J A S O N D

Actualsales

Movingaverage

Weightedmovingaverage

Figure 4.2


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Form of weighted moving average

Weights decline exponentially

Most recent data weighted most

Requires smoothing constant ()

Ranges from 0 to 1

Subjectively chosen

Involves lit tle record keeping of past data

Exponential Smoothing

Exponential SmoothingNew forecast = Last periods forecast

+ (Last periods actual demand

Last periods forecast)

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

Where, Ft = new forecast

Ft 1 = previous forecastAt 1 = previous actual demand

= smoothing (or weighting)constant (0 1)


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Predicted demand = 142 Ford Mustangs

Actual demand = 153

Smoothing constant = .20

New forecast = 142 + .2(153 142)

= 142 + 2.2= 144.2 144 cars

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

Impact of Different

225

200

175

150 | | | | | | | | |

1 2 3 4 5 6 7 8 9

Quarter

Demand

= .1

Actualdemand

= .5

Chose high values of when underlying average is likely to change

Choose low values of when underlying average is stable


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Choosing The objective is to obtain the mostaccurate forecast no matter thetechnique

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

Forecast error = Actual demand - Forecast value= At - Ft


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Common Measures of Error

Mean Absolute Deviation (MAD)

MAD = |Actual - Forecast|

n

Mean Squared Error (MSE)

MSE = (Forecast Errors)2

n

Mean Absolute Percent Error (MAPE)

MAPE =100|Actuali - Forecasti|/Actuali

n

n

i = 1

Comparison of Forecast Error

Rounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast Deviation

Tonnage with for with forQuarter Unloaded = .10 = .10 = .50 = .50

1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30

82.45 98.62

Fill these

columns

Fill these

columns


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Comparison of Forecast Error

Rounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast Deviation

Tonnage with for with forQuarter Unloaded = .10 = .10 = .50 = .50

1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.61

8 182 178.22 3.78 186.30 4.3082.45 98.62

MAD = |deviations|

n

= 82.45/8 = 10.31

For = .10

= 98.62/8 = 12.33

For = .50

Comparison of Forecast ErrorRounded Absolute Rounded Absolute

Actual Forecast Deviation Forecast DeviationTonnage with for with for

Quarter Unloaded = .10 = .10 = .50 = .50

1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.78

7 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30

82.45 98.62MAD 10.31 12.33

= 1,526.54/8 = 190.82

For = .10

= 1,561.91/8 = 195.24

For = .50

MSE = (forecast errors)2

n


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1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.61

8 182 178.22 3.78 186.30 4.3082.45 98.62

MAD 10.31 12.33MSE 190.82 195.24

= 44.75/8 = 5.59%

For = .10

= 54.05/8 = 6.76%

For = .50

MAPE =100|deviationi|/actuali

n

n

i = 1




1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.78

7 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30

82.45 98.62MAD 10.31 12.33MSE 190.82 195.24MAPE 5.59% 6.76%


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Exponential Smoothingwith Trend Adjustment

When a trend is present, exponentialsmoothing must be modified

2nd Order Smoothing

Forecast

including (FITt) =trend

Exponentially Exponentially

smoothed (Ft) + smoothed (Tt)Forecast Trend


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Exponential Smoothing with Trend

Adjustment

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

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

Step 1: Compute Ft

Step 2: Compute Tt

Step 3: Calculate the forecast FITt = Ft + Tt


with Trend Adjustment

ForecastActual Smoothed Smoothed Including

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

1 12 11 2 13.002 173 204 195 246 21

7 318 289 36

10

F2 = A1 + (1 - )(F1 + T1)F2 = (.2)(12) + (1 - .2)(11 + 2)

= 2.4 + 10.4 = 12.8 units

Step 1: Forecast for Month 2


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1 12 11 2 13.002 17 12.803 204 195 246 217 31

8 289 36

10

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

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

= .72 + 1.2 = 1.92 units

Step 2: Trend for Month 2





1 12 11 2 13.002 17 12.80 1.923 204 195 246 21

7 318 289 36

10

FIT2 = F2 + T1FIT2 = 12.8 + 1.92

= 14.72 units

Step 3: Calculate FIT for Month 2


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1 12 11 2 13.002 17 12.80 1.92 14.723 204 195 246 217 31

