1 4 4 Forecasting PowerPoint presentation to accompany Heizer and Render Operations Management, 10e...

1

44 ForecastingForecasting

PowerPoint presentation to accompany Heizer and Render Operations Management, 10e Principles of Operations Management, 8e

PowerPoint slides by Jeff Heyl

2

Outline What Is Forecasting?

Forecasting Time Horizons

Forecasting Approaches Overview of Qualitative Methods and Quantitative Methods

Time-Series Forecasting Decomposition of a Time Series Naive Approach

Time-Series Forecasting (cont.) Moving Averages Exponential Smoothing(with trend)

Associative Forecasting Methods: Regression and Correlation

Using Regression Analysis for Forecasting Correlation Coefficients for Regression Lines Multiple-Regression Analysis

3

Learning Objectives

When you complete this chapter you should be able to :

1. Understand the three time horizons and which models apply for each use

2. Explain when to use each of the four qualitative models

3. Apply the naive, moving average, and exponential smoothing

4. Compute measures of forecast accuracy

4

Forecasting at Disney World

Revenues are derived from people Forecast used to adjust opening times, rides,

shows, staffing levels, and guests admitted Model includes gross domestic product, cross-

exchange rates, arrivals into the USA Survey 1 million park guests, employees, and

travel professionals each year Inputs are airline specials, Federal Reserve

policies, Wall Street trends, vacation/holiday schedules for 3,000 school districts around the world

5

Why Forecast?

What are we trying to Forecast?A very well known attribute of a forecast is that

they are always wrong.For example, Snackwell Cookies (1993), But . . .

L. L. BeanTaco BellAMR

Characteristics of ForecastsA forecast is more than a single numberAggregate forecasts are betterThe further in the future, the more inaccuracyForecasts only predict from past events

6

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

Forecasting Time Horizons

7

Forecasting Approaches

Qualitative Methods Used when situation is vague and little data exist Involves intuition, experience

Quantitative Methods Used when situation is ‘stable’ - historical data exist Involves mathematical techniques

8

Overview of Qualitative Methods

1. Jury of executive opinion Pool opinions of high-level experts

2. Delphi method

3. Sales force composite Aggregated estimates from salespersons

4. Consumer Market Survey

9

Delphi Method Iterative group

process, continues until consensus is reached

3 types of participants Decision makers Staff Respondents

Staff(Administering

survey)

Decision Makers(Evaluate

responses and make decisions)

Respondents(People who can make valuable

judgments)

10

Overview of Quantitative Approaches

1. Naive approach

2. Moving averages

3. Exponential smoothing

4. Trend projection

5. Linear regression

time-series models

associative model

11

Set of evenly spaced numerical data

Forecast based only on past values, no other variables important

Components of a Time Series: Trend Seasonal Cyclical Random

Time Series Forecasting

12

Components of DemandD

eman

d f

or

pro

du

ct o

r se

rvic

e

| | | |1 2 3 4

Time (years)

Average demand over 4 years

Trend component

Actual demand line

Random variation

Figure 4.1

Seasonal peaks

13

Naive Approach

Assumes demand in next period is the same as demand in most recent period e.g., If January sales were 68, then

February sales will be 68

Sometimes cost effective and efficient

Can be good starting point

14

MA is a series of arithmetic means Used if little or no trend

Used often for smoothing Provides overall impression of data

over time

Moving Average Method

Moving average =∑ demand in previous n periods

n

15

January 10February 12March 13April 16May 19June 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 Example

101213

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

16

Graph of Moving Average

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

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

Sh

ed S

ales

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

Actual Sales

Moving Average Forecast

17

Used when some trend might be 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

18

January 10February 12March 13April 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

Weighted Moving Average

101213

[(3 x 13) + (2 x 12) + (10)]/6 = 121/6

Weights Applied Period

3 Last month2 Two months ago1 Three months ago

6 Sum of weights

19

Moving Average And Weighted Moving Average

30 –

25 –

20 –

15 –

10 –

5 –

Sa

les

de

man

d

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

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

Actual sales

Moving average

Weighted moving average

Figure 4.2

20

Form of weighted moving average Weights decline exponentially Most recent data weighted most

