Feynman’s perspective illuminates our journey:  “In its efforts to learn as much as possible about nature, modern physics has found that certain things can never be “known” with certainty. Much of our knowledge must always remain uncertain. The most we can know is in terms of probabilities.” ― Richard Feynman, The Feynman Lectures on Physics.

When we try to understand the complex world of logistics, randomness plays a pivotal role. This introduces an interesting paradox: In a reality where precision and certainty are prized, could the unpredictable nature of supply and demand actually serve as a strategic ally?

The quest for accurate forecasts is not just an academic exercise; it’s a critical component of operational success across numerous industries. For demand planners who must anticipate product demand, the ramifications of getting it right—or wrong—are critical. Hence, recognizing and harnessing the power of randomness isn’t merely a theoretical exercise; it’s a necessity for resilience and adaptability in an ever-changing environment.

Embracing Uncertainty: Dynamic, Stochastic, and Monte Carlo Methods

Dynamic Modeling: The quest for absolute precision in forecasts ignores the intrinsic unpredictability of the world. Traditional forecasting methods, with their rigid frameworks, fall short in accommodating the dynamism of real-world phenomena. By embracing uncertainty, we can pivot towards more agile and dynamic models that incorporate randomness as a fundamental component. Unlike their rigid predecessors, these models are designed to evolve in response to new data, ensuring resilience and adaptability. This paradigm shift from a deterministic to a probabilistic approach enables organizations to navigate uncertainty with greater confidence, making informed decisions even in volatile environments.

Stochastic modeling guides forecasters through the fog of unpredictability with the principles of probability. Far from attempting to eliminate randomness, stochastic models embrace it. These models eschew the notion of a singular, predetermined future, presenting instead an array of possible outcomes, each with its estimated probability. This approach offers a more nuanced and realistic representation of the future, acknowledging the inherent variability of systems and processes. By mapping out a spectrum of potential futures, stochastic modeling equips decision-makers with a comprehensive understanding of uncertainty, enabling strategic planning that is both informed and flexible.

Named after the historical hub of chance and fortune, Monte Carlo simulations harness the power of randomness to explore the vast landscape of possible outcomes. This technique involves the generation of thousands, if not millions, of scenarios through random sampling, each scenario painting a different picture of the future based on the inherent uncertainties of the real world. Decision-makers, armed with insights from Monte Carlo simulations, can gauge the range of possible impacts of their decisions, making it an invaluable tool for risk assessment and strategic planning in uncertain environments.

Real-World Successes: Harnessing Randomness

The strategy of integrating randomness into forecasting has proven invaluable across diverse sectors. For instance, major investment firms and banks constantly rely on stochastic models to cope with the volatile behavior of the stock market. A notable example is how hedge funds employ these models to predict price movements and manage risk, leading to more strategic investment choices.

Similarly, in supply chain management, many companies rely on Monte Carlo simulations to tackle the unpredictability of demand, especially during peak seasons like the holidays. By simulating various scenarios, they can prepare for a range of outcomes, ensuring that they have adequate stock levels without overcommitting resources. This approach minimizes the risk of both stockouts and excess inventory.

These real-world successes highlight the value of integrating randomness into forecasting endeavors. Far from being the adversary it’s often perceived to be, randomness emerges as an indispensable ally in the intricate ballet of forecasting. By adopting methods that honor the inherent uncertainty of the future—bolstered by advanced tools like Smart IP&O—organizations can navigate the unpredictable with confidence and agility. Thus, in the grand scheme of forecasting, it may be wise to embrace the notion that while we cannot control the roll of the dice, we can certainly strategize around it.

Measuring the accuracy of forecasts is an undeniably important part of the demand planning process. This forecasting scorecard could be built based on one of two contrasting viewpoints for computing metrics. The error viewpoint asks, “how far was the forecast from the actual?” The accuracy viewpoint asks, “how close was the forecast to the actual?” Both are valid, but error metrics provide more information.

Accuracy is represented as a percentage between zero and 100, while error percentages start at zero but have no upper limit. Reports of MAPE (mean absolute percent error) or other error metrics can be titled “forecast accuracy” reports, which blurs the distinction.  So, you may want to know how to convert from the error viewpoint to the accuracy viewpoint that your company espouses.  This blog describes how with some examples.

Accuracy metrics are computed such that when the actual equals the forecast then the accuracy is 100% and when the forecast is either double or half of the actual, then accuracy is 0%. Reports that compare the forecast to the actual often include the following:

• The Actual
• The Forecast
• Unit Error = Forecast – Actual
• Absolute Error = Absolute Value of Unit Error
• Absolute % Error = Abs Error / Actual, as a %
• Accuracy % = 100% – Absolute % Error

Look at a couple examples that illustrate the difference in the approaches. Say the Actual = 8 and the forecast is 10.

Unit Error is 10 – 8 = 2

Absolute % Error = 2 / 8, as a % = 0.25 * 100 = 25%

Accuracy = 100% – 25% = 75%.

Now let’s say the actual is 8 and the forecast is 24.

