Principles of Operations Management:

Sustainability and Supply Chain Management

Eleventh Edition, Global Edition

Chapter 4
Forecasting

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Outline (1 of 2)
• Global Company Profile: Walt Disney Parks & Resorts
• What Is Forecasting?
• The Strategic Importance of Forecasting
• Seven Steps in the Forecasting System
• Forecasting Approaches

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Outline (2 of 2)
• Time-Series Forecasting
• Associative Forecasting Methods: Regression and
Correlation Analysis
• Monitoring and Controlling Forecasts
• Forecasting in the Service Sector

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Forecasting Provides a Competitive
Advantage for Disney (1 of 4)
• Global portfolio includes parks in Shanghai, Hong Kong,
Paris, Tokyo, Orlando, and Anaheim
• Revenues are derived from people - how many visitors and
how they spend their money
• Daily management report contains only the forecast and
actual attendance at each park

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Forecasting Provides a Competitive
Advantage for Disney (2 of 4)
• Disney generates daily, weekly, monthly, annual, and 5-
year forecasts
• Forecast used by labor management, maintenance,
operations, finance, and park scheduling
• Forecast used to adjust opening times, rides, shows,
staffing levels, and guests admitted

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Forecasting Provides a Competitive
Advantage for Disney (3 of 4)
• 20% of customers come from outside the USA
• Economic model includes gross domestic product, cross-
exchange rates, arrivals into the USA
• A staff of 35 analysts and 70 field people survey 1 million
park guests, employees, and travel professionals each
year

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Forecasting Provides a Competitive
Advantage for Disney (4 of 4)
• Inputs to the forecasting model include airline specials,
Federal Reserve policies, Wall Street trends,
vacation/holiday schedules for 3,000 school districts
around the world
• Average forecast error for the 5-year forecast is 5%
• Average forecast error for annual forecasts is between 0%
and 3%

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Learning Objectives (1 of 2)
When you complete this chapter you should be able to:
4.1 Understand the three time horizons and which models
apply for each
4.2 Explain when to use each of the four qualitative models
4.3 Apply the naive, moving-average, exponential
smoothing, and trend methods

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Learning Objectives (2 of 2)
When you complete this chapter you should be able to:
4.4 Compute three measures of forecast accuracy
4.5 Develop seasonal indices
4.6 Conduct a regression and correlation analysis
4.7 Use a tracking signal

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What is Forecasting?
• Process of predicting a future
event
• Underlying basis of all
business decisions
– Production
– Inventory
– Personnel
– Facilities

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Forecasting Time Horizons
1. Short-range forecast
– Up to 1 year, generally less than 3 months
– Purchasing, job scheduling, workforce levels, job
assignments, production levels
2. Medium-range forecast
– 3 months to 3 years
– Sales and production planning, budgeting
3. Long-range forecast
– 3+ years
– New product planning, facility location, capital expenditures,
research and development

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Distinguishing Differences
1. Medium/long range forecasts deal with more comprehensive
issues and support management decisions regarding planning
and products, plants and processes
2. Short-term forecasting usually employs different
methodologies than longer-term forecasting
3. Short-term forecasts tend to be more accurate than longer-
term forecasts

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Influence of Product Life Cycle
Introduction – Growth – Maturity – Decline

• Introduction and growth require longer forecasts than

maturity and decline
• As product passes through life cycle, forecasts are useful
in projecting
– Staffing levels
– Inventory levels
– Factory capacity

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Product Life Cycle (1 of 2)
Figure 2.5

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Product Life Cycle (2 of 2)
Figure 2.5

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Types of Forecasts
1. Economic forecasts
– Address business cycle – inflation rate, money supply,
housing starts, etc.
2. Technological forecasts
– Predict rate of technological progress
– Impacts development of new products
3. Demand forecasts
– Predict sales of existing products and services