Requires smoothing constant () Ranges from 0 to 1

Less need for keeping past data

Exponential Smoothing

21

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)

22

Exponential Smoothing Example

Predicted demand = 142 Ford MustangsActual demand = 153Smoothing constant a = .20

23



New forecast = 142 + .2(153 – 142)

24



New forecast = 142 + .2(153 – 142)

= 142 + 2.2

= 144.2 ≈ 144 cars

25

Impact of Different

225 –

200 –

175 –

150 –| | | | | | | | |

1 2 3 4 5 6 7 8 9

Quarter

De

ma

nd

a = .1

Actual demand

a = .5

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Impact of Different

225 –

200 –

175 –

150 –| | | | | | | | |

1 2 3 4 5 6 7 8 9

Quarter

De

ma

nd

a = .1

Actual demand

a = .5 Chose high values of when underlying average is likely to change

Choose low values of when underlying average is stable

27

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

28

Common Measures of Error

• Mean Absolute Deviation (MAD)

• Mean Squared Error (MSE)

• Mean Absolute Percent Error (MAPE)

29

Comparison of Forecast Error

Rounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast Deviation

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

30




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

MAD =∑ |deviations|

n

= 82.45/8 = 10.31

For a = .10

= 98.62/8 = 12.33

For a = .50

31




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 98.62MAD 10.31 12.33

= 1,526.54/8 = 190.82

For a = .10

= 1,561.91/8 = 195.24

For a = .50

MSE =∑ (forecast errors)2

n

32




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 98.62MAD 10.31 12.33MSE 190.82 195.24

= 44.75/8 = 5.59%

For a = .10

= 54.05/8 = 6.76%

For a = .50

MAPE =∑100|deviationi|/actuali

n

n

i = 1

33




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

34© 2011 Pearson Education, Inc. publishing as Prentice Hall

Exponential Smoothing with Trend Adjustment

When a trend is present, exponential smoothing must be modified

Forecast including (FITt) = trend

Exponentially Exponentiallysmoothed (Ft) + smoothed (Tt)forecast trend


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


Exponential Smoothing with Trend Adjustment Example

ForecastActual Smoothed Smoothed Including

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

1 12 11 2 13.002 173 204 195 246 217 318 289 36

10

Table 4.1





1 12 11 2 13.002 173 204 195 246 217 318 289 36

10

Table 4.1

F2 = aA1 + (1 - a)(F1 + T1)

F2 = (.2)(12) + (1 - .2)(11 + 2)

= 2.4 + 10.4 = 12.8 units

Step 1: Forecast for Month 2





1 12 11 2 13.002 17 12.803 204 195 246 217 318 289 36

10

Table 4.1

T2 = b(F2 - F1) + (1 - b)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 1.923 204 195 246 217 318 289 36

10

Table 4.1

FIT2 = F2 + T2

FIT2 = 12.8 + 1.92

= 14.72 units

Step 3: Calculate FIT for Month 2





1 12 11 2 13.002 17 12.80 1.92 14.723 204 195 246 217 318 289 36

10

Table 4.1

15.18 2.10 17.2817.82 2.32 20.1419.91 2.23 22.1422.51 2.38 24.8924.11 2.07 26.1827.14 2.45 29.5929.28 2.32 31.6032.48 2.68 35.16



Figure 4.3

| | | | | | | | |

1 2 3 4 5 6 7 8 9

Time (month)

Pro

du

ct d

eman

d

35 –

30 –

25 –

20 –

15 –

10 –

5 –

0 –

Actual demand (At)

Forecast including trend (FITt)with = .2 and = .4

42

Associative Forecasting

Used when changes in one or more independent variables can be used to predict

the changes in the dependent variable

Most common technique is linear regression analysis

We apply this technique just as we did in the time series example

43

Associative ForecastingForecasting an outcome based on predictor variables using the least squares 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 though to predict the value of the dependent variable

