Operations
Management
Forecasting
Chapter 4
4-1
Examples
 Predict the next number in the pattern:
a) 3.7, 3.7, 3.7, 3.7, 3.7,
?
b) 2.5, 4.5, 6.5, 8.5, 10.5, ?
c) 5.0, 7.5, 6.0, 4.5, 7.0, 9.5, 8.0, 6.5, ?
4-2
Examples
 Predict the next number in the pattern:
a) 3.7, 3.7, 3.7, 3.7, 3.7,
y = 3.7
b) 2.5, 4.5, 6.5, 8.5, 10.5,
y = 0.5 + 2x
c) 5.0, 7.5, 6.0, 4.5, 7.0, 9.5, 8.0, 6.5,
y = 4.5 + 0.5x + ci
c1 = 0; c2 = 2; c3 = 0; c4 = -2; etc
4-3
Outline
 What is Forecasting?

Time horizons.

Life cycle.
 Types of Forecasts.
 Eight Steps in the Forecasting System.
 Forecasting Approaches:
Overview of Qualitative Methods.
 Overview of Quantitative Methods.

4-4
Outline - Continued
 Time-Series Forecasting:

Moving Averages.

Exponential Smoothing.

Trend Projection.
 Associative Forecasting Methods: Regression
and Correlation Analysis.
 Monitoring and Controlling Forecasts.
 Forecasting in the Service Sector.
4-5
What is Forecasting?
 Art and science of
predicting future events.
 Underlying basis of
all business decisions.

Production & Inventory.

Personnel & Facilities.
 Focus on forecasting
demand.
4-6
Sales will
be $200
Million!
Types of Forecasts by Time Horizon
Short-range forecast: Usually < 3 months.

Job scheduling, worker assignments.
Medium-range forecast: 3 months to 3 years.

Sales & production planning, budgeting.
Long-range forecast: > 3 years.

New product planning, facility location.
4-7
Short- vs. Long-term Forecasting
Medium & Long range forecasts:
Long range for design of system.
 Deal with comprehensive issues.
 Support management decisions regarding planning.

Short-term forecasts:
To plan detailed use of system.
 Usually use quantitative techniques.
 More accurate than longer-term forecasts.

4-8
Influence of Product Life Cycle
Stages of introduction and growth require
longer forecasts than maturity and decline.
Forecasts useful in projecting:

staffing levels,

inventory levels, and

factory capacity (expansion and contraction),
as product passes through life cycle stages.
4-9
Forecasting During the Life Cycle
Introduction
Growth
Hard to forecast.
Forecasting
critical, both for
future magnitude
and growth rate.
Need long-range
forecasts.
Often use
qualitative
models.
Maturity
Easier to
forecast.
Use quantitative
models.
Long-range
forecasts still
important.
Sales
4-10
Time
Decline
Hard to forecast,
but forecasting
is less important.
Eight Steps in Forecasting
Determine the use of the forecast.
Select the items to be forecast.
Determine the time horizon of the forecast.
Select the forecasting model(s).
Gather the data.
Make the forecast.
Validate and implement results.
Monitor forecasts and adjust when needed.
4-11
Realities of Forecasting
Assumes future will be like the past (causal
factors will be the same).
Forecasts are imperfect.
Forecasts for groups of product are more
accurate than forecasts for individual products.
Accuracy decreases with length of forecast.
4-12
Forecasting Approaches
Qualitative Methods
Quantitative Methods
 Used when little data or time  Used when situation is
‘stable’ & historical data
exist.
exist.
 New products & technology.
Existing products &
current technology.
 No significant changes
expected.
Long time horizon.
 Major changes expected.


 Involves intuition,
experience.

 Involves mathematical
techniques.
Example: forecasting for
e-commerce sales.

4-13
Example: forecasting sales
of color televisions.
Overview of Qualitative Methods
Jury of executive opinion.

Combine opinions from executives.
Sales force composite.

Aggregate estimates from salespersons.
Delphi method.

Query experts interatively.
Consumer market survey.

