demand forecasting

Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.

ChapChapterter

Demand Forecasting

33

Slides prepared byLaurel DonaldsonDouglas College


Learning Objectives

2

LO 1

LO 3

LO 2

LO 4

LO 5

LO 6

LO 7

LO 8

Identify uses of demand forecasts, distinguish between forecasting time frames, describe common features of forecasts, list the elements of a good forecast and steps of forecasting process, and contrast different forecasting approaches.

Describe at least three judgmental forecasting methods.

Describe the components of a time series model, and explain averaging techniques and solve typical problems.

Describe trend forecasting and solve typical problems.

Describe seasonality forecasting and solve typical problems.

Describe associative models and solve typical problems.

Describe three measures of forecast accuracy, and two ways of controlling forecasts, and solve typical problems.

Identify the major factors to consider when choosing a forecasting technique.

Identify uses of demand forecasts, distinguish between forecasting time frames, describe common features of forecasts, list the elements of a good forecast and steps of forecasting process, and contrast different forecasting approaches.






Describe three measures of forecast accuracy, and two ways of controlling forecasts, and solve typical problems.



Chapter Outline

What is forecasting? Features common to all forecasts Elements of a good forecast Steps in the forecasting process Approaches to forecasting Judgmental methods Time series models Associative models Accuracy and control of forecasts Choosing a forecasting technique Excel Templates

3


LO 1

What is Forecasting?

4

I see that you willget a 100 in OM this semester.

A demand forecast is an estimate of demand expected over a future

time period

A demand forecast is an estimate of demand expected over a future

time period


LO 1

How big a facility do I need to manufacture a new videophone?

How much money do I need to run operations of my accounting office?

How many pairs of white shoes should I order for the summer season in my store?

How many operators should I schedule next month for my call centre?

How much lettuce should I buy for next week in my restaurant?

5

Need to FORECAST demand!Need to FORECAST demand!


LO 1

3 Uses for Forecasts:

6


LO 1

Features of ForecastsAssumes causal system

past ==> future

Forecasts rarely perfect because of randomness

Forecasts more accurate forgroups vs. individuals

Forecast accuracy decreases as time horizon increases

7


LO 1

Elements of a Good Forecast

8


LO 1

Steps in the Forecasting Process

9


LO 1

Approaches to ForecastingJudgmental

non-quantitative analysis of subjective inputsconsiders “soft” information such as

human factors, experience, gut instinct

Judgmental non-quantitative analysis of subjective inputsconsiders “soft” information such as

human factors, experience, gut instinct

10

QuantitativeTime series models

extends historical patterns of numerical data

Associative models create equations with explanatory variables

to predict the future

QuantitativeTime series models

extends historical patterns of numerical data

Associative models create equations with explanatory variables

to predict the future


LO 2

Judgmental Methods

Executive opinionspool opinions of high-level executiveslong term strategic or new product

development

11

Expert opinions Delphi method: iterative questionnaires

circulated until consensus is reached. technological forecasting


LO 2

Judgmental Methods

Sales force opinionsbased on direct customer contact

12

Consumer surveysquestionnaires or focus groups

Historical analogiesuse demand for a similar product


LO 3

What is a Time Series?Time series:

a time ordered sequence of observations

taken at regular intervals of time

Time series: a time ordered sequence of

observations taken at regular intervals of time

13

Level: (average) horizontal pattern Trend: steady upward or downward movement Seasonality: regular variations related to time of year or

day Cycles: wavelike variations lasting more than one year Irregular variations: caused by unusual circumstances,

not reflective of typical behaviour Random variations: residual variations after all other

behaviours are accounted for (called noise)

The following 6 patterns could be identified in a time series:The following 6 patterns could be identified in a time series:


LO 3

Patterns of a Time Series

14

Year1

Year2

Year3

Year4

Seasonal peaks (winters) Trend component

Actual demand line

Dem

and

for s

now

boar

ds

Random variation


LO 3

Time series modelsNaive methodsAveraging methods

Moving averageWeighted moving averageExponential smoothing

Trend modelsLinear and non-linear trendTrend adjusted exponential

smoothingTechniques for seasonality

Techniques for cycles

Naive methodsAveraging methods

Moving averageWeighted moving averageExponential smoothing

Trend modelsLinear and non-linear trendTrend adjusted exponential

smoothingTechniques for seasonality

Techniques for cycles

15


LO 3

Naive Methods

Next period = last period Simple to use and understand Very low cost Low accuracy

16

211

1

:d with trenData

:s variationSeasonal

:data series timeStable

tttt

ntt

tt

AAAF

AF

AF

F = forecast A = actual


LO 3

Naive Method - Example

17

Uh, give me a minute.... We sold 250 wheels lastweek.... Now, next week we should sell....


