project sales or production levels using the rolling average © dale r. geiger 20111

© 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…


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


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


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


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


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

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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


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


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


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


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

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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


Regression Analysis

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Regression Analysis

Regression Analysis

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Regression Analysis

Regression Analysis

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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


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


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?


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


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



• 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



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



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


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



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


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



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


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



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


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


Graph of Rolling Average

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Actual3-mo. avg.

This is a time series. X-axis represents sequential time periods


Graph of Rolling Average

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Actual3-mo. avg.



Rolling Average vs. Regression

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ActualLinear (Actual)3-mo. avg.



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



• 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



• 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”?


Rolling Average vs. Regression

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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


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


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?


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


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


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%


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)


Check on Learning

• What are planning factors? • How are planning factors generally expressed?


Practical Exercise

project sales or production levels using the rolling average © dale r. geiger 20111

Documents

future demand dale

future dale

regression analysis

spreadsheet exercise

demand drives

past demand

importance of demand

rolling average dale