Transcript No Slide Title

TOPICS TO BE DISCUSSED
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Introduction
Features Common to all Forecasts
Steps in Forecasting
Forecasting Approaches
Forecasting Using Time Series
Time Series Smoothing
Trend Forecasting
Associative Forecasting Techniques
Choosing a Good Forecast
1
Class-1
Introduction
What is a Forecast?
• A guess or estimation of future events based on previous experience.
How does your area of study use forecasts?
How does an Operations Manager use a forecast?
• Help managers design a system
• Help managers plan a use for the system
• Used for Capacity Planning, Sales, Manpower, & Inventory
Forecasting is Both Long Term and Short Term.
• Strategic, Tactical and Operational
Forecasting is not an Exact Science.
• Based on Experience, Judgment, Technical Expertise, & Luck
Generally Forecasting is Done on Many Levels.
• Product Demand is forecasted by Marketing or Sales
• Manpower and Equipment needs are forecasted by Operations
• Monetary Needs is forecasted by Finance
2
Class-2
How Forecasting Fits in Production Cycle
Make or Buy
Forecasting
Facility Definition
Resource Planning
Aggregate Plan
Master Production Schedule
Rough Cut Capacity
Planning
Detailed Capacity
Planning
Purchasing
MRP
Shop Floor Control
3
Class-3
Features Common to All Forecasts
• Assumes that the same underlying causes that existed in the past will be present
in the future.
• Forecasts are rarely perfect.
• Group Forecasts tend to be more accurate as forecasting errors among groups
usually have a canceling effect.
• Accuracy decreases as the time period increases.
If Forecasts are not perfect then why should we spend time
and money on developing them?
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Class-4
Steps in Forecasting
1. Determine the Purpose of the Forecast and When it will be needed.
• Level of Detail
• Level of Accuracy
• Budget constraints
• Intended use
2. Establish a Time Horizon that the forecast must cover.
• The longer the less accurate
• Sufficient amount of data
3. Select the Forecast Technique.
• Depends on accuracy
• Experience
• Time Span
• Cost
4. Gather and Analyze the appropriate Data & Prepare the Forecast.
5. Monitor the Forecast Performance
• If not performing then modify the technique, data, and/or requirements.
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Class-5
Forecasting Approaches
Qualitative vs Quantitative
Qualitative Forecasting is very subjective.
• Based on judgment, opinion, consumer surveys, Delphi & sales people.
• Use when:
• Conditions are changing
- Time is short
- Obsolete Data
• Consumer surveys get Buyer’s feedback, if handled correctly
• To act as a sanity check for quantitative results
Quantitative approach is based on historical or associative models.
• Quantitative models are based on some abstract mathematical model to describe
future events.
• Time Series Analysis is a historical method
• It tries to uncover a pattern or cycle in the empirical data relative to time.
• Also tries to remove any random and nonrandom errors.
• Associative Method attempts to predict the future based on the relationship
between two variables.
• The variable that is being predicted is dependent on the value of the known
variable.
Delphi
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Class-6
Forecasting Using Time Series Data
• Time Series is a time ordered sequence of observations taken at regular intervals
over a period of time.
• Future values of a series are predicated on the assumption that past information is
repeatable.
• The forecaster must determine if a pattern exists and what is the cycle of the pattern.
• These patterns might be classified in terms of:
• Trends: long term upward or downward movement of data
• Seasonal: short term regular variations
• Cycles: longer term variations
• Irregular Variations: Unpredictable random variations.
• A demand forecast should be based on the time series of past demand rather than
sales.
• Differentiate between demand and sales
• Previous sales may not have kept up with demand
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Class-7
Time Based Smoothing
Naïve Forecasts
• Use last period’s actual results for this period’s forecast.
• Benefits: Easy of use; Low Costs; Easy to understand; Quick
• Disadvantages: Questionable accuracy
• Is the increased accuracy warrant the extra time and cost of another method?
Moving Average
• Uses a number of the most recent actual data values in generating a forecast.