LO 3

Naive Method with Trend: Example

18

2 years ago we sold 50 memberships. Last year we sold 75 memberships. This year we expect to sell …

100100


LO 3

Averaging Methods

19

111 :Smoothing

lExponentia tttt FAFF

n

nFt

periods previousin Demand

: Average

Moving

Weights

Demand Weight :

Average Moving

Weighted period period nntF

F = forecast A = actual = smoothing constant


LO 3

Moving Average

average of last few actual data values, updated each period easy to calculate and understandsmoothes bumps, lags behind changes

choose number of periods to includefewer data points = more sensitive to

changesmore data points = smoother, less

responsive

20


LO 3

Moving Average - ExampleCompute a three-period moving average

forecast for period 6, given the demand below

21

33.413

414043

3

415

404

433

402

421

DemandPeriod

5436

FFFF


LO 3

Weighted Moving Average - Example Compute a 4-period weighted moving average

forecast for period 6 using a weight of 0.4 for the most recent period, 0.3 for the next, 0.2 for the next, and 0.1 for the next.

22

414.03.02.01.0

4.03.02.01.0

0.4415

0.3404

0.2433

0.1402

421

WeightDemandPeriod

54326

FFFFF

The choice of weights may involve the use of trial and error to find a suitable weighting scheme

Weights must add up to 100%


LO 3

Moving Average Example

23

(14 + 16 + 19)/3 = 16 1/3

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

91214

(9 + 12 + 14)/3 = 11 2/3 (12 + 14 + 16)/3 = 14


LO 3

Graph of Moving Average

24

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

1 2 3 4 5 6 7 8 9 10 11 12

Qu

an

tity

30 –28 –26 –24 –22 –20 –18 –16 –14 –12 –10 –

Actual Sales

Moving Average Forecast


LO 3

Moving Average Example

25

1 92 123 144 165 196 237 26

Period Demand Forecast

Apply weights of .5 for most recent period, then .3, then .2

[(.5 x 16) + (.3 x 14) + (.2 x 12)] = 14.6

[(.5 x 19) + (.3 x 16) + (.2 x 14)] = 17.1

[(.5 x 23) + (.3 x 19) + (.2 x16)] = 20.4

91214

[(.5 x 14) + (.3 x 12) + (.2 x 9)] = 12.4


LO 3

Moving Average And Weighted Moving Average

26

30 –

25 –

20 –

15 –

10 –

5 –

Qu

an

tity

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

1 2 3 4 5 6 7 8 9 10 11 12

Actual sales

Moving average

Weighted moving average


LO 3

Exponential Smoothing

sophisticated weighted moving averageweights decline exponentiallymost recent data weighted most

subjectively choose smoothing constant ranges from 0 to 1 (commonly .05 to .5)

widely used easy to use easy to alter weighting 27


LO 3

Exponential Smoothing FormulaForecast = previous forecast plus a

percentage of the forecast errorActual - Forecast is the error term is the % feedback

28

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



LO 3

Exponential Smoothing: Alternate FormulaForecast = previous forecast plus a

percentage of the forecast error is the weight on actual demand is the weight on previous

forecast

29

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



LO 3

Exponential Smoothing: ExampleForecasted demand = 142 video gamesActual demand = 153Smoothing constant = .20

30

New forecast = .2 (153) + (1 - .2)(142)

= 30.6 + 113.6

= 144.2 ≈ 144 games


LO 3

Exponential Smoothing: ExampleForecasted demand = 142 video gamesActual demand = 153Smoothing constant = .20

31

New forecast = 142 + .2 (153 - 142)

= 30.6 + 113.6

= 144.2 ≈ 144 games


LO 3

Exponential Smoothing: Example

32

72.5859.2-580.42.95FA0.4FF644

2.5962-550.462FA0.4FF583

6260-650.460FA0.4FF552

60651

nsCalculatioForecastActualPeriod

3334

2223

1112

Prepare a forecast using smoothing constant = 0.40.

