Demand Forecasting: A Cross Discipline Perspective Part II: Probabilistic and Ensemble Forecasting

Published on: Apr, 27, 2012 By: Christopher A Dyke,

In forecasting for demand there are two predominant methods of modeling available: deterministic and probabilistic. Normally just saying the names of these techniques is enough to turn someone off from the topic, however, it is important to understand the strengths and weaknesses of each.

Deterministic is simply defined as a forecast in which the results of the model are completely determined by present conditions (Lewis 2005). Simply stated, forecasted demand is completely and solely dependent on what we know right here and now. This sounds somewhat absurd since we know market volatility and global economic conditions can change the demand outlook almost daily. Although this is true, it is the technique that many companies employ for forecasting demand. Examples of this include linear regression (extrapolation) and exponential smoothing models.

The other type of modeling technique, probabilistic, provides model output in ranges with degrees of confidence. This technique takes into account imprecision and uncertainty when appropriate (Abramsia & Finizza 1995). By incorporating a range of values there is room for error and you can better plan for a range of outcomes. This modeling technique can also take into account multiple scenarios as it has for the oil industry.

Post Gulf War I, the oil industry started to incorporate probabilistic forecasting so it could account for decisions that OPEC made concerning the levels of oil production (Abramsia & Finizza 1995). These decisions involved the probability that OPEC would increase, decrease, or maintain supply levels. The most popular modeling technique for this type of forecast is the Monte Carlo simulation.

So, if probabilistic forecasting is such a flexible tool for more accurately planning procurement, production, and logistics demand, why don’t more companies use it? There are three main factors that discourage many companies from leveraging this capability: First, retraining and a new understanding of forecasting techniques and analysis. Second, a paradigm shift in the way S&OP is conducted. And third, a full understanding of what impacts their demand.

New Forecast Technique and Analysis

When many people see forecast output, they think in terms of an exact number of units sold (or produced) during a period of time (500 units in January). The problem with this is that when that exact number isn’t reached, natural instinct tells us the forecast should lose credibility and eventually become ignored. Instead of an exact number that may be correct 70% of the time, what if we used a range of output to plan off of (400-600 units in January)?

Now we are planning for the potential to see a little more or less. If we end up actually needing 550 units instead of 500, it’s not as difficult to produce. We can also give planners and idea of how certain we are in this projection by attaching a confidence level with it (90% confident January demand will be 400-600 units). As uncertainty in markets and the economy increases, confidence level decreases signaling to the S&OP team that variation to the plan is highly likely.

Now teams are empowered with much more information than just a number attached to a month and can plan accordingly. When considering a range of 200 units, such as in the example given, the thought of material shortages and inventory surpluses comes up. The goal of the demand planning team is to narrow this range as much as possible (no easy task given all the uncertainties already mentioned above).

S&OP Paradigm Shift

Now that S&OP teams have this new format of forecast information, how do they fully leverage it? The first step is to fully understand what the forecast is saying. Yes, the confidence level may be lower than last month, but what is this really telling us? Where is there more uncertainty? Is the uncertainty in demand or available supply? Having identified that uncertainty is increasing, we can begin to diagnose and prepare for that increased uncertainty. This tool enables a new way to view S&OP, not just as a plan for production and sales, but also as a risk mitigation process.

What impacts demand?

The results will also better help a company understand much of what impacts their demand. Initially, a company has to account for all the proper uncertainties for the model to produce an acceptable range. In many cases, companies may have an idea what impacts their demand but it’s similar to forecasting the weather, just when you think you have a handle on it, something happens to shake things up. With deterministic models, inaccuracy of the model could be the result of any change in the in the environment, industry, or economy from the time the model is run until now.

With probabilistic models, inaccuracy is the result of not accounting for the proper factors impacting your demand. The more accurate the model, the better understanding you have of what is impacting the demand (or even to what extent certain variables impact it).

How to implement

This process can impact everything from future inventory levels, response time, delivery time, production variability, and quality control (Min & Zhou 2002). While this requires a shift in thought about the forecast, there is an easier way to transition to it. In the weather community a modeling technique called ensemble forecasting is used to capture variations in future outcomes.

This technique involves looking at one forecasting technique, linear regression for example, and running the forecast multiple times under different conditions. In the case of linear regression, the forecast is defined as:


Where m is the rate of change in demand and b is the initial demand the model starts with. If we run the model using pessimistic, most likely, and optimistic scenarios for m and b, we will have 9 different outputs for the forecast. In this “ensemble” of forecasts we get a variety of output that looks similar to Figure 1. From this we can gather a potential range of solutions or we can consolidate this output by finding the ensemble average solution and highlighting one standard deviation above and below that (Figure 2).

Now we have a range of solutions that we can feel more confident about than just one model producing one forecast. Interpreting the results of this is fairly easy. We have the average solution which gives us the deterministic value, the standard deviation solutions which give us a “most likely” range, and we can judge uncertainty based on the difference between the standard deviation solutions (the larger the difference, the more uncertain the forecast).


Ensemble Outputs: Figure 1 and Figure 2


Abramson, B., & Finizza, A. (1995). Probabilistic forecasts from probabilistic models: A case study in the oil market. International Journal of Forecasting, 11, 63-72.

Lewis, J. M. (2005). Roots of ensemble forecasting. Monthly Weather Review, 133(7), 1865-1885.

Min, H., & Zhou, G. (2002). Supply chain modeling: Past, present and future. Computers & Industrial Engineering, 43, 231-249.