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Strategic Importance of Forecasting
• Supply Chain Management – Good supplier relations,
advantages in product innovation, cost and speed to
market
• Human Resources – Hiring, training, laying off workers
• Capacity – Capacity shortages can result in undependable
delivery, loss of customers, loss of market share

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Seven Steps in Forecasting
1. Determine the use of the forecast
2. Select the items to be forecasted
3. Determine the time horizon of the forecast
4. Select the forecasting model(s)
5. Gather the data needed to make the forecast
6. Make the forecast
7. Validate and implement the results

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The Realities!
• Forecasts are seldom perfect; unpredictable outside
factors may impact the forecast
• Most techniques assume an underlying stability in the
system
• Product family and aggregated forecasts are more
accurate than individual product forecasts

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Forecasting Approaches (1 of 2)
Qualitative Methods
• Used when situation is vague and little data exist
– New products
– New technology
• Involves intuition, experience
– e.g., forecasting sales on Internet

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Forecasting Approaches (2 of 2)
Quantitative Methods
• Used when situation is ‘stable’ and historical data exist
– Existing products
– Current technology
• Involves mathematical techniques
– e.g., forecasting sales of color televisions

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Overview of Qualitative Methods
(1 of 2)

1. Jury of executive opinion

– Pool opinions of high-level experts, sometimes
augmented by statistical models

2. Delphi method

– Panel of experts, queried iteratively

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Overview of Qualitative Methods
(2 of 2)

3. Sales force composite

– Estimates from individual salespersons are reviewed
for reasonableness, then aggregated

4. Market Survey

– Ask the customer

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Jury of Executive Opinion
• Involves small group of high-level experts and managers
• Group estimates demand by working together
• Combines managerial experience with statistical models
• Relatively quick
• ‘Group-think’ disadvantage

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Delphi Method
• Iterative group process,
continues until
consensus is reached
• Three types of
participants
– Decision makers
– Staff
– Respondents

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Sales Force Composite
• Each salesperson projects his or her sales
• Combined at district and national levels
• Sales reps know customers’ wants
• May be overly optimistic

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Market Survey
• Ask customers about purchasing plans
• Useful for demand and product design and planning
• What consumers say and what they actually do may be
different
• May be overly optimistic

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Overview of Quantitative Approaches

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Time-Series Forecasting
• Set of evenly spaced numerical data
– Obtained by observing response variable at regular
time periods
• Forecast based only on past values, no other variables
important
– Assumes that factors influencing past and present will
continue influence in future

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Time-Series Components

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Components of Demand
Figure 4.1

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Trend Component
• Persistent, overall upward or downward pattern
• Changes due to population, technology, age, culture, etc.
• Typically several years duration

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Seasonal Component
• Regular pattern of up and down fluctuations
• Due to weather, customs, etc.
• Occurs within a single year
PERIOD LENGTH “SEASON” LENGTH NUMBER OF
“SEASON” IN
PATTERN
Week Day 7
Month Week 4 – 4.5
Month Day 28 – 31
Year Quarter 4
Year Month 12
Year Week 52

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Cyclical Component
• Repeating up and down movements
• Affected by business cycle, political, and economic factors
• Multiple years duration
• Often causal or associative relationships

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Random Component
• Erratic, unsystematic, ‘residual’ fluctuations
• Due to random variation or unforeseen events
• Short duration and nonrepeating

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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

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Moving Averages
• 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 =
å demand in previous n periods
n

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Moving Average Example

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Weighted Moving Average (1 of 3)
• Used when some trend might be present
– Older data usually less important
• Weights based on experience and intuition

Weighted moving average =

 ( ( Weight for period n )( Demand in period n ) )
 Weights

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Weighted Moving Average (2 of 3)

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Weighted Moving Average (3 of 3)

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Potential Problems With Moving
Average (1 of 2)
1. Increasing n smooths the forecast but makes it less
sensitive to changes
2. Does not forecast trends well
3. Requires extensive historical data

