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© Dale R. Geiger 2011 1
Project Sales Or Production Levels Using The Rolling Average
Principles of Cost Analysis and Management
© Dale R. Geiger 2011
What if?
You planned for 10 but…
© Dale R. Geiger 2011 3
Terminal Learning Objective
• Task: Project Sales Or Production Levels Using The Rolling Average
• Condition: You are a cost advisor technician with access to all regulations/course handouts, and awareness of Operational Environment (OE)/Contemporary Operational Environment (COE) variables and actors
• Standard: with at least 80% accuracy• Demonstrate understanding of Trend Projection
concepts
© Dale R. Geiger 2011 4
Importance of Demand
• We have seen how demand drives cost• Flexible forecasting
• Assumptions about probabilities may not yield useful information• “Precisely wrong”
• Examining trends gives another perspective on demand
© Dale R. Geiger 2011 5
Predicting the Future
• Take your M77 Crystal Ball and predict the number of burgers needed
• Would your prediction change if you knew the last six cookouts needed• 5 6 7 8 9 10 ? Or• 16 15 14 13 12 11 ?
• If yes, then you are recognizing that the past can help us make better decisions about the future
© Dale R. Geiger 2011 6
What is Trend Projection?
• Uses historical data about past demand to make estimates of future demand
• Relies on systematic methodologies and assumptions
• Cannot predict the future or anticipate catastrophic events
© Dale R. Geiger 2011 7
Three Methods
• Regression• Represents a straight line with the least
squared error from actual• Rolling average• Uses average of prior period demand to predict
future period demand• Planning factors• Assumes a relationship between a current
value and future demand
8
Regression Analysis
• Plots a linear relationship between multiple data points
• Minimizes the “squared errors”• Square difference between mean and actual to
eliminate negative values• Uses the format y = mx + b where:
m = n(Σxy) - (Σx)( Σy)n(Σx2) - (Σx)2
b = (Σy)( Σx2) - (Σx)( Σxy)n(Σx2) - (Σx)2
© Dale R. Geiger 2011
© Dale R. Geiger 2011 9
Regression Results
• Very predictable • The ascending series is y = x + 4 and we can predict that
the 7th period would need 11 burgers• The descending series is y = -x + 17 and we can predict that
the 7th period would need 10
© Dale R. Geiger 2011 10
Regression Exercise
• Use spreadsheet to predict the 8th, 9th, and 10th event burger demand if the first six demands were:• 8 10 9 12 13 15
© Dale R. Geiger 2011 11
Spreadsheet Exercise
The spreadsheet returns the equation:y = 1.3429x + 6.4667
Enter the data as shown
Enter the values in the spreadsheet to
predict demandPer. 8 demand = 17
© Dale R. Geiger 2011 12
Regression Analysis
• Regression can be used to separate mixed costs into fixed and variable components
Total cost = VC $/unit * # units + Fixed Costis a linear equation just like
y = mx + b• in a time-s• This is a much more sophisticated approach than
the high-low analysis from Day 6can plot linear trends over time
13
Example: Using Regression to Estimate Fixed and Variable Costs
• Consider four quarters of data
• Regression returns y = 2.2x +13.7
Q1 Q2 Q3 Q4
Units 5 6 7 8
Total Cost 25 27 28 32
Fixed cost is 13.7
Variable cost is 2.2 per unit
Total cost is 13.7 + 2.2*units
© Dale R. Geiger 2011 14
Regression Analysis
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Periods
Regression Analysis
Regression Analysis
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Periods
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Periods
Regression Analysis
Regression Analysis
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Periods
Notice that four very different sets of data all have very similar regression lines
The x-axis in these graphs represents time periods in series
© Dale R. Geiger 2011 15
Regression Strengths and Weaknesses
• Can be calculated very precisely• But cumbersome to do by hand(use spreadsheet!)• May be precisely wrong
• Can be used to identify trends• But by definition cannot predict downturns or
upturns• Assumes relationship is linear and will remain
linear
© Dale R. Geiger 2011 16
Check on Learning
• In the context of trend projection, what does the regression line represent?
• What is the main weakness of regression in trend projection?
