Probabilistic Forecasting – One Man’s (Somewhat Informed) Opinion

A reasonable probability is the only certainty. – E. W. Howe

My, how methods for have evolved over time:

  • Naive, flat line forecasts (e.g. moving averages) were once used to estimate demand for triggering orders.
  • Time series decomposition type mathematical models added more intelligence around detecting trends and seasonality to enable better long term forecasting.
  • Causal forecasting models allowed different time series to influence each other (e.g. the effect of future planned price changes on forecasted volumes)

All of these methods are deterministic, meaning that their output is a single value representing the “most likely outcome” for each future time period. Ironically, the “most likely outcome” almost never actually materializes.

This brings us to probabilistic forecasting. In addition to calculating a mean (or median) value for each future time period (can be interpreted as the most likely outcome), probabilistic methods also calculate a distinct confidence interval for each individual future forecast period. In essence, instead of having an individual point for each time period into the future, you instead have a cloud of “good forecasts” for various types of scenario modeling and decision making.

But how do you apply this in supply chain management where all of the physical activities driven by the forecast are discrete and deterministic? You can't submit a purchase order line to a supplier that reads “there's a 95% chance we'll need 1 case, a 66% chance we'll need 2 cases and a 33% chance we'll need 3 cases”. They need to know exactly how many cases they need to pick, full stop.

The probabilistic forecasting approach can address many “self evident truths” about forecasting that have plagued supply chain planners for decades by better informing the discrete decisions in the supply chain:

  • That not only is demand variable, but variability in demand is also variable over time. Think about a product that is seasonal or highly promotional in nature. The amount of safety stock you need to cover demand variability for a garden hose is far greater in the summer than it is in the winter. By knowing how not just demand but demand variability changes over time, you can properly set discrete safety stock levels at different times of the season. 
  • That uncertainty is inherent in every prediction. Measuring forecasts using the standard “every forecast is wrong, but by how much” method provides little useful information and causes us to chase ghosts. By incorporating a calculated expectation of uncertainty into forecast measurements, we can instead make meaningful determinations about whether or not a “miss” calculated by traditional means was within an expected range and not really a miss at all. The definition of accuracy changes from an arbitrary percentage to a clear judgment call, forecast by forecast, because the inherent and unavoidable uncertainty is treated as part of the signal (which it actually is), allowing us to focus on the true noise.
  • That rollups of granular unit forecasts by item/location to higher levels for capacity and financial planning can be misleading and costly. The ability to also roll up the specific uncertainty by item/location/day allows management to make much more informed decisions about risk before committing resources and capital.

Now here's the “somewhat informed” part. In order to gain widespread adoption, proponents of probabilistic methods really do need to help us old dogs learn their new tricks. It's my experience that demand planners can be highly effective without knowing every single rule and formula driving their forecast outputs. If they use off the shelf software packages, the algorithms are proprietary and they aren't able to get that far down into the details anyhow.

What's important is that – when looking at all of the information available to the model – a demand planner can look at the output and understand what it was “thinking”, even if they may disagree with it. All models make the general assumption that patterns of the past will continue into the future. Knowing that, a demand planner can quickly address cases where that assumption won't hold true (i.e. they know something about why the future will be different from the past that the model does not) and take action.

As the pool of early adopters of probabilistic methods grows, I'm looking forward to seeing heaps of case studies and real world examples covering a wide range of business scenarios from the perspective of a demand planner – without having to go back to school for 6 more years to earn a PhD in statistics. Some of us are just too old for that shit.

I see great promise, but for the time being, I remain only somewhat informed.

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