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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
Exponential Smoothing Example
Predicted demand = 142 Ford MustangsActual demand = 153Smoothing constant a = .20
New forecast = 142 + .2(153 – 142)
24
Exponential Smoothing Example
Predicted demand = 142 Ford MustangsActual demand = 153Smoothing constant a = .20
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
26
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
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
MAD =∑ |deviations|
n
= 82.45/8 = 10.31
For a = .10
= 98.62/8 = 12.33
For a = .50
31
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 98.62MAD 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
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 98.62MAD 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
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 98.62MAD 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
35© 2011 Pearson Education, Inc. publishing as Prentice Hall
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
36© 2011 Pearson Education, Inc. publishing as Prentice Hall
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
37© 2011 Pearson Education, Inc. publishing as Prentice Hall
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
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
38© 2011 Pearson Education, Inc. publishing as Prentice Hall
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 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
39© 2011 Pearson Education, Inc. publishing as Prentice Hall
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 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
40© 2011 Pearson Education, Inc. publishing as Prentice Hall
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 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
41© 2011 Pearson Education, Inc. publishing as Prentice Hall
Exponential Smoothing with Trend Adjustment Example
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
In-Class Problems from the Lecture Guide Practice Problems
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
In-Class Problems from the Lecture Guide Practice Problems
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
In-Class Problems from the Lecture Guide Practice Problems
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