© Dale R. Geiger 2011 17
Rolling Average
• Uses average of prior periods to predict future periods
• Evens out highs and lows by using a number of periods
• Key assumption for predictions:• Assumes that the average will be maintained• Example: Average of Periods 2, 3 & 4 will equal
average of periods 1, 2 & 3
© Dale R. Geiger 2011 18
Rolling Average Calculation
• The demand for our last twelve periods has been:
• Task: Calculate the 3-month rolling average for periods 3-12
Period 1 2 3 4 5 6 7 8 9 10 11 12
Value 6 8 4 3 7 5 6 8 3 6 4 5
© Dale R. Geiger 2011 19
Rolling Average Calculation
• The 3-month rolling average is the average value for the most recent 3 months
Per1 + Per2 + Per33
• Add the most recent period to the calculation and drop the oldest
Per2 + Per3 + Per43
© Dale R. Geiger 2011 20
Rolling Average Calculation
Period 1 2 3 4 5 6 7 8 9 10 11 12Value 6 8 4 3 7 5 6 8 3 6 4 53mo. Avg.
Period1 not enough data2 not enough data3 (6 + 8 + 4)/3 = 6.04 (8 + 4 + 3)/3 = 5.05 (4 + 3 + 7)/3 = 4.76 (3 + 7 + 5)/3 = 5.0
Period7 (7 + 5 + 6)/3 = 6.08 (5 + 6 + 8)/3 = 6.39 (6 + 8 + 3)/3 = 5.710 (8 + 3 + 6)/3 = 5.711 (3 + 6 + 4)/3 = 4.312 (6 + 4 + 5)/3 = 5.0
© Dale R. Geiger 2011 21
Rolling Average Calculation
Period 1 2 3 4 5 6 7 8 9 10 11 12Value 6 8 4 3 7 5 6 8 3 6 4 53mo. Avg. X X 6.0
Period1 not enough data2 not enough data3 (6 + 8 + 4)/3 = 6.04 (8 + 4 + 3)/3 = 5.05 (4 + 3 + 7)/3 = 4.76 (3 + 7 + 5)/3 = 5.0
Period7 (7 + 5 + 6)/3 = 6.08 (5 + 6 + 8)/3 = 6.39 (6 + 8 + 3)/3 = 5.710 (8 + 3 + 6)/3 = 5.711 (3 + 6 + 4)/3 = 4.312 (6 + 4 + 5)/3 = 5.0
© Dale R. Geiger 2011 22
Rolling Average Calculation
Period 1 2 3 4 5 6 7 8 9 10 11 12Value 6 8 4 3 7 5 6 8 3 6 4 53mo. Avg. X X 6.0 5.0
Period1 not enough data2 not enough data3 (6 + 8 + 4)/3 = 6.04 (8 + 4 + 3)/3 = 5.05 (4 + 3 + 7)/3 = 4.76 (3 + 7 + 5)/3 = 5.0
Period7 (7 + 5 + 6)/3 = 6.08 (5 + 6 + 8)/3 = 6.39 (6 + 8 + 3)/3 = 5.710 (8 + 3 + 6)/3 = 5.711 (3 + 6 + 4)/3 = 4.312 (6 + 4 + 5)/3 = 5.0
© Dale R. Geiger 2011 23
Rolling Average Calculation
Period 1 2 3 4 5 6 7 8 9 10 11 12Value 6 8 4 3 7 5 6 8 3 6 4 53mo. Avg. X X 6.0 5.0 4.7
Period1 not enough data2 not enough data3 (6 + 8 + 4)/3 = 6.04 (8 + 4 + 3)/3 = 5.05 (4 + 3 + 7)/3 = 4.76 (3 + 7 + 5)/3 = 5.0
Period7 (7 + 5 + 6)/3 = 6.08 (5 + 6 + 8)/3 = 6.39 (6 + 8 + 3)/3 = 5.710 (8 + 3 + 6)/3 = 5.711 (3 + 6 + 4)/3 = 4.312 (6 + 4 + 5)/3 = 5.0
© Dale R. Geiger 2011 24
Rolling Average Calculation
Period 1 2 3 4 5 6 7 8 9 10 11 12Value 6 8 4 3 7 5 6 8 3 6 4 53mo. Avg. X X 6.0 5.0 4.7 5.0 6.0 6.3 5.7 5.7 4.3 5.0
Period1 not enough data2 not enough data3 (6 + 8 + 4)/3 = 6.04 (8 + 4 + 3)/3 = 5.05 (4 + 3 + 7)/3 = 4.76 (3 + 7 + 5)/3 = 5.0
Period7 (7 + 5 + 6)/3 = 6.08 (5 + 6 + 8)/3 = 6.39 (6 + 8 + 3)/3 = 5.710 (8 + 3 + 6)/3 = 5.711 (3 + 6 + 4)/3 = 4.312 (6 + 4 + 5)/3 = 5.0
© Dale R. Geiger 2011 25
Graph of Rolling Average
1 2 3 4 5 6 7 8 9 10 11 120
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6
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8
9
Actual3-mo. avg.
