Forecast Error

Forecast error is the difference between forecast and actual sales.

Variability is the quality of being variable in the time. In this context, the forecast error variability is the measure of the forecast error fluctuations over time.

This is the measure of demand fluctuations over time.

Demand variability and forecast error variability are outputs of the calculation. When the best-fit method is analyzed, finding a best fit for historical sales can ignore exiting time-varying forecasts. This search considers forecast error rather than only demand variability. This method connects planning with execution through a realistic and sophisticated calculation.

On the slide, we can see two results from the calculation:

When the Demand Variability on this example is 1.05, based on the historical data for demand, we see a soft positive trend higher than one. On the other hand, we see that the Forecast Error represents 32% of missed values over time.

In case there are missing values, the algorithm recognizes periods with no data and can recompute forecast error CV based solely on periods with sales and forecasts, therefore, as a result explained on the slide, the forecast error CV can change from 0.90 to 0.42.

• Replace null values by zero: If you select this checkbox, the system replaces null values with zeroes. The algorithms disregard periods that have null values for either forecast or sales because it cannot calculate using null values.
• Start history from first sales period: If you select this checkbox, the system takes the first period where data for sales history exists and uses this period as the first period in the calculation of forecast errors.

A positive bias reflects a tendency to inflate forecasts, resulting in overestimation of forecast error CV and excess inventory.

In addition, a negative bias reflects a tendency to deflate forecasts, resulting in service level misses from holding less than required inventory.

On the example, we see a strong change within the forecast error CV, with bias correction from 1.2 to 0.74.

• Adjust bias of forecast: determines whether the system applies the bias adjustment to historical forecasts in the calculation of forecast error.
• Bias adjustment method: determines the types of forecast bias adjustment (adjust positive bias, adjust negative bias, adjust positive and negative bias.
• Bias confidence interval: determines level of confidence required in estimating bias.
• Maximum positive bias value: specifies the upper bound limit for the bias.
• Minimum negative bias value: specifies the lower bound limit for the bias.

Stocking point classified as intermittent if:

• No positive sales history
• Average demand interval (ADI) exceeds intermittent demand interval (IDI)
• Not classified as seasonal
• Does not have sufficient forecast timing accuracy

In the example, both forecast and sales are:

• Positive in 10 weeks
• Past positive sales in 10 weeks
• Past positive forecast in 52 weeks
• If we compare the user input for the forecast timing accuracy of 0.5 to 10, divided by the maximum value between 10 and 52, we come to 0,1923, which is less than 0,5. Therefore, the forecast timing accuracy is not sufficient, that is, we are dealing with an intermittent demand.

The average sales interval (ADI) is used to determine how many weeks of sales and forecasts to aggregate. On the slide, the example shows an ADI of 5, so sales and forecasts are summed across 5 periods. CV calculation algorithm is then used on 5-periods sales and forecasts, including filtering, outlier detection, and bias detection.

• 1) Mean absolute percentage error (MAPE) multiplied by a factor
• 2) The division of mean absolute deviation (MAD) by a maximum between two values (average forecast and average sales), multiplied by a factor

The CV can be calculated through two options:

MAPE can be useful to determine the forecast accuracy. Depending on the circumstances a Weighted MAPE can be calculated, considering the forecast or the sales as a reference factor. The equations used by the algorithm are presented on the slide, where F represents the forecast and S represents the sales, both changing over time (i).

In time phased planning, we need to scale historical variability relative to the future forecast. CV is a constant scaling factor to calculate the time phased forecast error standard deviation.

• Default CV Value: defines the default coefficient of variation (CV), when CV cannot be calculated with the provided data.
• Maximum CV Value: defines the maximum CV for CV.
• Basis of percentage error: determines whether forecast or actual is used as the basis in calculating the percentage error.
• Default percentage error for one period: specifies the default percentage error for a period, where both historical forecast and sales are zero.
• Maximum percentage error for one period: specifies the maximum percentage error for a period, where forecast error is strictly greater than zero and the basis value of percentage error is zero.
• CV computation method: Choose aMAD or MAPE-based calculation.