• MAn = ( Di)/n
• i = “age” of the data
• n = number of periods in the moving average
• D = Actual Demand with the age i
• MA3 would imply a three period moving average
• The more period used the less accurate
• Doesn’t reflect the current environment
• Slower to respond to changes
• Each data point is weighted the same
• Advantage
• Easy to compute • Easy to Understand
• Disadvantage
• Accuracy
• Responsiveness to changes
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Class-8
Time Based Smoothing (con’t)
Weighted Moving Average
• Addresses one of the disadvantages of not being responsive to change
associated with the Simple Moving Average.
• Applies a weighted factor to each of the periods used in the averaging.
• The more recent periods are weighted more heavily.
• MAn = ( WDi)
• w is the weight of the period demand D: {0< w < 1}
• An issue is how to define the a value for the weighting factor.
Exponential Smoothing
• Each new forecast is based on the previous forecast plus a percentage of the difference
between the previous forecast and the actual value of the previous period.
• New Forecast = Old Forecast + (percentage of error)(Actual - Old Forecast)
•
Ft = Ft-1 +  ( D t-1 -
F t-1 )
• 0 <  < 1 ; Commonly values between .05 and .5 are used.
• The closer it’s value to zero the slower the forecast will be adjust to forecast errors
• Selecting the smoothing constant is basically a matter of trial and error.
• Take the average of the first four values average
• value will change until forecasting error is minimal
• Impact of the error of a single period is ;  (1- ) t-1
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Class-9
Time Based Smoothing (con’t)
Strengths of Exponential Smoothing
• Easy to use especially on a large number of short term forecasts.
• Emphasis is placed on recent data
• Little skilled labor requirements to upkeep
• Can Incorporate trend and seasonal components
Weaknesses of Exponential Smoothing
• Not appropriate for small data collection requiring accuracy
• Not based on statistical model building methods
• Arbitrary of initial smoothing constants
Relationship to Moving Average
• Moving average is based on N number of data points. (i.e.N= 3 for 3 month MA)
• Exponential smoothing will be impacted by all previous data points, with the impact
diminishing with age.
The comparison of influence of the MA to the Exponential Smoothing is found by calculating α.
α = 2/(N+1)
So a 3 month moving average would have an α = 2/(3+1) = 0.5
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Class-10
Trend Forecasting
Techniques for Trend
• The trend component of a time series reflects the effects of any long term factors
on the series.
Linear Trend
• Plot data and transcribe a line through the data points (graphical).
• Develop a Linear Trend Equation
• Yt = a + bt
• Y is the forecast for period t
• t is the number of time periods
• a is the value of Y when t=0
• b is the slope of the line
• Once you have determined the equation of the line then you can predict any
future point by changing t.
Equations:
b = n (t*y) -  t  y
n  t2 - ( t)2
a =y-bt
n
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Class-11
Associative Forecasting Techniques
Associative Techniques rely on identification of relayed variables that can be used to
predict values of the variable of interest.
• The predictor variable is called the Independent variable.
• The variable being predicted is called the Dependent variable.
Linear Regressions use describes the linear relationships between two variable.
There are a number of methods for defining the linear regression equation. The most
common is the Least Squares method.
• Yc = a + bx
• Yc = Dependent variable
x = Independent variable
b = slope of line
a = Y value when x = 0
• Notice the similarity to the Linear Time series
• Equations:
b = n (x*y) -  x  y
n  x2 - ( x)2
a =y-bx
n
Multiple Linear Regressions use multiple Independent variables to predict the
Dependent variable.
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Class-12
Associative Forecasting Techniques (con’t)
There are several measures to determine how well an Independent variable can
predict a Dependent variable.
Standard Error of the Estimate (SEE)
• Measures the mean square vertical deviations of the actual observations from the
fitted regression line.
• Provides bounds within which the true value will fall. (Standard Deviation)
Correlation Coefficient (r) can define the strength and direction of the relationship.