Survey current and potential customers.
4-14
Jury of Executive Opinion
 Seek opinions/estimates from small
group of high-level managers
working together.
 Combines managerial experience
with statistical models.
+ Relatively quick.
- ‘Group-think’.
- Leader may dominate.
4-15
Sales Force Composite
 Each salesperson projects
their sales.
 Aggregate projections at
district & national levels.
+ Sales rep’s know customers.
- Must not reward inaccurate
forecasts.

May over- or under-forecast to
acquire more resources.
4-16
Sales
Delphi Method
 Iterative group process.
 3 types of people:
Decision makers.
 Staff.
 Respondents.
Decision Makers
(Make forecast)

Staff
(Administer)
+ Reduces ‘group-think’.
- Takes time.
Respondents
(Provide input to decision makers)
4-17
Consumer Market Survey
How many hours will
you use the Internet
next week?
 Ask customers about
purchasing plans.
+ Relatively simple.
- What consumers say, and
what they actually do are
often different.
4-18
Quantitative Forecasting Methods
Quantitative
Forecasting
Associative
Models
Time Series
Models
Moving
Average
Exponential
Smoothing
Trend
Projection
4-19
Linear
Regression
What is a Time Series?
 Set of evenly spaced numerical data.

From observing response variable at regular time
periods.
 Forecast based only on past values.

Assumes that factors influencing past will continue
influence in future.
 Example:
Year:
Sales:
1
78.7
2
63.5
4-20
3
89.7
4
93.2
5
92.1
Time Series Components
Trend
Cyclical
Seasonal
Random
4-21
Demand for product or service
Product Demand over 4 Years
Year
1
Year
2
4-22
Year
3
Year
4
Product Demand over 4 Years
Trend component
Demand for product or service
Seasonal peaks
Random
variation
Year
1
Year
2
4-23
Actual
demand line
Year
3
Year
4
Cyclic
component
Trend Component
 Persistent, overall upward or downward
pattern.
 Due to population, technology etc.
 Several years duration.
Time
4-24
Seasonal Component
 Regular pattern of up & down fluctuations.
 Due to weather, customs etc.
 Occurs within 1 year.
 Quarterly, monthly, weekly, etc.
Summer
Demand
Time
4-25
Cyclical Component
 Repeating up & down movements.
 Due to interactions of factors influencing
economy.
 Usually 2-10 years duration.
Cycle
Demand
Year
4-26
Random Component
 Erratic, unsystematic, ‘residual’ fluctuations.
 Due to random variation or unforeseen events.

Union strike

Tornado
 Short duration & non-repeating.
4-27
General Time Series Models
Any value in a time series is a combination
of the trend, seasonal, cyclic, and random
components.
Multiplicative model: Yi = Ti · Si · Ci · Ri
Additive model: Yi = Ti + Si + Ci + Ri
4-28
Naive Approach
 Demand in next period is the
same as demand in most recent
period.

e.g., If May sales were 48, then June
sales will be 48.
 Sometimes cost effective &
efficient.
 Usually not good.
4-29
Moving Average Method
 MA is a series of arithmetic means.
 Used if little or no trend.
 Used often for smoothing.
Demand in previous n periods