What is the starting point? average of several periods of actual data subjective estimate (for this example, use 60) first actual value (naïve approach)

Prepare a forecast using smoothing constant = 0.40.

What is the starting point? average of several periods of actual data subjective estimate (for this example, use 60) first actual value (naïve approach)


LO 3

Week Demand1 8202 7753 6804 6555

Exponential Smoothing: Your Turn!What are the exponential smoothing

forecasts for periods 2-5 using =0.5?Use naïve approach for 1st week

What are the exponential smoothing forecasts for periods 2-5 using =0.5?

Use naïve approach for 1st week

33


LO 3

Week Demand 0.51 820 820.002 775 820.003 680 797.504 655 738.755 696.88

Exponential Smoothing: Your Turn!

34


LO 3

Selecting a Smoothing Constant

35

225 –

200 –

175 –

150 –| | | | | | | | |

1 2 3 4 5 6 7 8 9Period

Dem

an

d

a = .1

Actual deman

d

a = .5


LO 3

Choosing When demand is fairly stable, use a lower

value for smoothes out random fluctuations

When demand increasing or decreasing, use a higher value for more responsive to real changes

Try to find balance trial and error can change over time.

36


LO 3

True or False?

A moving average forecast tends to be more responsive to changes in the data series when more data points are included in the average.

False

As compared to a simple moving average, the weighted moving average is more reflective of the recent changes.

True

A smoothing constant of .1 will cause an exponential smoothing forecast to react more quickly to a sudden change than a value of .3 will.

False

37


LO 3

Excel: Exponential Smoothing

38

Solved Problem 1: Excel Template


LO 4

Techniques for Trend

39

– Develop an equation

that describes the trend

– Look at historical data

– Develop an equation

that describes the trend

– Look at historical data


LO 4

Nonlinear Trends

40


LO 4

Linear Trend Equation

– Fit a trend line to a series of historical data– Use regression to find the equation of the line

(called the Least Squares Line)

41

n

tbya

ttn

yttynb

btayt

:intercept-y

:Slope

:Equation

22


LO 4

Linear Trend

42

Deviation

Deviation

Deviation

Deviation

Deviation

Deviation

Deviation

Time

Dem

and

Actual observation

Points on the line

btayt


LO 4

Linear Trend: Example

43

tbtay

a

b

t

tytyt

tytyt

t 3.65.143

5.1435

153.6812

3.6225275

180,12495,12

225555

81215499,25

225

499,25581215

885251775

664161664

48691623

31441572

15011501

Salesweek

2

2

2


LO 4

Excel - Linear Trend

44

Insert Chart

Scatter

Highlight data range

Right Click on a data point

Add TrendlineType: LinearOptions: Show equation on chart

Scatter with Trendline

y = 10.171x - 20242

0

20

40

60

80

100

120

140

160

1996 1997 1998 1999 2000 2001 2002 2003 2004

Year

Sal

es

Or Insert Functions:

=SLOPE(Range of y's,Range of x's)

=INTERCEPT(Range of y's,Range of x's)


LO 4

Excel - Linear Trend

45


LO 4

Trend-Adjusted Exponential Smoothingselect values (usually through trial and

error) for = smoothing constant for average = smoothing constant for trend

estimate starting smoothed average and smoothed trend use most recent data

46


LO 4

Trend-Adjusted Exponential Smoothing

47

TAFt+1 = St + Tt (3–6)

whereSt = smoothed average at the end of period tTt = smoothed trend at the end of period t

St = TAFt +α(At TAFt) (3–7)Tt = Tt-1 + ( St St-1 Tt-1)


LO 4

Trend-Adjusted Forecast: Example

48


LO 5

Techniques for SeasonalityAdditive or Multiplicative Model

quantity added to average or trendor proportion x average or trend

49time

Dem

and

Additive Model

Demand = Trend + Seasonality

Multiplicative Model

Demand = Trend x Seasonality

Multiplicative Model

Demand = Trend x Seasonality


LO 5

Using Seasonal Relatives

Seasonal Relative (or index) = proportion of average or trend for a season in

the multiplicative modelseasonal relative of 1.2 = 20% above average

Deseasonalize remove seasonal component to more clearly see

other componentsdivide by seasonal relative

Reseasonalize adjust the forecast for seasonal componentmultiply by seasonal relative

