##### Author: Michael Gamper

### Knowing the accuracy of a number which is incorrect is useless. Knowing the probability distribution of how a number is composed is valuable.

What does that mean in practice? Supply chain practitioners are familiar with measures of accuracy, however, is this really the right approach? Are we not better off managing risk levels? Let us have a closer look.

### Forecast Accuracy

The most commonly used measure of forecast accuracy is MAPE or Mean Absolute Percent Error. Statistically, MAPE is defined as the average of percentage errors. In practice, MAPE is used as a measurement of the mean absolute deviation divided by average sales, expressed as a percentage. The calculation of the MAPE is defined as follows:

### Example:

**Forecast (F) =** 100 units in January and 80 units in February

**Actual (A) =** 80 units in January and 90 units in February

**MAPE =** 18%

**Calculated for each Month (Absolute Percentage Error (APE): APE for January =** 25% and APE for February = 11% which results in a mean (MAPE) of 18%

### Meaning:

This tells a practitioner that the mean absolute error is 18% and that for any given month the forecast error could lie, on average, in a band of +/- 18% of the forecasted number! Applied to the month of January the units actually sold could be between 82 to 118 units – a 36-unit band in which the actual could lie.

### Consequence:

In reality, because MAPE is an average, the actual could lie outside this band of +/- 18%. If a supply chain organisation has to commit to a sales number, or commit to a factory capacity, then this approach is not usable to manage the risk of the deviation between forecast and actual. In particular capacity is a critical area, since it is perishable, if capacity is not used, it cannot be used in the future. Inventory is not perishable, unless it has a limited shelf life, and hence if the forecast is used to calculate inventory, then the risk is usually absorbed in the safety stock level, but this absorption of risk comes at a cost.

### Probability Distribution:

Probability distribution is an alternative approach, answering the following question: How many of the 100 units forecasted for January are at low risk, and how many are at high risk?

Whilst the below investigates the risk of overstock, the same can be applied to understock situations where the risk is defined as the “loss of sale”.

In probability and statistics, a probability distribution is a mathematical function that, stated in simple terms, can be thought of as providing the probability of occurrence of different possible outcomes in an experiment. For instance, if the random variable X is used to denote the outcome of a coin toss (‘the experiment’), then the probability distribution of X would take the value 0.5 for X=Heads, and 0.5 for X=Tails.

### Approach:

There are various approaches deriving a probability distribution. Below are some of the more practical and tested approaches:

- Historical sales performance based analysing historical sales and their confidence of closing certain sales quantities
- CRM pipeline based with percentage win associations on contracts or customer orders
- Coefficient of Variance (CoV) based using SKU’s with a CoV below 50% representing high stability and hence low risk
- Forecast decomposition, extracting the baseline, trend, seasonality, cycle and residual from a time series, the baseline would equate to the lowest risk component, and the residual to the highest risk component

### Example:

To review the principle of a probability distribution and explain the rationale, we are using the historical sales performance. The number of occurrences are counted (P(X)), when a certain level of sales (X) has been accomplished in each time bucket over the defined time period of 6 months. Risk is calculated as the inverse function of the number of occurrences.

This tells a practitioner that monthly sales of 70 is at zero risk and any quantity above comes at increasing levels of risk until the quantity reaches 100 units, where the risk becomes 100%.

### Consequence:

This approach will enable a supply chain and sales to commit to 70 units per months without risk while evaluating the increasing risk of sales above 70 units. This means committing to quantities with confidence because one has a fuller understanding of what the forecast represents. A clear assessment of risk is an important mechanism for making decisions about supply based on a historical assessment of demand.

More to come…

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