^

44

Least Squares Method

Time period

Va

lue

s o

f D

ep

end

en

t V

ari

able

Figure 4.4

Deviation1

(error)

Deviation5

Deviation7

Deviation2

Deviation6

Deviation4

Deviation3

Actual observation (y-value)

Trend line, y = a + bx^

45

Associative Forecasting Example

Sales Area Payroll($ millions), y ($ billions), x

2.0 13.0 32.5 42.0 22.0 13.5 7

4.0 –

3.0 –

2.0 –

1.0 –

| | | | | | |0 1 2 3 4 5 6 7

Sal

es

Area payroll

46

Associative Forecasting Example

y = 1.75 + .25x^ Sales = 1.75 + .25(payroll)

If payroll next year is estimated to be $6 billion, then:

Sales = 1.75 + .25(6)Sales = $3,250,000

4.0 –

3.0 –

2.0 –

1.0 –

| | | | | | |0 1 2 3 4 5 6 7

No

del

’s s

ales

Area payroll

3.25

47

How strong is the linear relationship between the variables?

Coefficient of correlation r measures degree of association

Values range from -1 to +1

Coefficient of Determination r2

the % change in y predicted by the change in x Values range from 0 to 1

For example, when r = .901 r2 = .81

Correlation

48

Correlation Coefficient

y

x(a) Perfect positive

correlation: r = +1

y

x(b) Positive correlation:

0 < r < 1

y

x(c) No correlation:

r = 0

y

x(d) Perfect negative

correlation: r = -1

49

Multiple Regression Analysis

If more than one independent variable is to be used in the model, linear regression can be

extended to multiple regression to accommodate several independent variables

y = a + b1x1 + b2x2 …^

Computationally, this is quite complex and generally done on the

computer

50

Multiple Regression Analysis

y = 1.80 + .30x1 - 5.0x2^

In the Nodel example, including interest rates in the model gives the new equation:

An improved correlation coefficient of r = .96 means this model does a better job of predicting the change in construction sales

Sales = 1.80 + .30(6) - 5.0(.12) = 3.00Sales = $3,000,000

51

Forecasting in the Service Sector

Presents unusual challenges Special need for short term records Needs differ greatly as function of

industry and product Holidays and other calendar events Unusual events

52

Fast Food Restaurant Forecast

20% –

15% –

10% –

5% –

11-12 1-2 3-4 5-6 7-8 9-1012-1 2-3 4-5 6-7 8-9 10-11

(Lunchtime) (Dinnertime)Hour of day

Per

cen

tag

e o

f sa

les

Figure 4.12

53

FedEx Call Center Forecast

Figure 4.12

12% –

10% –

8% –

6% –

4% –

2% –

0% –

Hour of dayA.M. P.M.

2 4 6 8 10 12 2 4 6 8 10 12

54

In-Class Problems from the Lecture Guide Practice Problems

Problem 1:Auto sales at Carmen’s Chevrolet are shown below. Develop a 3-week moving average.

Week Auto Sales

1 82 103 94 115 106 137 -

55


Problem 2:Carmen’s decides to forecast auto sales by weighting the three weeks as follows:

Weights Applied

Period

3 Last week

2 Two weeks ago

1 Three weeks ago

6 Total

56


Problem 3:A firm uses simple exponential smoothing with α=0.1 to forecast demand. The forecast for the week of January 1 was 500 units whereas the actual demand turned out to be 450 units. Calculate the demand forecast for the week of January 8.

57


Problem 4:Exponential smoothing is used to forecast automobile battery sales. Two value of α are examined α = 0.8 and α=0.5. Evaluate the accuracy of each smoothing constant. Which is preferable? (Assume the forecast for January was 22 batteries.) Actual sales are given below:

Month Actual Battery Sales

Forecast

January 20 22

February 21

March 15

April 14

May 13

June 16

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