•The range is between -1.00 and +1.00
• A -1.00 says that there is a one to one relationship but that they move in opposite
directions.
• A +1.00 says that there is a one to one relationship and they move in the same
direction.
• A 0.00 says there is no relationship.
• A value of -1.00 is just as valuable as a +1.00
Coefficient of Determination (R2)indicates the percentage of total variation explained
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by the regression line.
Class-13
Accuracy of Forecast
Monitor for erratic demand, look for outliers
Is forecasting method effectively tracking demand
Which parameters (N & alpha) provides best accuracy
Allow for safety stock
Two Measures of Forecast Accuracy:
MAD (Mean Average Deviation)
MAD =  | Actual – Forecast|
n
MSE ( Mean Squared Error)
MSE =  ( Actual – Forecast) 2
n-1
MSE will highlight outliers more so than MAD.
USE MAD and MSE for Selection of appropriate forecast.
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Class-14
Controlling the Forecast
A forecast is appropriate when the errors exhibit only random variations.
If the forecast exhibits a non random error then it needs to be reevaluated.
Forecasts can be monitored by either
Tracking Signals or Control Charts
Tracking Signal
Tracking Signal =  ( Actual – Forecast)
MAD
Focus is on evaluating cumulative error
MAD is updated using Exponential smoothing
MAD t = MAD t-1 +  ( |Actual – Forecast| t – MAD t-1 )
MAD1 =  | Actual – Forecast| / n
Tracking Signal results are compared to predetermined limits .
Based on judgment and experience
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Class-15
Controlling the Forecast
Control Charts
Evaluated of validity is based on error being within a upper and lower
control limits.
Monitors individual error
Assumptions of methods:
1. Forecast errors are randomly distributed around a mean of zero.
2. The distribution of errors is normal.
Control limits are defined as a predetermined number of standard deviations
from the mean.
The square root of the MSE is used as the standard deviations.
UCL = 0 + z (MSE) ½
LCL = 0 - z (MSE) ½
Use when:
1. Mean is equal to zero
2. There is no trend in error
3. Error can be described by a normal distribution
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Class-16
Choosing A Good Forecast
• No one technique works best in every situation.
• The two most important factors are: Cost & Accuracy
• Best Forecast is not necessarily the most accurate; It is the most Cost Effective one
.
• Other Relevant Factors
• Availability of data
• Experience with different types of forecasting models
• Time allotment
• Forecast horizon
• Moving Averages & Exponential Smoothing are Short Term in nature;
Trend Equations tend to be more Long Term
• Use more than one technique for comparison
• Never accept a Quantitative result without doing a sanity check.
• Elements of a Good Forecast
• Timely
• Sufficient Accuracy
• In Writing
• Simple to Understand & use
• Meaningful units to the decision maker
• Reliable
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Class-17
18
Class-18
Delphi Approach
Delphi approach is based on obtaining various expert opinions. If the estimates are
widely varied the information is shared and the experts are asked to resubmit a new
estimate.
The assumption is that the experts will modify their estimates towards the mean.