This is a time series. X-axis represents sequential time periods
© Dale R. Geiger 2011 26
Graph of Rolling Average
1 2 3 4 5 6 7 8 9 10 11 120
1
2
3
4
5
6
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8
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Actual3-mo. avg.
This is a time series. X-axis represents sequential time periods
© Dale R. Geiger 2011 27
Rolling Average vs. Regression
1 2 3 4 5 6 7 8 9 10 11 120
1
2
3
4
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ActualLinear (Actual)3-mo. avg.
This is a time series. X-axis represents sequential time periods
© Dale R. Geiger 2011 28
Using Rolling Average to Project Future Demand
• Assume that the previous rolling average will be maintained
• Our forecast for period 13 will assume a rolling average of 5, same as period 12
(Per11 + Per12 + Per13)/3 = 5
Period 1 2 3 4 5 6 7 8 9 10 11 12Value 6 8 4 3 7 5 6 8 3 6 4 53mo. Avg. X X 6.0 5.0 4.7 5.0 6.0 6.3 5.7 5.7 4.3 5.0
© Dale R. Geiger 2011 29
Using Rolling Average to Project Future Demand
• Plug in the known values and solve the equation:
(Per11 + Per12 + Per13)/3 = 5(4 + 5 + Per13)/3 = 5
3 * (4 + 5 + Per13)/3 = 5 * 39 + Per13 = 15
Per13 = 6
© Dale R. Geiger 2011 30
Using Rolling Average to Project Future Demand
• Plug in the known values and solve the equation:
(Per11 + Per12 + Per13)/3 = 5(4 + 5 + Per13)/3 = 5
3 * (4 + 5 + Per13)/3 = 5 * 39 + Per13 = 15
Per13 = 6
What would regression analysis project?
Which is “right”?
© Dale R. Geiger 2011 31
Rolling Average vs. Regression
1 2 3 4 5 6 7 8 9 10 11 120
1
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This is a time series. X-axis represents sequential time periods13
3 month rolling average suggests an inflection point has
changed the trend
Regression picks up the long term downward trend,
predicting another decrease
© Dale R. Geiger 2011 32
Rolling Average Strengths and Weaknesses
• Can be calculated very precisely• But may be precisely wrong
• Simple to calculate• The main strength of rolling averages is that they
dampen the effect of short term changes• This helps decision makers avoid knee jerk responses to
changes in demand that may not be significant• Decision makers are often looking for inflection points• An inflection point in a six month rolling average carries a
lot of weight
© Dale R. Geiger 2011 33
Check on Learning
• What would be the equation for a six-month rolling average calculation?
• What is the primary assumption when using rolling average to project future demand?
© Dale R. Geiger 2011 34
Planning Factors
• Assume some cause and effect relationship• If we suspect that demand for education
counseling decreases when a unit deploys• We could study the history of that relationship
and determine a planning factor (or ratio) of sessions per soldier as “a”
• We could then use that factor to plan for the drop in session demand when X soldiers deploy as
• New demand = a*X
© Dale R. Geiger 2011 35
Planning Factor Example
• Given the recent history determine the planning factor relating sessions and soldiers
• Use that factor to predict sessions as population goes to• 8000• 7000• 6000
Counseling Sessions
Soldiers on Post
327 10856
369 10012
285 10255
301 10566
349 10467
363 10200
© Dale R. Geiger 2011 36
Planning Factor Example
• Given the recent history determine the planning factor relating sessions and soldiers
• Use that factor to predict sessions as population goes to• 8000 * .032 = 256• 7000 * .032 = 224• 6000 * .032 = 192
Counseling Sessions
Soldiers on Post
327 10856
369 10012
285 10255
301 10566
349 10467
363 10200
Total = 1994 623651994/62365 = .032 or 3.2%
© Dale R. Geiger 2011 37
Leading Indicators
• Leading indicators are similar to planning factors with a couple differences• Leading indicators often have a weaker cause and
effect relationship• Changes in consumer confidence index may
foreshadow an increase in sales at the post exchange
• There is a period of time before the effect is seen (i.e. that’s why they are called leading indicators)
© Dale R. Geiger 2011 38
Check on Learning
• What are planning factors? • How are planning factors generally expressed?
© Dale R. Geiger 2011 39
Practical Exercise