Unit Error is 24– 8 = 16

Absolute % Error = 16 / 8 as a % = 2 * 100 = 200%

Accuracy = 100% – 200% = negative is set to 0%.

In the first example, accuracy measurements provide the same information as error measurements since the forecast and actual are already relatively close. But when the error is more than double the actual, accuracy measurements bottom out at zero. It does correctly indicate the forecast was not at all accurate. But the second example is more accurate than a third, where the actual is 8 and the forecast is 200. That’s a distinction a 0 to 100% range of accuracy doesn’t register. In this final example:

Unit Error is 200 – 8 = 192

Absolute % Error = 192 / 8, as a % = 24 * 100 = 2,400%

Accuracy = 100% – 2,400% = negative is set to 0%.

Error metrics continue to provide information on how far the forecast is from the actual and arguably better represent forecast accuracy.

We encourage adopting the error viewpoint. You simply hope for a small error percentage to indicate the forecast was not far from the actual, instead of hoping for a large accuracy percentage to indicate the forecast was close to the actual.  This shift in mindset offers the same insights while eliminating distortions.

Automatic forecasting is the most popular and most used feature of SmartForecasts and Smart Demand Planner. Creating Automatic forecasts is easy. But, the simplicity of Automatic Forecasting masks a powerful interaction of a number of highly effective methods of forecasting. In this blog, we discuss some of the theory behind this core feature. We focus on Automatic forecasting, in part because of its popularity and in part because many other forecasting methods produce similar outputs. Knowledge of Automatic forecasting immediately carries over to Simple Moving Average, Linear Moving Average, Single Exponential Smoothing, Double Exponential Smoothing, Winters’ Exponential Smoothing, and Promo forecasting.

Forecasting tournament

Automatic forecasting works by conducting a tournament among a set of competing methods. Because personal computers and cloud computing are fast, and because we have coded very efficient algorithms into the SmartForecasts’ Automatic forecasting engine, it is practical to take a purely empirical approach to deciding which extrapolative forecasting method to use. This means that you can afford to try out a number of approaches and then retain the one that does best at forecasting the particular data series at hand. SmartForecasts fully automates this process for you by trying the different forecasting methods in a simulated forecasting tournament. The winner of the tournament is the method that comes closest to  predicting new data values from old. Accuracy is measured by average absolute error (that is, the average error, ignoring any minus signs). The average is computed over a set of forecasts, each using a portion of the data, in a process known as sliding simulation.

Sliding simulation

The sliding simulation sweeps repeatedly through ever-longer portions of the historical data, in each case forecasting ahead the desired number of periods in your forecast horizon. Suppose there are 36 historical data values and you need to forecast six periods ahead. Imagine that you want to assess the forecast accuracy of some particular method, say a moving average of four observations, on the data series at hand.

At one point in the sliding simulation, the first 24 points (only) are used to forecast the 25th through 30th historical data values, which we temporarily regard as unknown. We say that points 25-30 are “held out” of the analysis. Computing the absolute values of the differences between the six forecasts and the corresponding actual historical values provides one instance each of a 1-step, 2-step, 3-step, 4-step, 5-step, and 6-step ahead absolute forecast error. Repeating this process using the first 25 points provides more instances of 1-step, 2-step, 3-step ahead errors, and so on. The average over all of the absolute error estimates obtained this way provides a single-number summary of accuracy.

Methods used in Automatic forecasting

Normally, there are six extrapolative forecasting methods competing in the Automatic forecasting tournament:

• Simple moving average
• Linear moving average
• Single exponential smoothing
• Double exponential smoothing
• Additive version of Winters’ exponential smoothing
• Multiplicative version of Winters’ exponential smoothing

The latter two methods are appropriate for seasonal series; however, they are automatically excluded from the tournament if there are fewer than two full seasonal cycles of data (for example, fewer than 24 periods of monthly data or eight periods of quarterly data).

These six classical, smoothing-based methods have proven themselves to be easy to understand, easy to compute and accurate. You can exclude any of these methods from the tournament if you have a preference for some of the competitors and not others.

1. Forecasting is an art that requires a mix of professional judgment and objective statistical analysis. Successful demand forecasts require a baseline prediction leveraging statistical forecasting methods. Once established, the process can focus on how best to adjust statistical forecasts based on your own insights and business knowledge.

2. The forecasting process is usually iterative. You may need to make several refinements of your initial forecast before you are satisfied. It is important to be able to generate and compare alternative forecasts quickly and easily. Tracking accuracy of these forecasts over time, including alternatives that were not used, helps inform and improve the process.

3. The credibility of forecasts depends heavily on graphical comparisons with historical data.  A picture is worth a thousand words, so always display forecasts via instantly available graphical displays with supporting numerical reports.

4. One of the major technical tasks in forecasting is to match the choice of forecasting technique to the nature of the data. Effective demand forecasting processes employ capabilities that identify the right method to use.  Features of a data series like trend, seasonality or abrupt shifts in level suggest certain techniques instead of others. An automatic selection, which selects and uses the appropriate forecasting method automatically, saves time and ensures your baseline forecast is as accurate as possible.