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Graph of Moving Averages
Figure 4.2

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Potential Problems With Moving
Average (2 of 2)
• Form of weighted moving average
– Weights decline exponentially
– Most recent data weighted most
• Requires smoothing constant (α)
– Ranges from 0 to 1
– Subjectively chosen
• Involves little record keeping of past data

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Exponential Smoothing
New forecast = Last period’s forecast
+ α (Last period’s actual demand
− Last period’s forecast)

Ft = Ft – 1+ α ( At – 1 – Ft – 1 )

where Ft = new forecast

Ft – 1 = previous period’s forecast
α = smoothing (or weighting) constant (0 ≤ α ≤ 1)
At – 1 = previous period’s actual demand

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Exponential Smoothing Example
(1 of 3)

• Predicted demand = 142 Ford Mustangs

• Actual demand = 153
• Smoothing constant α = .20

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Exponential Smoothing Example
(2 of 3)

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Exponential Smoothing Example
(3 of 3)

Predicted demand = 142 Ford Mustangs

Actual demand = 153
Smoothing constant α = .20

New forecast = 142 + .2(153 − 142)

= 142 + 2.2

= 144.2 ≈ 144 cars

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Effect of Smoothing Constants
• Smoothing constant generally .05 ≤ α ≤ .50
• As α increases, older values become less significant

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Impact of Different α (1 of 2)

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Impact of Different α (2 of 2)

• Choose high values of α when underlying average is

likely to change
• Choose low values of α when underlying average is
stable
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Selecting the Smoothing Constant
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 according to one of three
preferred measures:
• Mean Absolute Deviation (MAD)
• Mean Squared Error (MSE)
• Mean Absolute Percent Error (MAPE)

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Common Measures of Error (1 of 3)
Mean Absolute Deviation (MAD)

MAD =
å Actual - Forecast
n

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Determining the MAD (1 of 2)

ACTUAL FORECAST
TONNAGE WITH
QUARTER UNLOADED FORECAST WITH α = .10 α = .50
1 180 175 175
2 168 175.50 = 175.00 + .10(180 − 175) 177.50
3 159 174.75 = 175.50 + .10(168 − 175.50) 172.75
4 175 173.18 = 174.75 + .10(159 − 174.75) 165.88
5 190 173.36 = 173.18 + .10(175 − 173.18) 170.44
6 205 175.02 = 173.36 + .10(190 − 173.36) 180.22
7 180 178.02 = 175.02 + .10(205 − 175.02) 192.61
8 182 178.22 = 178.02 + .10(180 − 178.02) 186.30
9 ? 178.59 = 178.22 + .10(182 − 178.22) 184.15

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Determining the MAD (2 of 2)

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Common Measures of Error (2 of 3)
Mean Squared Error (MSE)

 (Forecast errors )2

MSE =
n

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Determining the MSE

 (Forecast errors )2

MSE = = 1,526.52/8 = 190.8

n
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Common Measures of Error (3 of 3)
Mean Absolute Percent Error (MAPE)

100 Actual − Forecast /Actual

i i i
MAPE = i =1
n

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Determining the MAPE

MAPE =
 absolute percent error 44.75%
= = 5.59%
n 8
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Comparison of Measures
Table 4.1 Comparison of Measures of Forecast Error
APPLICATION TO CHAPTER
MEASURE MEANING EXAMPLE
Mean absolute How much the forecast For α = .10 in Example 4, the
deviation (MAD) missed the target forecast for grain unloaded was off
by an average of 10.31 tons.
Mean squared error The square of how much For α = .10 in Example 5, the
(MSE) the forecast missed the square of the forecast error was
target 190.8. This number does not have
a physical meaning, but is useful
when compared to the MSE of
another forecast.
Mean absolute The average percent For α = .10 in Example 6, the
percent error (MAPE) error forecast is off by 5.59% on
average. As in Examples 4 and 5,
some forecasts were too high, and
some were low.