Seasonal Relative (or index) = proportion of average or trend for a season in

the multiplicative modelseasonal relative of 1.2 = 20% above average

Deseasonalize remove seasonal component to more clearly see

other componentsdivide by seasonal relative

Reseasonalize adjust the forecast for seasonal componentmultiply by seasonal relative

50


LO 5

Times Series Decomposition

51


LO 5

Techniques for Seasonality - ExamplePredict quarterly demand for a certain loveseatThe series has both trend and seasonality. Quarterly relatives : Q1 = 1.20, Q2 = 1.10, Q3 = 0.75, Q4 = 0.95. Trend equation yt=124+7.5t (t = 1 in first quarter of 2003)

Predict demand for quarter 3 of 2006

52

38.17775.05.236

5.236155.7124

15 2006 of 3quarter for

15

15

F

y

t


LO 6

Associative Forecasting

53

If I want to predict ridership originating from a If I want to predict ridership originating from a new train station, what data might I look at?new train station, what data might I look at?

1. Find (predictor) variables that are associated with ridership at other stations.

2. Associated = correlated = as one moves the other moves

3. Create a model that shows the relationship between the predictor variables and the predicted variable (e.g. ridership)

4. Technique is regression analysis• Simple linear regression with one variable• Multiple regression (can be non-linear)

5. Test the model to see which variables most useful in predicting ridership (look at r2)

6. Use the model to predict ridership, given values of the predictor variables.


LO 6

Associative ModelsPredictor variables (x): used to predict values of

the variable of interest (y)(also called independent variables)

Predictor variables (x): used to predict values of the variable of interest (y)(also called independent variables)

54

Linear regression: process of finding a straight line that best fits a set of points on a graph (use the Least Squares Equation)

Linear regression: process of finding a straight line that best fits a set of points on a graph (use the Least Squares Equation)

Multiple regression: models with more than one predictor variable (computations complex, created with computer)

Multiple regression: models with more than one predictor variable (computations complex, created with computer)


LO 6

Simple Linear Regression

would a linear model be reasonable?55

0

10

20

30

40

50

0 5 10 15 20 25

X Y7 152 106 134 15

14 2515 2716 2412 2014 2720 4415 347 17

Computed relationship


LO 6

Excel: Simple Linear Regression

56


LO 6

Correlation and ExcelCorrelation coefficient (r): measure of the strength

of relationship between two variablesranges from -1 to +1

-1 = two variables move together in same direction+1 = two variables move together in opposite direction

=CORREL(Range of y values, Range of x values)

r2 measures proportion of variation in the values of y that is “explained” by the predictor variables in the regression modelranges from 0 to 1

higher values = more useful predictors=RSQ(Range of y values, Range of x values)

57


LO 6

Linear Regression AssumptionsPredictions are being made only within the

range of observed valuesrelationship may be non-linear outside that rangey-intercept often not meaningful

Variations around the line are random and normally distributed

For best results:Always plot the data to verify linearitySmall correlation may imply that

other variables are important

58


LO 7

Accuracy and Control of ForecastsError = Actual value - Forecast value

+ve = forecast too low, -ve = too highThree measures of forecasts are used:

Mean absolute deviation (MAD)Mean squared error (MSE)Mean absolute percent error (MAPE)

Control chartsplot errors to see if within pre-set control limits

Tracking signalRatio of cumulative error and MAD

Error = Actual value - Forecast value+ve = forecast too low, -ve = too high

Three measures of forecasts are used:Mean absolute deviation (MAD)Mean squared error (MSE)Mean absolute percent error (MAPE)

Control chartsplot errors to see if within pre-set control limits

Tracking signalRatio of cumulative error and MAD

59


LO 7

Error, MAD, MSE and MAPE

60

nMAD

ForecastActual

n

MSE

2ForecastActual

%100n

Actual

Forecast Actual

MAPE

tt FAe ForecastActualError


LO 7

MAD, MSE and MAPE

61


LO 7

Error, MAD, MSE and MAPE: ExampleCompute MAD, MSE, and MAPE for the following data.