5. Successful demand forecasting processes work in tandem with other business processes.   For example, forecasting can be an essential first step in financial analysis.  In addition, accurate sales and product demand forecasts are fundamental inputs to a manufacturing company’s production planning and inventory control processes.

6. A good planning process recognizes that forecasts are never exactly correct. Because some error creeps into even the best forecasting process, one of the most useful supplements to a forecast are honest estimates of its margin of error and forecast bias.

What’s all the hoopla around the term “probabilistic forecasting?” Is it just a more recent marketing term some software vendors and consultants have coined to feign innovation? Is there any real tangible difference compared to predecessor “best fit” techniques?  Aren’t all forecasts probabilistic anyway?

To answer this question, it is helpful to think about what the forecast really is telling you in terms of probabilities.  A “good” forecast should be unbiased and therefore yield a 50/50 probability being higher or lower than the actual.  A “bad” forecast will build in subjective buffers (or artificially depress the forecast) and result in demand that is either biased high or low.  Consider a salesperson that intentionally reduces their forecast by not reporting sales they expect to close to be “conservative.” Their forecasts will have negative forecast bias as actuals will nearly always be higher than what they predicted.   On the other hand, consider a customer that provides an inflated forecast to their manufacturer.  Worried about stockouts, they overestimate demand to ensure their supply.  Their forecast will have a positive bias as actuals will nearly always be lower than what they predicted. 

These types of one-number forecasts described above are problematic.  We refer to these predictions as “point forecasts” since they represent one point (or a series of points over time) on a plot of what might happen in the future.   They don’t provide a complete picture because to make effective business decisions such as determining how much inventory to stock or the number of employees to be available to support demand requires detailed information on how much lower or higher the actual will be!  In other words, you need the probabilities for each possible outcome that might occur.  So, by itself, the point forecast isn’t probabilistic one.   

To get a probabilistic forecast, you need to know the distribution of possible demands around that forecast.  Once you compute this, the forecast becomes “probabilistic.”  How forecasting systems and practitioners such as demand planners, inventory analysts, material managers, and CFOs determine these probabilities is the heart of the question: “what makes a forecast probabilistic?”     

Normal Distributions
Most forecasts and the systems/software that produce them start with a prediction of demand.  Then they figure out the range of possible demands around that forecast by making incorrect theoretical assumptions about the distribution.  If you’ve ever used a “confidence interval” in your forecasting software, this is based on a probability distribution around the forecast.  The way this range of demand is determined is to assume a particular type of distribution.  Most often this means assuming a bell shaped, otherwise known as a normal distribution.  When demand is intermittent, some inventory optimization and demand forecasting systems may assume the demand is Poisson shaped. 

After creating the forecast, the assumed distribution is slapped around the demand forecast and you then have your estimate of probabilities for every possible demand – i.e., a “probabilistic forecast.”  These estimates of demand and associated probabilities can then be used to determine extreme values or anything in between if desired.  The extreme values at the upper percentiles of the distribution (i.e., 92%, 95%, 99%, etc.) are most often used as inputs to inventory control models.  For example, reorder points for critical spare parts in an electrical utility might be planned based on a 99.5% service level or even higher.  While a non-critical service part might be planned at an 85% or 90% service level.

The problem with making assumptions about the distribution is that you’ll get these probabilities wrong.  For example, if the demand isn’t normally distributed but you are forcing a bell shaped/normal curve on the forecast then how can then the probabilities will be incorrect.  Specifically, you might want to know the level of inventory needed to achieve a 99% probability of not running out of stock and the normal distribution will tell you to stock 200 units.  But when compared to the actual demand, you come to find out that 200 units only filled demand entirely in 40/50 observations.  So, instead of getting a 99% service level you only achieved an 80% service level!  This is a gigantic miss resulting from trying to fit a square peg into a round hole.  The miss would have led you to take an incorrect inventory reduction.

Empirically Estimated Distributions are Smart
To produce a smart (read accurate) probabilistic forecast you need to first estimate the distribution of demand empirically without any naïve assumptions about the shape of the distribution.  Smart Software does this by running tens of thousands of simulated demand and lead time scenarios.  Our solution leverages patented techniques that incorporate Monte Carlo simulation, Statistical Bootstrapping, and other methods.  The scenarios are designed to simulate real life uncertainty and randomness of both demand and lead times.  Actual historical observations are utilized as the primary inputs, but the solution will give you the option of simulating from non-observed values as well.  For example, just because 100 units was the peak historical demand, that doesn’t mean you are guaranteed to peak out at 100 in the future.  After the scenarios are done you will know the exact probability for each outcome. The “point” forecast then becomes the center of that distribution.  Each future period over time is expressed in terms of the probability distribution associated with that period.

Leaders in Probabilistic Forecasting
Smart Software, Inc. was the first company to ever introduce statistical bootstrapping as part of a commercially available demand forecasting software system twenty years ago.  We were awarded a US patent at the time for it and named a finalist in the APICS Corporate Awards of Excellence for Technological Innovation.  Our NSF Sponsored research that led to this and other discoveries were instrumental in advancing forecasting and inventory optimization.    We are committed to ongoing innovation, and you can find further information about our most recent patent here.