1. Project Sales or Production Levels Using the Rolling Average
Principles of Cost Analysis and Management

2. What if?
You planned for 10 but…

3. Terminal Learning Objective
Action: Project Sales or Production Levels Using the Rolling Average
Condition: FM Leaders in a classroom environment working individually and as a member of a small group, using doctrinal and administrative publications, self-study exercises, personal experiences, practical exercises, handouts, and discussion.
Standard: With at least 80% accuracy (70% for International learners):
Communicate the purpose of trend projection using historical data
Calculate Rolling Average
Demonstrate planning factors

4. 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:
? Or ?
If yes, then you are recognizing that the past can help us make better decisions about the future.

5. 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.

6. Three Methods Regression Rolling average Planning factors
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.

7. 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)

8. 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

9. Regression Exercise
Use spreadsheet to predict the 8th, 9th, and 10th event burger demand if the first six demands were:

10. Spreadsheet Exercise The spreadsheet returns the equation:
y = x
Enter the values in the spreadsheet to predict demand
Per. 8 demand = 17
Enter the data as shown

11. Regression Analysis
Regression can be used to separate mixed costs into fixed and variable components.
Total cost = VC $/unit * # units + Fixed Cost
is 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

12. 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 *units

13. Regression Analysis
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

14. 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

15. LSA #1 Check on Learning
Q1. In the context of trend projection, what does the regression line represent? Q2. What is the main weakness of regression in trend projection?
A1.
Q1. In the context of trend projection, what does the regression line represent?
A1. It represents the linear relationship for a set of data points in a time series or sequence.
Q2. What is the main weakness of regression in trend projection?
A2. It is cumbersome to calculate, and since it is linear it cannot project or display upturns and downturns.
A2.

16. LSA #1 Summary
In this lesson, We covered demand in an organization, as well as predicting future decisions based off past performance. Also, trend projections with methods along with regression analysis in times of strengths and weaknesses.

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

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

19. Rolling Average Calculation (Cont.)
The 3-month rolling average is the average value for the most recent 3 months
Per1 + Per2 + Per3 3
Add the most recent period to the calculation and drop the oldest
Per2 + Per3 + Per4

20. Rolling Average Calculation (Cont.)
Period 1 2 3 4 5 6 7 8 9 10 11 12
Value
3mo. Avg.
Period
1 not enough data
2 not enough data
3 ( )/3 = 6.0
4 ( )/3 = 5.0
5 ( )/3 = 4.7
6 ( )/3 = 5.0
Period
7 ( )/3 = 6.0
8 ( )/3 = 6.3
9 ( )/3 = 5.7
10 ( )/3 = 5.7
11 ( )/3 = 4.3
12 ( )/3 = 5.0

21. Rolling Average Calculation (Cont.)
Period 1 2 3 4 5 6 7 8 9 10 11 12
Value
3mo. Avg. X
6.0
Period
1 not enough data
2 not enough data
3 ( )/3 = 6.0
4 ( )/3 = 5.0
5 ( )/3 = 4.7
6 ( )/3 = 5.0
Period
7 ( )/3 = 6.0
8 ( )/3 = 6.3
9 ( )/3 = 5.7
10 ( )/3 = 5.7
11 ( )/3 = 4.3
12 ( )/3 = 5.0

22. Rolling Average Calculation (Cont.)
Period 1 2 3 4 5 6 7 8 9 10 11 12
Value
3mo. Avg. X
6.0
5.0
Period
1 not enough data
2 not enough data
3 ( )/3 = 6.0
4 ( )/3 = 5.0
5 ( )/3 = 4.7
6 ( )/3 = 5.0
Period
7 ( )/3 = 6.0
8 ( )/3 = 6.3
9 ( )/3 = 5.7
10 ( )/3 = 5.7
11 ( )/3 = 4.3
12 ( )/3 = 5.0

