Forecasting
Chapter 5
OPS 370
Forecasting
• What is Forecasting?
– Determining Future Events Based on Historical Facts
and Data
• Some Thoughts on Forecasts
– Forecasts Tend to Be Wrong!
– Forecasts Can Be Biased! (Marketing, Sales, etc.)
– Forecasts Tend to Be Better for Near Future
• So, Why Forecast?
– Better to Have “Educated Guess” About Future Than
to Not Forecast At All!
2
Examples of “Bad” Forecasts
• "I think there is a world market for maybe five
computers." – Thomas Watson, IBM (1943)
• "The Americans have need of the telephone, but we
do not. We have plenty of messenger boys.“ –
William Preece, British Post Office (1876)
• "Who the hell wants to hear actors talk?“ – H.M.
Warner, Warner Brothers (1927)
What to Forecast?
Demand for Individual
Products & Services
Short Term
(0-3 Months)
Demand for Product &
Service Families
Medium Term
(3 Months – 2 Years)
Total Sales, New Offerings
Long Term
(>2 Years)
How to Forecast?
• Qualitative Methods
– Based On Educated Opinion & Judgment
(Subjective)
– Particularly Useful When Lacking Numerical Data
(Example: Design and Introduction Phases of a
Product’s Life Cycle)
• Quantitative Methods
– Based On Data (Objective)
5
Quantitative Methods
• Time Series  Popular Forecasting Approach
in Operations Management
• Assumption:
– “Patterns” That Occurred in the Past Will Continue
to Occur In the Future
6
Components of Demand
• Demand for products or services can consist of
one or more patterns:
–
–
–
–
–
–
average demand
trend
seasonal component
cyclical component
autocorrelation
random variation
Textbook Figure 5.2:
Components of Demand
Monthly Champagne Sales
1600
1400
1200
1000
800
600
400
200
0
0
12
24
36
48
Time (t)
60
72
84
Forecasting Steps
Data Collection
Data Analysis
Collect Relevant/Reliable Data
Be Aware of “Garbage-In,
Garbage Out”
Model Selection
Monitoring
Forecasting Steps
Data Collection
Data Analysis
Plot the Data
Identify Patterns
Model Selection
Monitoring
Forecasting Steps
Data Collection
Choose Model Appropriate for Data
Data Analysis
Consider Complexity Trade-Offs
Perform Forecast(s)
Model Selection
Monitoring
Select Model Based on Performance
Measure(s)
Forecasting Steps
Data Collection
Data Analysis
Model Selection
Monitoring
Track Forecast Performance
(Conditions May and Often Do
Change)
Time Series Models
• Basic Time Series Methods
– Naïve
– Moving Average
– Weighted Moving Average
– Exponential Smoothing
14
Forecasting Example
• L&F Bakery has been forecasting by “gut feel.”
They would like to use a formal
(i.e., quantitative) forecasting technique.
15
Forecasting Methods
• Naïve
• Forecast for July =
Actual for June
• Ft+1 = At
• FJul = AJun = 600
• Forecast Very
Sensitive to Demand
Changes; Good for
stable demand
Forecasting Methods
• Naïve (Excel)
=C4
=C5
17
Forecasting - Chapter 4
Forecasting Methods
• Moving Average
• Forecast for July =
Average of June, May,
and April
• Ft+1 = (At+At-1+…)/n
• FJul = (600+500+400)/3 =
500
• Values Equally Weighted;
Good for stable demand;
Sensitive to fluctuation;
Lags
• Common application:
Stock price forecasting
Moving Averages of TSLA Price
Forecasting Methods
• Moving Average (Excel)
=AVERAGE(C4:C6)
= AVERAGE(C5:C7)
Forecasting Methods
• Moving Average Example
• Assume n = 2
Week
1
2
3
4
5
Demand
125
175
150
150
160
Forecasting Methods
• Moving Average Example
• Assume n = 2
Week
1
2
3
4
5
Demand
125
175
150 (125+175)/2 = 150
150 (175+150)/2 = 162.5
160 (150+150)/2 = 150
(150+160)/2 = 155
Forecasting Methods
• Weighted Moving
Average
• Ft+1 = (W1At+W2At-1+…)
• Assume that W1 = 0.5, W2
=0.3 and W3 = 0.2
• FJul = (0.5)(600) +
(0.3)(500) + (0.2)(400) =
300 + 150 + 80 = 530
• Typically Gives More
Weight to Newer Data
• Lags; Sensitive
Forecasting Methods
• Weighted Moving Average
=$G$6*C6+$G$5*C5+$G$4*C4
=$G$6*C7+$G$5*C6+$G$4*C5
Forecasting Methods
• Weighted Moving Average Example
• Assume n = 2, W1 = 0.7, W2 = 0.3
Week
1
2
3
4
5
Demand
125
175
150
150
160
Forecasting Methods
• Weighted Moving Average Example
• Assume n = 2, W1 = 0.7, W2 = 0.3
Week
1
2
3
4
5
Demand
125
175
150 (0.7)(175) + (0.3)(125) = 160
150 (0.7)(150) + (0.3)(175) = 157.5
160 (0.7)(150) + (0.3)(150) = 150
(0.7)(160) + (0.3)(150) = 157
Forecasting Methods
• Exponential Smoothing
• General Formula:
Ft+1 = aDt +(1-a)Ft
• a is a constant between 0 and 1
Forecasting Methods
• Exponential Smoothing
• Assume that a = 0.3
• What is the forecast for
July?
