Arguably, SKUs with Intermittent Demand are some of the most challenging to forecast with any modicum of accuracy.  We generally define Intermittent Demand as follows:

Intermittent series has demand appear at random with many time periods showing no demand at all. The prominent characteristics of such series are:

  1. The time-series contains embedded zeroes
  2. The time-series does NOT exhibit any seasonal behavior

I have struggled for many years to find an alternative to the conventional approaches.  As far back as the 1990’s, I began reading about machine learning and particularly neural networks.  This work was in its infancy, relative to today, due to the lack of computing power required for such artificial intelligence techniques.  However, I felt that we may be able to leverage machine learning at some time in forecasting difficult time-series in the future.  My thoughts that I lay out here in this article were not well received at the time.  I do not know if it is because of the novelty of machine learning and lack of computing power at the time to effectively give adequate results, or if it was just a poor idea.  

We at the Anamind Consulting Company are constantly seeking to leverage any and all technologies that will yield superior results in demand planning for our clients.  To that end, I am documenting this proposal, not as a dogmatic approach, but for the purposes of starting a discussion in the demand planning community about this potential approach.  I will begin with a review of the current status of Intermittent Demand time-series forecasting and then summarize my thoughts in the second half of the article.  Again, these ideas are only summarized and there is room for suggested improvements.  Of that, I am very certain.

Current State of Forecasting SKUs with Intermittent Demand

Croston’s Intermittent Demand model is a favorite of today’s automated demand planning tools for those SKUs which have apparently randomly distributed non-positive demand values.  Essentially, Croston’s model will take the total of positive demand and distribute it over all past time periods, taking that average and extending it into the future.  This has been a good model that has stood the test of time and it does a good job of taking highly variable demand and smoothing it out for the upstream supply chain processes of production scheduling and distribution.

However, at the end of the day, we have a constant forecast that, by definition, will have high period-to-period error when compared to the actual demand values.  This drives the inventory up to maintain an adequate customer service.  This is usually not a large problem for companies as these SKUs tend to be in the minority and their average demands are small.  That said, I have often wondered if there would not be a better way to forecast these SKUs.  

Forecasting the Intermittent Demand Series – Another Thought

For our discussion, we are going to use the following time-series.  This is a screen print from the PLANAMIND Demand Planning Statistical Model Optimizing Tool.
Planamind Tool Sample Forecast for Intermittent Demand

Figure 1
Source: Planamind

Intermittent Demand Time-Series Forecasting Proposal

This proposal splits the Intermittent Demand time-series into two obvious components.  The first one is the sub-series consisting of the non-positive historical observations (see the red circle in the graph in Figure 1 above).  Conversely, the second sub-series would be those observations consisting of positive demand values (see the blue circle in the graph in Figure 1 above).

Forecasting the Non-Positive Component

Typically, the forecasting challenge with a time-series such as this is those pesky non-positive values.  To the naked eye they appear random.  However my 20-year old thought was to eliminate the negative demand values and consider them as zeroes.  As a parenthetical, negative demand values should compose a minimum amount of the total demand.  Secondly, these values are usually caused by returns in a given time period in excess of regular orders for the SKU.  My contention is that in this case, the demand collection logic should be modified to properly associate the return with the appropriate order in its original time frame.  This association would then cause the original demand to be decremented.  It only makes common sense that if one purchases 100 units of a product in February and returns 40 from that order in May that the ‘real’ demand should be adjusted for that order (customer, product and location) to 60 (i.e. 100-40).  It is misleading and will cause forecast inaccuracies and supply chain problems to allow the 100 units to remain in February and allow a -40 to be ‘booked’ in May.   While it is easy to allow the demand collection system to operate in this way, it is not right.  Being easy does not mean something is ‘right’ (correct).  I managed the demand system in a multi-billion dollar organization that had this demand collection problem.  Sure, it was difficult to fix, but we did and increased forecast accuracy measurably.

Having said all that, I am suggesting this portion of the demand series now consists of a sequence of time-sensitive zero values and that we can apply powerful machine intelligence routines (i.e. a neural net) to ‘tease out’ a pattern of subsequent zero demand values for the future time series.

Forecasting the Positive Component

If we are able to use machine intelligence to lay in the pattern of non-positive demand points, then the demand planner will have a significant number of options at her disposal to calculate the forecast for the positive component.  Remember one of the characteristics of the Intermittent Demand time-series is that: The time-series does NOT exhibit any seasonal behavior.  Therefore, we could apply a non-seasonal exponential model (either NN or LN) to the remaining points.  Another option would be to use one of the simpler models like the Simple Moving Average (SMA) or even the Same as Last Year (SALY) or SALY with growth if growth can indeed be detected.  The point here is that there are several tools in the demand planner’s tool-kit for solving this part of the problem.


While this article in no means attempts to disparage the brilliant work that has been done by Croston, we at Anamind are always seeking better ways to fit the forecast as close to actual demand with the proper lead time to improve performance in the Supply Chain.  Croston’s will do a fine job by providing a level forecast to build inventory for the peaks of demand and maintain lower levels of inventory for those periods in which no demand occurs.  However, a more accurate forecast on these time-series will further reduce the investment in working capital via maintenance of safety stock.

I will close with a quote from Charles Chase, a very respected demand planning expert:

‘The objective of demand-driven forecast is to predict unconstrained demand as accurately as possible.  This would include predicting the peaks and valleys that resonate in true demand.  When we smooth the forecasts, we normally overlook the peaks and valleys.’

Charles Chase, “Demand-Driven Forecasting – A Structured Approach to Forecasting” pp. 142

I am excited to hear from you on improvements to these thoughts.  I thank you for reading this article.