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Comparison of Forecast Error (1 of 5)

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Comparison of Forecast Error (2 of 5)

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Comparison of Forecast Error (3 of 5)

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Comparison of Forecast Error (4 of 5)

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Comparison of Forecast Error (5 of 5)

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Exponential Smoothing with Trend
Adjustment (1 of 3)
When a trend is present, exponential smoothing must be
modified

MONTH ACTUAL DEMAND FORECAST (Ft) FOR MONTHS 1 – 5

1 100 F1 = 100 (given)

2 200 F2 = F1 + α(A1 − F1) = 100 + .4(100 − 100)
= 100
3 300 F3 = F2 + α(A2 − F2) = 100 + .4(200 − 100)
= 140
4 400 F4 = F3 + α(A3 − F3) = 140 + .4(300 − 140)
= 204
5 500 F5 = F4 + α(A4 − F4) = 204 + .4(400 − 204)
= 282

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Exponential Smoothing with Trend
Adjustment (2 of 3)
Forecast Exponentially Exponentially
including ( FITt ) = smoothed ( Ft ) = smoothed (Tt )
trend forecast forecast

Ft =  (A t- 1 ) + (1 - a)( Ft- 1 + Tt- 1 )

Tt =  ( Ft - Ft - 1 ) + (1 -  )Tt- 1

where Ft = exponentially smoothed forecast average

Tt = exponentially smoothed trend
At = actual demand
α = smoothing constant for average (0 ≤ α ≤ 1)
β = smoothing constant for trend (0 ≤ β ≤ 1)
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Exponential Smoothing with Trend
Adjustment (3 of 3)

Step 1: Compute Ft
Step 2: Compute Tt
Step 3: Calculate the forecast FITt = Ft + Tt

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Exponential Smoothing with Trend
Adjustment Example
MONTH ACTUAL MONTH (t) ACTUAL DEMAND (At)
(t) DEMAND (At)
1 12 6 21
2 17 7 31
3 20 8 28
4 19 9 36
5 24 10 ?

α = .2 β = .4

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Exponential Smoothing with Trend
Adjustment Example (1 of 5)
Table 4.2 Forecast with α = .2 and β = .4

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Exponential Smoothing with Trend
Adjustment Example (2 of 5)
Table 4.2 Forecast with α = .2 and β = .4

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Exponential Smoothing with Trend
Adjustment Example (3 of 5)
Table 4.2 Forecast with α = .2 and β = .4

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Exponential Smoothing with Trend
Adjustment Example (4 of 5)
Table 4.2 Forecast with α = .2 and β = .4
SMOOTHED
ACTUAL SMOOTHED FORECAST INCLUDING
MONTH FORECAST
DEMAND TREND, Tt TREND, FITt
AVERAGE, Ft
1 12 11 2 13.00
2 17 12.80 1.92 14.72

3 20 15.18 2.10 17.28

4 19 17.82 2.32 20.14

5 24 19.91 2.23 22.14
6 21 22.51 2.38 24.89
7 31 24.11 2.07 26.18
8 28 27.14 2.45 29.59
9 36 29.28 2.32 31.60
10 blank 32.48 2.68 35.16

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Exponential Smoothing with Trend
Adjustment Example (5 of 5)
Figure 4.3

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Trend Projections (1 of 2)
• Fitting a trend line to historical data points to project into
the medium to long-range
• Linear trends can be found using the least-squares
technique

yˆ = a + bx
where yˆ = computed value of the variable to be predicted
( dependent variable)
a = y-axis intercept
b = slope of the regression line
x = the independent variable
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Least Squares Method (1 of 2)
Figure 4.4

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Least Squares Method (2 of 2)
Equations to calculate the regression variables

ŷ = a + bx

b=
å xy - nxy
å x - nx
2 2

a = y - bx

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Least Squares Example (1 of 4)
ELECTRICAL ELECTRICAL
YEAR YEAR
POWER DEMAND POWER DEMAND
1 74 5 105
2 79 6 142
3 80 7 122
4 90 blank blank