1st estimate
Demand
2nd estimate
3rd estimate
Dual result
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Class-19
Linear Trend
y
V
a
l
u
e
Y- Intercept
(a)
Rise ( y)
Run ( t)
b=
( y)
( t)
Time (t)
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Class-20
Linear Trend
y
yi
y0
yi
yi
yi
V
a
l
u
e
yi
yi
yi
yi
yi
yi
yi
Time (t)
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Class-21
Moving Average
Period (t) Demand (D)
1
42
2
40
3
43
4
40
5
41
6
39
7
46
8
44
9
45
10
38
11
40
Moving Average
n = 3 months
MA3 = 42+40+43 /3
= 40+43+40 /3
= 43+40+41 /3
= 40+41+39 /3
= 41+39+46 /3
= 39+46+44 /3
= 46+44+45 /3
= 44+45+38 /3
= 45+38+40 /3
= 41.66
= 41.0
= 41.33
= 40.0
= 42.0
= 43.0
= 45.0
= 42.33
= 41.0
4
7
Assumes:
each period
has a .333
weighting
47
45
43
41
39
37
35
1
2
3
5
6
8
9
10
11
22
Class-22
Weighted Moving Average
Period (t) Demand (D)
1
42
2
40
3
43
4
40
5
41
6
39
7
46
8
44
9
45
10
38
11
40
47
45
43
41
39
37
35
1
2
3
Weighted Moving Average
Let: t-1 = 50%; t-2 = 30%; t-3 = 20%
MA3 = (.2)42+(.3)40+(.5)43
= (.2)40+(.3)43+(.5)40
= (.2)43+(.3)40+(.5)41
= (.2)40+(.3)41+(.5)39
= (.2)41+(.3)39+(.5)46
= (.2)39+(.3)46+(.5)44
= (.2)46+(.3)44+(.5)45
= (.2)44+(.3)45+(.5)38
= (.2)45+(.3)38+(.5)40
4
5
6
7
= 41.9
= 40.9
= 41.1
= 39.8
= 42.9
= 43.6
= 44.9
= 41.3
= 40.4
8
9
10
11
23
Class-23
Naïve Approach
Period (t) Demand (D) Forecast (F)
1
42
2
40
42
50
3
43
40
4
40
43
5
41
40
6
39
45
41
7
46
39
8
44
9
45
46
10
38
44
40
11
40
45
12
38
40
35
24
Class-24
Exponential Smoothing
Ft = Ft-1 +  (D t-1 - F t-1 )
Period (t) Demand (D) Forecast (F0.2) Forecast (F0.9)
1
42
45
45
2
40
44.4
42.3
3
43
43.5
40.2
4
40
43.4
42.7
5
41
42.7
40.3
6
39
42.4
40.9
7
46
41.7
39.2
8
44
42.6
45.3
9
45
42.9
44.1
Let F0 = 45  = .2
10
38
43.3
44.9
11
40
42.2
38.7
41.8
39.9
F2 = 45 + .2 (42 - 45 ) = 44.4
F8 = 41.7 + .2 (46 - 41.7 ) = 42.6
F3 = 44.4 + .2 (40 - 44.4 ) = 43.5
F9 = 42.6 + .2 (44 - 42.6 ) = 42.9
F4 = 43.5 + .2 (43 - 43.5 ) = 43.4
F5 = 43.4 + .2 (40 - 43.4 ) = 42.7
F10 = 42.9 + .2 (45 - 42.9 ) = 43.3
F6 = 42.7 + .2 (41 - 42.7 ) = 42.4
F11 = 43.3 + .2 (38 - 43.3 ) = 42.2
F7 = 42.4 + .2 (39 - 42.4 ) = 41.7
F12 = 42.2 + .2 (40 - 42.2 ) = 41.8
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Class-25
Exponential Smoothing
47
45
43
41
39
37
35
26
Class-26
Linear Trend
Period (t) Demand (D)
1
42
2
40
3
43
4
40
5
41
6
39
7
46
8
44
9
45
10
38
11
40
66
458
t*y
t2
42
80
129
160
205
234
322
405
380
440
2749
1
4
9
16
25
36
49
81
100
121
506
Forecast
41.59
41.6
41.61
41.62
41.63
41.64
41.65
41.66
41.67
41.68
Yt = a + b*t
Yt = 41.58 + .0091*t
b = n (x*y) -  x  y = (11)(2749) - (66)(458)
n  x2 - ( x)2
11(506) - (66)2
= .0091
a =y-bx
n
= 41.58
=
(458) - .0091(66)
11
27
Class-27
Example 4: SEE
SEE =  (Yi - Y)2
n-2
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Class-28
Tracking Signal
+3.75
Time
-3.75
29
Class-29
Control Chart
UCL
0
LCL
Time
UCL = 0 + z (MSE) ½
LCL = 0 - z (MSE) ½
30
Class-30