8 289 36

10

15.18 2.10 17.2817.82 2.32 20.1419.91 2.23 22.1422.51 2.38 24.8924.11 2.07 26.18

27.14 2.45 29.5929.28 2.32 31.6032.48 2.68 35.16

Fill these columns



| | | | | | | | |

1 2 3 4 5 6 7 8 9

Time (month)

Productdemand

35

30

25

20

15

10

5

0

Actual demand (At)

Forecast including trend (FITt)

with = .2 and = .4


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Trend ProjectionsFitting a trend line to historical data points toproject into the medium to long-range

Linear trends can be found using the leastsquares technique

y = a + bx^

where y = computed value of the variable to be

predicted (dependent variable)a = y-axis interceptb = slope of the regression linex = the independent variable

^


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Least SquaresMethod

Time period

Value

sofDependentVariable

Deviation1

(error)

Deviation5

Deviation7

Deviation2

Deviation6

Deviation4

Deviation3

Actual observation(y value)

Trend line, y = a + bx^

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

Least Squares Method

Equations to calculate the regression variables

b =xy - nxy

x2 - nx2

y = a + bx^

a = y - bx

n= Number of data pointsor Observations


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Least Squares

b = = = 10.54xy - nxy

x2 - nx2

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

140 - (7)(42)

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

Time Electrical PowerYear Period (x) Demand x2 xy

2001 1 74 1 742002 2 79 4 1582003 3 80 9 2402004 4 90 16 3602005 5 105 25 5252005 6 142 36 8522007 7 122 49 854

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

x = 4 y = 98.86

Least Squares

b = = = 10.54xy - nxy

x2 - nx2

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

140 - (7)(42)

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

Time Electrical PowerYear Period (x) Demand x2 xy

1999 1 74 1 742000 2 79 4 1582001 3 80 9 2402002 4 90 16 3602003 5 105 25 5252004 6 142 36 8522005 7 122 49 854

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

x = 4 y = 98.86

The trend line is

y = 56.70 + 10.54x^


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Least Squares

| | | | | | | | |2001 2002 2003 2004 2005 2006 2007 2008 2009

160

150

140

130

120

110

100

90

80

70

60

50

Year

Powerdemand

Trend line,y = 56.70 + 10.54x^


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Seasonal Variations In Data

The multiplicativeseasonal model canadjust trend data forseasonal variationsin demand

Seasonal Variations In Data

1. Find average historical demand for each season

2. Compute the average demand over all seasons

3. Compute a seasonal index for each season

4. Estimate next years total demand

5. Divide this estimate of total demand by the

number of seasons, then multiply it by theseasonal index for that season

Steps in the process:


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Seasonal 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 94Oct 77 78 85 80 94

Nov 75 72 83 80 94

Dec 82 78 80 80 94

= 1,128

Demand Average Average SeasonalMonth 2005 2006 2007 2005-2007 Monthly Index

Seasonal 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


0.957

Seasonal index =average 2005-2007 monthly demand

average monthly demand

= 90/94 = .957


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Seasonal 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

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


Expected annual demand = 1,200

Jan x .957 = 961,200

12

Feb x .851 = 851,20012

Forecast for 2008


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San Diego Hospital

10,200

10,000

9,800

9,600

9,400

9,200

9,000 | | | | | | | | | | | |

Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec67 68 69 70 71 72 73 74 75 76 77 78

Month

InpatientDays

9530

9551

9573

9594

9616

9637

9659

9680

9702

9724

9745

9766

Trend Data

y = 8090 + 21.5x^

San Diego Hospital

1.06

1.04

1.02

1.00

0.98

0.96

0.94 0.92 | | | | | | | | | | | |


Month

In

dexforInpatientDays

1.04

1.021.01

0.99

1.031.04

1.00

0.98

0.97

0.99

0.970.96

Seasonal Indices


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San Diego Hospital

10,200

10,000

9,800

9,600

9,400

9,200

9,000 | | | | | | | | | | | |


Month

InpatientDays

9911

9265

9764

9520

9691

9411

9949

9724

9542

9355

10068

9572

Combined Trend and Seasonal Forecast


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REFERENCES

Operations ManagementWilliam J. Stevenson

Operations ManagementBarry Render & Jay Heizer

Unit08 - Demand Forecasting

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