• = a(June Sales) +
(1-a) (June Forecast) =
(0.3)(600) + (1-0.3)(275)
= 420
• Requires less data; Good
for stable data
Month
Jan (1)
Feb (2)
Mar (3)
Apr (4)
May (5)
Jun (6)
Jul (7)
Sales
200
300
200
400
500
600
-
Forecast
200
200
230
221
275
343
-
Forecasting Methods
• Exponential Smoothing (Excel)
Initial forecast
=D4+$G$4*(C4-D4)
=D5+$G$4*(C5-D5)
Forecasting Methods
• Exponential Smoothing Example
• Assume a = 0.4
Week Demand
1
125 Need initial forecast; Assume 125
2
175
3
150
4
150
5
160
Forecasting Methods
• Exponential Smoothing Example
• Assume a = 0.4
Week Demand
1
125 Need initial forecast; Assume 125
2
175 (0.4)(125) + (0.6)(125) = 125
3
150 (0.4)(175) + (0.6)(125) = 145
4
150 (0.4)(150) + (0.6)(145) = 147
5
160 (0.4)(150) + (0.6)(147) = 148.2
(0.4)(160) + (0.6)(148.2) = 152.9
Forecasting Methods
• How to Select Value of a?
• Alpha determine importance of recent forecast
results in new forecasts
• Small alpha  Less importance on recent
results (Good for products with stable demand)
• Large alpha  Recent forecast results more
important (Good for product with varying
demands)
Determining Forecast Quality
• How Well Did a Forecast Perform?
• Determine Forecast Error
Error = Actual Demand – Forecasted Demand
Month
Jan (1)
Feb (2)
Mar (3)
Apr (4)
May (5)
Jun (6)
Jul (7)
Sales
200
300
200
400
500
600
-
Forecast
200
200
230
221
274.7
342.3
419.6
Error
0
100
-30
179
225.3
257.7
NA
Determining Forecast Quality
• Better Measures:
Mean Absolute Deviation
n
MAD 
e
t
1
n
 e )
n
Mean Squared Error
MSE 
2
t
1
n
e
t
Mean Absolute Percentage
Error
MAPE
D
(100)
n
Determining Forecast Quality
Month
Jan (1)
Feb (2)
Mar (3)
Apr (4)
May (5)
Jun (6)
Jul (7)
Actual
200
300
200
400
500
600
-
ES
Error
|Error|
Error2 Abs %Error
200.0
0
0
0
0
200.0
100
100
10000.0
33.3
230.0
-30
30
900.0
15.0
221.0
179
179
32041.0
44.8
274.7
225.3
225.3 50760.1
45.1
342.3
257.71
257.71 66414.4
43.0
419.6
SUMs
792.0 160115.5 181.1
Averages
158.4 32023.1
36.2
MAD
MAPE
MSE
Determining Forecast Quality
Determining Forecast Quality
For this MA(2) forecast. What is MAD, MSE, and MAPE?
Week
1
2
3
4
5
6
Sales
125
175
150
150
160
-
Forecast
150
162.5
150
155
Determining Forecast Quality
For this MA(2) forecast. What is MAD, MSE, and MAPE?
Week
1
2
3
4
5
6
Sales
125
175
150
150
160
-
Forecast
150
162.5
150
155
SUMs
AVERAGEs
Error
0
-12.5
10
-2.5
-0.8
|Error|
0
12.5
10
22.5
7.5
MAD
Error2 Abs % Error
0
0.0
156.25
7.7
100
6.7
256.3
14.4
85.4
4.8
MAPE
MSE