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Least Squares Example (2 of 4)

x=
 x 28
= =4 y=
 y 692
= = 98.86
n 7 n 7
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Least Squares Example (3 of 4)

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Least Squares Example (4 of 4)
Figure 4.5

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Least Squares Requirements
1. We always plot the data to insure a linear relationship
2. We do not predict time periods far beyond the database
3. Deviations around the least squares line are assumed to
be random

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Seasonal Variations In Data (1 of 2)
The multiplicative seasonal
model can adjust trend
data for seasonal variations
in demand

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Seasonal Variations In Data (2 of 2)
Steps in the process for monthly seasons:
1. Find average historical demand for each month
2. Compute the average demand over all months
3. Compute a seasonal index for each month
4. Estimate next year’s total demand
5. Divide this estimate of total demand by the number of
months, then multiply it by the seasonal index for that
month

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Seasonal Index Example (1 of 6)

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Seasonal Index Example (2 of 6)

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Seasonal Index Example (3 of 6)

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Seasonal Index Example (4 of 6)

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Seasonal Index Example (5 of 6)
Seasonal forecast for Year 4

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Seasonal Index Example (6 of 6)

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San Diego Hospital (1 of 5)
Figure 4.6

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San Diego Hospital (2 of 5)

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San Diego Hospital (3 of 5)
Figure 4.7

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San Diego Hospital (4 of 5)

Period 67 68 69 70 71 72
Month Jan Feb Mar Apr May June
Forecast with Trend & 9,911 9,265 9,764 9,691 9,520 9,542
Seasonality
Period 73 74 75 76 77 78
Month July Aug Sept Oct Nov Dec
Forecast with Trend & 9,949 10,068 9,411 9,724 9,355 9,572
Seasonality

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San Diego Hospital (5 of 5)
Figure 4.8

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Adjusting Trend Data

yˆseasonal = Index  yˆ trend forecast

Quarter I: ŷ I = (1.30)($100,000) = $130,000

Quarter II: ŷ II = (.90)($120,000) = $108,000
Quarter III: ŷ III = (.70)($140,000) = $98,000
Quarter IV: ŷ IV = (1.10)($160,000) = $176,000

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Cyclical Variations
• Cycles – patterns in the data that occur every several
years
– Forecasting is difficult
– Wide variety of factors

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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

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Trend Projections (2 of 2)
Forecasting an outcome based on predictor variables using
the least squares technique

yˆ = a + bx

where yˆ = value of the dependent variable ( in our example, sales)

a = y-axis intercept
b = slope of the regression line
x = the independent variable

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Associative Forecasting Example
(1 of 6)

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Associative Forecasting Example
(2 of 6)

x=
 x 18
= =3 y=
 y 15
= = 2.5
6 6 6 6

b=
 xy − nxy 51.5 − (6)(3)(2.5)
= = .25 a = y − bx = 2.5 − (.25)(3) = 1.75
 x − nx
2 2
80 − (6)(3 ) 2

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Associative Forecasting Example
(3 of 6)

x=
 x 18
= =3 y=
 y 15
= = 2.5
6 6 6 6

b=
 xy − nxy 51.5 − (6)(3)(2.5)
= = .25 a = y − bx = 2.5 − (.25)(3) = 1.75
 x − nx
2 2
80 − (6)(3 ) 2

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Associative Forecasting Example
(4 of 6)

b=
 xy − nxy = 51.5 − (6)(3)(2.5) = .25 a = y − bx = 2.5 − (.25)(3) = 1.75
 x − nx
2 2
80 − (6)(3 )
2

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Associative Forecasting Example
(5 of 6)

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

Sales (in $ millions) = 1.75 + .25(6)
= 1.75 + 1.5 = 3.25
Sales = $3,250,000

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Associative Forecasting Example
(6 of 6)

