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

What if? You planned for 10 but…

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

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 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.

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)

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 values in the spreadsheet to predict demand Per. 8 demand = 17 Enter the data as shown

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

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 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

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.

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.

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

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

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 (6 + 8 + 4)/3 = 6.0 4 (8 + 4 + 3)/3 = 5.0 5 (4 + 3 + 7)/3 = 4.7 6 (3 + 7 + 5)/3 = 5.0 Period 7 (7 + 5 + 6)/3 = 6.0 8 (5 + 6 + 8)/3 = 6.3 9 (6 + 8 + 3)/3 = 5.7 10 (8 + 3 + 6)/3 = 5.7 11 (3 + 6 + 4)/3 = 4.3 12 (6 + 4 + 5)/3 = 5.0

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 (6 + 8 + 4)/3 = 6.0 4 (8 + 4 + 3)/3 = 5.0 5 (4 + 3 + 7)/3 = 4.7 6 (3 + 7 + 5)/3 = 5.0 Period 7 (7 + 5 + 6)/3 = 6.0 8 (5 + 6 + 8)/3 = 6.3 9 (6 + 8 + 3)/3 = 5.7 10 (8 + 3 + 6)/3 = 5.7 11 (3 + 6 + 4)/3 = 4.3 12 (6 + 4 + 5)/3 = 5.0

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 (6 + 8 + 4)/3 = 6.0 4 (8 + 4 + 3)/3 = 5.0 5 (4 + 3 + 7)/3 = 4.7 6 (3 + 7 + 5)/3 = 5.0 Period 7 (7 + 5 + 6)/3 = 6.0 8 (5 + 6 + 8)/3 = 6.3 9 (6 + 8 + 3)/3 = 5.7 10 (8 + 3 + 6)/3 = 5.7 11 (3 + 6 + 4)/3 = 4.3 12 (6 + 4 + 5)/3 = 5.0

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 (6 + 8 + 4)/3 = 6.0 4 (8 + 4 + 3)/3 = 5.0 5 (4 + 3 + 7)/3 = 4.7 6 (3 + 7 + 5)/3 = 5.0 Period 7 (7 + 5 + 6)/3 = 6.0 8 (5 + 6 + 8)/3 = 6.3 9 (6 + 8 + 3)/3 = 5.7 10 (8 + 3 + 6)/3 = 5.7 11 (3 + 6 + 4)/3 = 4.3 12 (6 + 4 + 5)/3 = 5.0

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 (6 + 8 + 4)/3 = 6.0 4 (8 + 4 + 3)/3 = 5.0 5 (4 + 3 + 7)/3 = 4.7 6 (3 + 7 + 5)/3 = 5.0 Period 7 (7 + 5 + 6)/3 = 6.0 8 (5 + 6 + 8)/3 = 6.3 9 (6 + 8 + 3)/3 = 5.7 10 (8 + 3 + 6)/3 = 5.7 11 (3 + 6 + 4)/3 = 4.3 12 (6 + 4 + 5)/3 = 5.0

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

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

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

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 * 3 9 + Per13 = 15 Per13 = 6

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 (4 + 5 + Per13)/3 = 5 3 * (4 + 5 + Per13)/3 = 5 * 3 9 + Per13 = 15 Per13 = 6 What would regression analysis project? Which is “right”?

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

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.

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.

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.

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 8000 * .032 = 256 7000 * .032 = 224 6000 * .032 = 192 Total = 1994 62356 1994/623656= .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)

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.

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

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.

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

Practical Exercise