MA 
n
4-30
Moving Average Example
You’re manager of a museum store that sells
historical replicas. You want to forecast
sales (in thousands) for months 4 and 5
using a 3-period moving average.
Month 1
Month 2
Month 3
Month 4
Month 5
4
6
5
?
?
4-31
Moving Average Forecast
Month
1
2
3
4
5
6
Response
Yi
4
6
5
?
?
?
Moving
Total
(n=3)
NA
NA
NA
4+6+5=15
4-32
Moving
Average
(n=3)
NA
NA
NA
15/3=5
Moving Average Graph
Sales
8
6
Actual
Forecast
44
22
95
1
96
2
97
3
984
Month
4-33
99
5
00
6
Actual Demand for Month 4 = 3
Month
1
2
3
4
5
6
Response
Yi
4
6
5
3
?
?
Moving
Total
(n=3)
NA
NA
NA
4+6+5=15
4-34
Moving
Average
(n=3)
NA
NA
NA
15/3 = 5
Moving Average Graph
Sales
8
6
Actual
Forecast
44
22
95
1
96
2
97
3
984
Month
4-35
99
5
00
6
Moving Average Forecast
Month
1
2
3
4
5
6
Response
Yi
4
6
5
3
7
?
Moving
Total
(n=3)
NA
NA
NA
15
6+5+3=14
4-36
Moving
Average
(n=3)
NA
NA
NA
5
14/3=4.667
Moving Average Graph
Sales
8
6
Actual
Forecast
44
22
95
1
96
2
97
3
984
Month
4-37
99
5
00
6
Actual Demand for Month 5 = 7
Month
1
2
3
4
5
6
Response
Yi
4
6
5
3
7
?
Moving
Total
(n=3)
NA
NA
NA
15
6+5+3=14
4-38
Moving
Average
(n=3)
NA
NA
NA
5
14/3=4.667
Moving Average Graph
Sales
8
6
Actual
44
Forecast
22
95
1
96
2
97
3
984
Month
4-39
99
5
00
6
Moving Average Forecasts
Month
1
2
3
4
5
6
Response
Yi
4
6
5
3
7
?
Moving
Total
(n=3)
NA
NA
NA
4+6+5=15
6+5+3=14
5+3+7=15
4-40
Moving
Average
(n=3)
NA
NA
NA
15/3=5.0
14/3=4.667
15/3=5.0
Moving Average Graph
Sales
8
6
Actual
44
Forecast
22
195
296
397
498
Month
4-41
599
600
Weighted Moving Average Method
 Gives more emphasis to recent data.
 Weights decrease for older data.
 Weights sum to 1.0.

May be based on intuition.

Sum of digits weights: numerators are consecutive.
 3/6, 2/6, 1/6
 4/10, 3/10, 2/10, 1/10
WMA =
Σ [(Weight for period n) (Demand in period n)]
ΣWeights
4-42
Weighted Moving Average: 3/6,
2/6, 1/6
Month
1
2
3
4
5
6
Response
Yi
4
6
5
?
?
?
4-43
Weighted
Moving
Average
NA
NA
NA
31/6 = 5.167
Weighted Moving Average: 3/6,
2/6, 1/6
Month
1
2
3
4
5
6
Response
Yi
4
6
5
3
7
?
4-44
Weighted
Moving
Average
NA
NA
NA
31/6 = 5.167
25/6 = 4.167
32/6 = 5.333
Moving Average Methods
 Increasing n makes forecast:

Less sensitive to changes.

Less sensitive to recent data.
 Weights control emphasis on recent data.
 Do not forecast trend well.
 Require historical data.
4-45
Moving Average Graph
Actual
Demand
Time
4-46
Moving Average Graph
Large n
Actual
Small n
Demand
Time
4-47
Weighted Moving Average Graph
Small weight
on recent data
Actual
Large weight
on recent data
Demand
Time
4-48
Exponential Smoothing Method
Form of weighted moving average.

Weights decline exponentially.

Most recent data weighted most.
Requires smoothing constant ().