62

%69.43010

%90.11644214

%46.0111215

%41.1933216

%92.0422215

2104

2163

2132

2171

100A

eeeeForecastActualPeriod 2

%17.1

100

5.7

5.2

2

n

A

e

MAPE

n

eMSE

n

eMAD


LO 7

Forecast Errors

bias = the sum of the forecast errors+ve bias = frequent underestimation-ve bias = frequent overestimation

bias = the sum of the forecast errors+ve bias = frequent underestimation-ve bias = frequent overestimation

63

possible sources of error include:Model may be inadequate (things have

changed)Incorrect use of forecasting techniqueIrregular variations


LO 7

Controlling the Forecasting ProcessControl chart

A visual tool for monitoring forecast errorsUsed to detect non-randomness in errorsSet limits that are multiples of the √MSE

Control chartA visual tool for monitoring forecast errorsUsed to detect non-randomness in errorsSet limits that are multiples of the √MSE

64

Forecasting errors are “in control” when only random errors, no errors from identifiable causes“in control” if

All errors are within control limitsNo patterns (e.g. trends or cycles) are present

errors outside limit = need corrective action


LO 7

Control Chart

65

0

Upper limit

Lower limit

Range of acceptable variation

Time

Err

or

Need for corrective action

Need for corrective action


LO 7

Controlling Forecasts: Control Limits

66

Standard deviation of error

=

Control Limits = 0 ± 2 (or 3) s

s MSEe

n

2

95% of all errors should be within 2s95% of all errors should be within 2s

97.7% of all errors should be within 3s97.7% of all errors should be within 3s


LO 7

Control Chart Example

67

s 1575

6262 5 16 2. .

Errors should be within ± 2(16.2).

Lower limit = -32.4 Upper limit = 32.4


LO 7

Control Chart Example

68

-32

-24

-16

-8

0

8

16

24

32

0 1 2 3 4 5 6 7

All the errors are within the control limits


LO 7

Below is a pharmacy’s actual sales and forecasted demand for a certain prescription drug for 5 months. How accurate is their forecast? Calculate MAD and MSE and create a control chart.

Below is a pharmacy’s actual sales and forecasted demand for a certain prescription drug for 5 months. How accurate is their forecast? Calculate MAD and MSE and create a control chart.

Pharmacy Forecast Control: Your Turn!

69


LO 7

10=4

40=

n

F-A

=MADtt

10=4

40=

n

F-A

=MADtt

137.5=4

550=

n

F-A

=MSE

2

tt 137.5=

4

550=

n

F-A

=MSE

2

tt


70


LO 7


71-23.4

-15.6

-7.8

0

7.8

15.6

23.4

0 1 2 3 4 5

All the errors are within the control limits

550137.5 11.7

4s

Errors should be within ± 2(11.7).Lower limit = -23.4 Upper limit = 23.4


LO 7

Tracking SignalTracking signal

ratio of cumulative error to MAD can be plotted on a control chart investigate if TS > 4

72

Tracking signal = (Actual -forecast)

MAD


LO 7

True or False?

When error values fall outside the limits of a control chart, this signals a need for corrective action

Ans: TrueWhen all errors plotted on a control chart are

either all positive, or all negative, this shows that the forecasting technique is performing adequately.

Ans: FalseA random pattern of errors within the limits of

a control chart signals a need for corrective action.

Ans: False

73


LO 8

Choosing a Forecasting TechniqueNo single technique works in every

situationTwo most important factors

CostAccuracy

Other factors include availability of:Historical dataComputersTime needed to gather and analyze the dataForecast horizon

74


LO 8

Choosing a Forecast Technique

75Source: J. Holton Wilson and D. Allison-Koerber, “Combining Subjective and Objective Forecasts Improves Results,” Journal of Business Forecasting Methods & Systems, 11(3) Fall 1992, p. 4.


LO 8

Choosing a Forecast TechniqueSource: C. L. Jain, “Benchmarking Forecasting Models,” Journal of Business Forecasting Methods & Systems, Fall 2002, pp. 18–20,

30.

76


LO 8

Which technique?Sales for a product have been fairly consistent over

several years, although showing a steady upward trend. The company wants to understand what drives sales. The best forecasting technique would be:A) trend modelsB) judgmental methodsC) moving averagesD) regression modelsE) exponential smoothing techniques

Ans: D

77


Learning Checklist






78


Learning Checklist Identify uses of demand forecasts Distinguish between forecasting time frames Describe common features of forecasts List the elements of a good forecast and steps

of forecasting process, Contrast different forecasting approaches. Describe three measures of forecast

accuracy, and two ways of controlling forecasts, and solve typical problems.


79

demand forecasting

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