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4 - 3 Summery of Previous Presentation (1/3) Global Company Profile: Disney World What Is Forecasting? Forecasting Time Horizons The Influence of Product Life Cycle Types Of Forecasts
Citation preview
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Course Title: Production and Operations Management
Course Code: MGT 362
Course Book: Operations Management 10th Edition. By Jay Heizer & Barry Render
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Chapter 4: Forecasting
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Summery of Previous Presentation (1/3)
Global Company Profile: Disney World What Is Forecasting?
Forecasting Time Horizons The Influence of Product Life Cycle Types Of Forecasts
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Summery of Previous Presentation (2/3)
The Strategic Importance of Forecasting Human Resources Capacity Supply Chain Management
Seven Steps in the Forecasting System
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Summery of Previous Presentation (3/3)
Forecasting Approaches Overview of Qualitative Methods Overview of Quantitative Methods
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Summary of Today's Presentation
Time-Series Forecasting Decomposition of a Time Series Naive Approach Moving Averages Exponential Smoothing Exponential Smoothing with Trend Adjustment Trend Projections
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Overview of Quantitative Approaches
1. Naive approach2. Moving averages3. Exponential smoothing4. Trend projection5. Linear regression
time-series models
associative model
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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 to influence in future
Time Series Forecasting
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Trend
Seasonal
Cyclical
Random
Time Series Components
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Components of DemandD
eman
d fo
r pro
duct
or s
ervi
ce
| | | |1 2 3 4
Time (years)
Average demand over 4 years
Trend component
Actual demand line
Random variation
Figure 4.1
Seasonal peaks
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Persistent, overall upward or downward pattern
Changes due to population, technology, age, culture, etc.
Typically several years duration
Trend Component
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Regular pattern of up and down fluctuations Due to weather, customs, etc. Occurs within a single year
Seasonal Component
Number ofPeriod Length SeasonsWeek Day 7Month Week 4-4.5Month Day 28-31Year Quarter 4Year Month 12Year Week 52
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Repeating up and down movements Affected by business cycle, political, and economic
factors Multiple years duration Often causal or associative relationships
Cyclical Component
0 5 10 15 20
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Erratic, unsystematic, ‘residual’ fluctuations Due to random variation or unforeseen events Short duration and no repeating
Random Component
M T W T F
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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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MA is a series of arithmetic means Used if little or no trend
Used often for smoothing
Moving Average Method
Moving average =∑ demand in previous n periods
n
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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
101012121313
(1010 + 1212 + 1313)/3 = 11 2/3
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Graph of Moving Average
| | | | | | | | | | | |J F M A M J J A S O N D
Shed
Sal
es
30 –28 –26 –24 –22 –20 –18 –16 –14 –12 –10 –
Actual Sales
Moving Average Forecast
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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
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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
101012121313
[(3 x 1313) + (2 x 1212) + (1010)]/6 = 121/6
Weights Applied Period33 Last month22 Two months ago11 Three months ago6 Sum of weights
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Increasing n smooth the forecast but makes it less sensitive to changes
Do not forecast trends well Require extensive historical data
Potential Problems With Moving Average
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Moving Average And Weighted Moving Average
30 –
25 –
20 –
15 –
10 –
5 –
Sale
s 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
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Form of weighted moving average Weights decline exponentially Most recent data weighted most
Requires smoothing constant () Ranges from 0 to 1 Subjectively chosen
Involves little record keeping of past data
Exponential Smoothing
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Exponential Smoothing
New forecast = Last period’s forecast+ (Last period’s actual demand
– Last period’s forecast)
Ft = Ft – 1 + (At – 1 - Ft – 1)
where Ft = new forecast
Ft – 1 = previous forecast
= smoothing (or weighting) constant (0 ≤ ≤ 1)
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Exponential Smoothing Example
Predicted demand = 142 Ford MustangsActual demand = 153Smoothing constant = .20
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Exponential Smoothing Example
Predicted demand = 142 Ford MustangsActual demand = 153Smoothing constant = .20
New forecast = 142 + .2(153 – 142)
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Exponential Smoothing Example
Predicted demand = 142 Ford MustangsActual demand = 153Smoothing constant = .20
New forecast = 142 + .2(153 – 142)= 142 + 2.2= 144.2 ≈ 144 cars
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Impact of Different
225 –
200 –
175 –
150 –| | | | | | | | |1 2 3 4 5 6 7 8 9
Quarter
Dem
and
= .1
Actual demand
= .5
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Impact of Different
225 –
200 –
175 –
150 –| | | | | | | | |1 2 3 4 5 6 7 8 9
Quarter
Dem
and
= .1
Actual demand
= .5 Chose high values of when underlying average is likely to change
Choose low values of when underlying average is stable
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Choosing
The objective is to obtain the most accurate forecast no matter the technique
We generally do this by selecting the model that We generally do this by selecting the model that gives us the lowest forecast errorgives us the lowest forecast error
Forecast error = Actual demand - Forecast value
= At - Ft
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Common Measures of Error
Mean Absolute Deviation (MAD)
MAD =∑ |Actual - Forecast|
n
Mean Squared Error (MSE)
MSE =∑ (Forecast Errors)2
n
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Common Measures of Error
Mean Absolute Percent Error (MAPE)
MAPE =∑100|Actuali - Forecasti|/Actuali
n
n
i = 1
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Comparison of Forecast Error
Rounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast Deviation
Tonnage with for with forQuarter Unloaded = .10 = .10 = .50 = .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
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Comparison of Forecast Error
Rounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast Deviation
Tonnage with for with forQuarter Unloaded = .10 = .10 = .50 = .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 = 10.31For = .10
= 98.62/8 = 12.33For = .50
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Comparison of Forecast Error
Rounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast Deviation
Tonnage with for with forQuarter Unloaded = .10 = .10 = .50 = .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 = .10
= 1,561.91/8 = 195.24
For = .50
MSE = ∑ (forecast errors)2
n
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Comparison of Forecast Error
Rounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast Deviation
Tonnage with for with forQuarter Unloaded = .10 = .10 = .50 = .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 = .10
= 54.05/8 = 6.76%For = .50
MAPE =∑100|deviationi|/actuali
n
n
i = 1
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Comparison of Forecast Error
Rounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast Deviation
Tonnage with for with forQuarter Unloaded = .10 = .10 = .50 = .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%
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Summary of Today's Presentation
Time-Series Forecasting Decomposition of a Time Series Naive Approach Moving Averages Exponential Smoothing Exponential Smoothing with Trend Adjustment Trend Projections