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Standard Error of the Estimate (1 of 4)
• A forecast is just a point estimate of a future value
• This point is actually the mean or expected value of a probability distribution
Figure 4.9

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Standard Error of the Estimate (2 of 4)

S y,x =
 (y − y c ) 2

n−2

where y = y-value of each data point

yc = computed value of the dependent variable,
from the regression equation
n = number of data points

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Standard Error of the Estimate (3 of 4)
Computationally, this equation is considerably easier to use

 y 2 − a  y − b  xy
S y,x =
n−2

We use the standard error to set up prediction intervals

around the point estimate

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Standard Error of the Estimate (4 of 4)
 y 2 − a  y − b  xy 39.5 − 1.75(15.0) − .25(51.5)
S y,x = =
n−2 6−2
= .09375
= .306(in $ millions )

The standard error of the

estimate is $306,000 in
sales

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Correlation (1 of 2)
• How strong is the linear relationship between the
variables?
• Correlation does not necessarily imply causality!
• Coefficient of correlation, r, measures degree of
association
– Values range from −1 to +1

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Correlation Coefficient (1 of 4)
Figure 4.10

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Correlation Coefficient (2 of 4)

n xy -  x  y
r=
 n x 2 ( x )2   n y 2 ( y )2 
      

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Correlation Coefficient (3 of 4)

( 6 )( 51.5 ) − (18 )(15.0 )

2

r=
( 6 )( 80 ) − (18 )2  (16 )( 39.5 ) − (15.0 )2 
  
309 − 270 39 39
= = = = .901
(156 ) (12 ) 1,872 43.3
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Correlation (2 of 2)
• Coefficient of Determination, r2, measures the percent of
change in y predicted by the change in x
– Values range from 0 to 1
– Easy to interpret
For the Nodel Construction example:
r = .901
r2 = .81

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Multiple-Regression Analysis (1 of 2)
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

ŷ = a + b1x1 + b 2 x 2
Computationally, this is quite complex and generally
done on the computer

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Multiple-Regression Analysis (2 of 2)
In the Nodel example, including interest rates in the model
gives the new equation:

ŷ = 1.80 + .30 x1 − 5.0 x2

An improved correlation coefficient of r = .96 suggests this

model does a better job of predicting the change in
construction sales
Sales = 1.80 + .30 ( 6 ) − 5.0 (.12 ) = 3.00
Sales = $3,000,000

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Monitoring and Controlling Forecasts
(1 of 2)

Tracking Signal
• Measures how well the forecast is predicting actual values
• Ratio of cumulative forecast errors to mean absolute
deviation (MAD)
– Good tracking signal has low values
– If forecasts are continually high or low, the forecast has
a bias error

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Monitoring and Controlling Forecasts
(2 of 2)

Cumulative error
Tracking signal =
MAD

=
 (Actual demand in period i - Forecast demad in period i)
 | Actual − Forecast |
n

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Correlation Coefficient (4 of 4)
Figure 4.11

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Tracking Signal Example

At the end of quarter 6, MAD =

 Forecast errors
=
85
= 14.2
n 6
Cumulative error 35
Tracking signal = = = 2.5 MADs
MAD 14.2
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Adaptive Smoothing
• It’s possible to use the computer to continually monitor
forecast error and adjust the values of the α and β
coefficients used in exponential smoothing to continually
minimize forecast error
• This technique is called adaptive smoothing

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Focus Forecasting
• Developed at American Hardware Supply, based on two
principles:
1. Sophisticated forecasting models are not always
better than simple ones
2. There is no single technique that should be used for
all products or services
• Uses historical data to test multiple forecasting models for
individual items
• Forecasting model with the lowest error used to forecast
the next demand

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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

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Fast Food Restaurant Forecast
Figure 4.12a

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FedEx Call Center Forecast
Figure 4.12b

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