23. Rolling Average Calculation (Cont.)
Period 1 2 3 4 5 6 7 8 9 10 11 12
Value
3mo. Avg. X
6.0
5.0
4.7
Period
1 not enough data
2 not enough data
3 ( )/3 = 6.0
4 ( )/3 = 5.0
5 ( )/3 = 4.7
6 ( )/3 = 5.0
Period
7 ( )/3 = 6.0
8 ( )/3 = 6.3
9 ( )/3 = 5.7
10 ( )/3 = 5.7
11 ( )/3 = 4.3
12 ( )/3 = 5.0

24. Rolling Average Calculation (Cont.)
Period 1 2 3 4 5 6 7 8 9 10 11 12
Value
3mo. Avg. X
6.0
5.0
4.7
6.3
5.7
4.3
Period
1 not enough data
2 not enough data
3 ( )/3 = 6.0
4 ( )/3 = 5.0
5 ( )/3 = 4.7
6 ( )/3 = 5.0
Period
7 ( )/3 = 6.0
8 ( )/3 = 6.3
9 ( )/3 = 5.7
10 ( )/3 = 5.7
11 ( )/3 = 4.3
12 ( )/3 = 5.0

25. Graph of Rolling Average
This is a time series. X-axis represents sequential time periods

26. Rolling Average vs. Regression
This is a time series. X-axis represents sequential time periods

27. 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 12
Value
3mo. Avg. X
6.0
5.0
4.7
6.3
5.7
4.3

28. Using Rolling Average to Project Future Demand
Plug in the known values and solve the equation:
(Per11 + Per12 + Per13)/3 = 5
( Per13)/3 = 5
3 * ( Per13)/3 = 5 * 3
9 + Per13 = 15
Per13 = 6

29. What would regression analysis project?
Using Rolling Average to Project Future Demand
Plug in the known values and solve the equation:
(Per11 + Per12 + Per13)/3 = 5
( Per13)/3 = 5
3 * ( Per13)/3 = 5 * 3
9 + Per13 = 15
Per13 = 6
What would regression analysis project?
Which is “right”?

30. Rolling Average vs. Regression
3 month rolling average suggests an inflection point has changed the trend
Regression picks up the long term downward trend, predicting another decrease 13
This is a time series. X-axis represents sequential time periods

31. 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.

32. LSA #2 Check on Learning
Q1. What would be the equation for a six-month rolling average calculation? Q2. What is the primary assumption when using rolling average to project future demand?
A1.
Q1. What would be the equation for a six-month rolling average calculation?
A1. (Month1 + Month 2 + Month 3 + Month 4 + Month 5 + Month 6) /6
Q2. What is the primary assumption when using rolling average to project future demand?
A2. That the prior period’s rolling average will be maintained.
A2.

33. LSA #2 Summary
During this block we discussed rolling average, and then plotted it on a graph. We used actual vs. 3 months average vs. regression. Future Demands were also Projected.

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

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
8000 * .032 = 256
7000 * .032 = 224
6000 * .032 = 192
Total =
1994/623656= .032 or 3.2%

36. 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)

37. LSA #3 Check on Learning
Q1. What are planning factors? Q2. How are planning factors generally expressed?
A1.
Q1. What are planning factors?
A1. Planning factors are other variables that have an observed effect on demand.
Q2. How are planning factors generally expressed?
A2. Planning factors are generally expressed as a ratio or percentage.
A2.

38. LSA #3 Summary
In this section, we went over planning factors and provided some examples.

39. In Summation
Successful planning for inputs to the process at hand is entirely dependent upon successful forecasting of demand.
Demand is generally the great unknown in planning because it is out of the control of the planner.
Regression analysis identifies a linear relationship from past demand.
Rolling average is simpler to calculate and does permit for the projection of upturns and downturns.
Planning Factors (or leading indicators) depend upon the relationship between a known quantity and demand.

40. TLO Summary
Action: Project Sales or Production Levels Using the Rolling Average
Condition: FM Leaders in a classroom environment working individually and as a member of a small group, using doctrinal and administrative publications, self-study exercises, personal experiences, practical exercises, handouts, and discussion.
Standard: With at least 80% accuracy (70% for International learners):
Communicate the purpose of trend projection using historical data
Calculate Rolling Average
Demonstrate planning factors

41. Practical Exercise