CPIM Part 1 - Formulas
Throughput formula - answer1. Revenues received - totally variable costs/unites of the
chosen time period
2. (Total units produced / Processing time) X (Processing time / Total time) X (Good
units / Total units)
Example:
A factory manager wants to know the throughput rate for bolts manufactured per
second. They know that every minute, 3000 bolts are in production and in stock
combined. In this example, I (inventory) = 3000 and T (time) = 60 seconds. Using the
equation R (throughput rate) = 3000 bolts divided by 60 seconds, they can determine
that their throughput rate is 50 bolts per second.
Inventory Turnover - answerInventory turnover = cost of sales (COGS) / the average
inventory ((Inventory at Period Start + Inventory at Period End) / 2)
Example: cost of sales of $21 million; average inventory of $3 million
Inventory turnover = = 7
means that inventory turned over seven times.
Seasonal index - answerSeasonal index = period average demand / by average
demand for all periods
1. Calculate the period average demand (here the quarterly average) by summing all
like periods in the series and dividing by the number of them. This could be all first
quarters, all Junes, etc. For quarter 1 (Q1), this is (1,422 units + 1,351 units + 1,388
units)/3 = 1,387 units for the three years.
2. Calculate the average demand for all periods. To do this, sum these period average
demands and divide by the number of periods. This might be all quarterly averages
divided by 4 or all monthly averages divided by 12. The period average demand for Q2,
Q3, and Q4 was 1,016, 677, and 920 units, respectively, so the average demand for all
periods is (1,387 units + 1,016 units + 677 units + 920 units)/4 = 1,000 units.
Seasonal index, Quarter 1:
1''000 = 1.387
, Deseasonalized Demand - answerDeseasonalized Demand = Period Average
Demand / Seasonal Index
Deseasonalized Demand = 1'.387 = 1'000
Forecasted Demand - answerSeasonal Index * Deseasonlized Period Forecast
Moving average - answerMoving Average Forecast = Sum of Demand for most recent
set of period / number of periods
Example of a three-quarter moving average forecast.
Moving Average Forecast = (965 units + 916 units + 967 units) / 3 = 949 units
A moving average is simply the average of a certain number of past periods of demand
Exponential Smoothing - answerNew forecast = (α * latest demand) + ((1 - α) * previous
forecast)
To follow a trend more closely but smooth random variation less, a higher alpha would
be used.
Exponential smoothing gives more weight to the most recent demand information
because it is based on three things: the last period's actual demand, the last period's
forecast result, and a smoothing constant called alpha (α).
Alpha is a number between 0.0 and 1.0 (it is typically set between only 0.0 and 0.3 in
practice) that is basically a percentage for how much to weight the prior actual demand
versus the forecast demand
Mean Absolute Deviation (MAD) - answerMean Absolute Deviation =
(Sum Actual + Sum Forecast) / numbers of periods
Actual Demand: 691, 940, 1388,
Forecast: 674, 919, 1408
MAD = Sum (691-674) + (940-919) + (1388-1408) / 3
MAD = (17 + 21 + 20) / 3
MAD =
MAD = 19
Tracking Signal - answerTracking Signal =
algebraic sum of forecast deviations /MAD
Used to signal when the validity of the forecasting model might be in doubt.
Throughput formula - answer1. Revenues received - totally variable costs/unites of the
chosen time period
2. (Total units produced / Processing time) X (Processing time / Total time) X (Good
units / Total units)
Example:
A factory manager wants to know the throughput rate for bolts manufactured per
second. They know that every minute, 3000 bolts are in production and in stock
combined. In this example, I (inventory) = 3000 and T (time) = 60 seconds. Using the
equation R (throughput rate) = 3000 bolts divided by 60 seconds, they can determine
that their throughput rate is 50 bolts per second.
Inventory Turnover - answerInventory turnover = cost of sales (COGS) / the average
inventory ((Inventory at Period Start + Inventory at Period End) / 2)
Example: cost of sales of $21 million; average inventory of $3 million
Inventory turnover = = 7
means that inventory turned over seven times.
Seasonal index - answerSeasonal index = period average demand / by average
demand for all periods
1. Calculate the period average demand (here the quarterly average) by summing all
like periods in the series and dividing by the number of them. This could be all first
quarters, all Junes, etc. For quarter 1 (Q1), this is (1,422 units + 1,351 units + 1,388
units)/3 = 1,387 units for the three years.
2. Calculate the average demand for all periods. To do this, sum these period average
demands and divide by the number of periods. This might be all quarterly averages
divided by 4 or all monthly averages divided by 12. The period average demand for Q2,
Q3, and Q4 was 1,016, 677, and 920 units, respectively, so the average demand for all
periods is (1,387 units + 1,016 units + 677 units + 920 units)/4 = 1,000 units.
Seasonal index, Quarter 1:
1''000 = 1.387
, Deseasonalized Demand - answerDeseasonalized Demand = Period Average
Demand / Seasonal Index
Deseasonalized Demand = 1'.387 = 1'000
Forecasted Demand - answerSeasonal Index * Deseasonlized Period Forecast
Moving average - answerMoving Average Forecast = Sum of Demand for most recent
set of period / number of periods
Example of a three-quarter moving average forecast.
Moving Average Forecast = (965 units + 916 units + 967 units) / 3 = 949 units
A moving average is simply the average of a certain number of past periods of demand
Exponential Smoothing - answerNew forecast = (α * latest demand) + ((1 - α) * previous
forecast)
To follow a trend more closely but smooth random variation less, a higher alpha would
be used.
Exponential smoothing gives more weight to the most recent demand information
because it is based on three things: the last period's actual demand, the last period's
forecast result, and a smoothing constant called alpha (α).
Alpha is a number between 0.0 and 1.0 (it is typically set between only 0.0 and 0.3 in
practice) that is basically a percentage for how much to weight the prior actual demand
versus the forecast demand
Mean Absolute Deviation (MAD) - answerMean Absolute Deviation =
(Sum Actual + Sum Forecast) / numbers of periods
Actual Demand: 691, 940, 1388,
Forecast: 674, 919, 1408
MAD = Sum (691-674) + (940-919) + (1388-1408) / 3
MAD = (17 + 21 + 20) / 3
MAD =
MAD = 19
Tracking Signal - answerTracking Signal =
algebraic sum of forecast deviations /MAD
Used to signal when the validity of the forecasting model might be in doubt.