Usually ranges from 0.05 to 0.5

Should be chosen to give good forecast.
Involves little record keeping of past data.
4-49
Exponential Smoothing Equation
 Ft = Ft-1 + (At-1 - Ft-1)
 Ft
= Forecast value for time t
 At-1 = Actual value at time t-1
  = Smoothing constant
 Need initial forecast Ft-1 to start.
 Could be given or use moving average.
4-50
Exponential Smoothing Example
You want to forecast product demand using
exponential smoothing with  = .10. Suppose in the
most recent month (month 6) the forecast was 175
and the actual demand was 180.
Month 6
Month 7
Month 8
Month 9
Month 10
180
?
?
?
?
4-51
Exponential Smoothing - Month 7
Ft = Ft-1 + α (At-1 - Ft-1)
Month
Actual
6
180
7
?
8
?
9
?
10
?
11
?
Forecast, F t
(α = .10)
175.00 (Given)
175.00 + .10(180 - 175.00) = 175.50
4-52
Exponential Smoothing - Month 8
Ft = Ft-1 + α (At-1 - Ft-1)
Forecast, F t
(α = .10)
Month
Actual
6
180
7
168
175.00 + .10(180 - 175.00) = 175.50
8
?
175.50 + .10(168 - 175.50) = 174.75
9
?
10
?
11
?
175.00 (Given)
4-53
Exponential Smoothing Solution
Ft = Ft-1 + α (At-1 - Ft-1)
Forecast, F t
(α = .10)
Month
Actual
6
180
7
168
175.00 + .10(180 - 175.00) = 175.50
8
159
175.50 + .10(168 - 175.50) = 174.75
9
?
174.75 + .10(159 - 174.75) = 173.18
10
?
11
?
175.00 (Given)
4-54
Exponential Smoothing Solution
Ft = Ft-1 + α (At-1 - Ft-1)
Forecast, F t
(α = .10)
Month
Actual
6
180
7
168
175.00 + .10(180 - 175.00) = 175.50
8
159
175.50 + .10(168 - 175.50) = 174.75
9
175
174.75 + .10(159 - 174.75) = 173.18
10
190
173.18 + .10(175 - 173.18) = 173.36
11
?
173.36 + .10(190 - 173.36) = 175.02
175.00 (Given)
4-55
Exponential Smoothing Graph
Sales
190
180
170
160
150
140
6
Actual
Forecast
7
8
9
Month
4-56
10
11
Exponential Smoothing Methods
Increasing α makes forecast:


More sensitive to changes.
More sensitive to recent data.
 α controls emphasis on recent data.
Do not forecast trend well.

Trend adjusted exponential smoothing - p. 90-93
4-57
Exponential Smoothing Graph
Actual
Demand
Time
4-58
Exponential Smoothing Graph
Small α
Actual
Large α
Demand
Time
4-59
Forecast Effects of
Smoothing Constant 
Ft =  At - 1 + (1- )At - 2 + (1- )2At - 3 + ...
Weights
=
Prior Period
2 periods ago 3 periods ago

(1 - )
(1 - )2
= 0.10
10%
9%
8.1%
= 0.90
90%
9%
0.9%
4-60
Choosing  - Comparing Forecasts
A good method has a small error.
Choose  to produce a small error.
 Error = Demand - Forecast
Error > 0 if forecast is too low
Error < 0 if forecast is too high
MAD = Mean Absolute Deviation: Average of absolute
values of errors.
MSE = Mean Squared Error: Average of squared errors.
MAPE = Mean Absolute Percentage Error: Average of
absolute value of percentage errors.
4-61
Forecast Error Equations
Mean Absolute Deviation (MAD)
n
| yi  yˆ i | | forecast errors |
MAD  i1

n
n
Mean Squared Error (MSE)
n
MSE 
 (y i  yˆ i )2
i1
n
forecast errors


n
4-62
2
Forecast Error Equations
Mean Absolute Percentage Error (MAPE)
| y i  yˆ i |
| forecast errors |


yi
i1
Actual
MAPE 

n
n
n
4-63
Forecast Error Example
Actual
20
10
24
20
F1
19
15
22
21
F1 error
1
-5
2
-1
F2
18
13
21
18
F2 error
2
-3
3
2
MAD
F1 = 9/4 = 2.25
F2 = 10/4 = 2.5
MSE
F1 = 31/4 = 7.75
F2 = 26/4 = 6.5
MAPE
F1 = 0.171 = 17.1%
F2 = 0.156 = 15.6%
4-64
Which Forecast is Best?
MAD
F1 = 9/4 = 2.25
F2 = 10/4 = 2.5
MSE
F1 = 31/4 = 7.75
F2 = 26/4 = 6.5
MAPE
F1 = 0.171 = 17.1%
F2 = 0.156 = 15.6%
4-65