The Smart Forecaster

 Pursuing best practices in demand planning,

forecasting and inventory optimization

If you keep up with the news about supply chain analytics, you are more frequently encountering the phrase “probabilistic forecasting.” If this phrase is puzzling, read on.

You probably already know what “forecasting” means. And you probably also know that there seem to be lots of different ways to do it. And you’ve probably heard pungent little phrases like “every forecast is wrong.” So you know that some kind of mathemagic might calculate that “the forecast is you will sell 100 units next month”, and then you might sell 110 units, in which case you have a 10% forecast error.

You may not know that what I just described is a particular kind of forecast called a “point forecast.” A point forecast is so named because it consists of just a single number (i.e., one point on the number line, if you recall the number line from your youth).

Point forecasts have one virtue: They are simple. They also have a flaw: They give rise to snarky statements like “every forecast is wrong.” That is, in most realistic cases, it is unlikely that the actual value will exactly equal the forecast. (Which isn’t such a big deal if the forecast is close enough.)

This gets us to “probabilistic forecasting.” This approach is a step up, because instead of producing a single-number (point) forecast, it yields a probability distribution for the forecast. And unlike traditional extrapolative models that rely purely on the historical data, probabilistic forecasts have the ability to simulate future values that aren’t anchored to the past.

“Probability distribution” is a forbidding phrase, evoking some arcane math that you may have heard of but never studied. Luckily, most adults have enough life experience to have an intuitive grasp of the concept.  When broken down, it’s quite straightforward to understand.

Imagine the simple act of flipping two coins. You might call this harmless fun, but I call it a “probabilistic experiment.” The total number of heads that turn up on the two coins will be either zero, one or two. Flipping two coins is a “random experiment.” The resulting number of heads is a “random variable.” It has a “probability distribution”, which is nothing more than a table of how likely it is that the random variable will turn out to have any of its possible values. The probability of getting two heads when the coins are fair works out to be ¼, as is the probability of no heads. The chance of one head is ½.

The same approach can describe a more interesting random variable, like the daily demand for a spare part.  Figure 2 shows such a probability distribution. It was computed by compiling three years of daily demand data on a certain part used in a scientific instrument sold to hospitals.


Probabilistic demand forecast 1

Figure 1: The probability distribution of daily demand for a certain spare part


The distribution in Figure 1 can be thought of as a probabilistic forecast of demand in a single day. For this particular part, we see that the forecast is very likely to be zero (97% chance), but sometimes will be for a handful of units, and once in three years will be twenty units. Even though the most likely forecast is zero, you would want to keep a few on hand if this part were critical (“…for want of a nail…”)

Now let’s use this information to make a more complicated probabilistic forecast. Suppose you have three units on hand. How many days will it take for you to have none? There are many possible answers, ranging from a single day (if you immediately get a demand for three or more) up to a very large number (since 97% of days see no demand).  The analysis of this question is a bit complicated because of all the many ways this situation can play out, but the final answer that is most informative will be a probability distribution. It turns out that the number of days until there are no units left in stock has the distribution shown in Figure 2.

Probabilistic demand forecast 2

Figure 2: Distribution of the number of days until all three units are gone


The average number of days is 74, which would be a point forecast, but there is a lot of variation around the average. From the perspective of inventory management, it is notable that there is a 25% chance that all the units will be gone after 32 days. So if you decided to order more when you were down to only three on the shelf, it would be good to have the supplier get them to you before a month has passed. If they couldn’t, you’d have a 75% chance of stocking out – not good for a critical part.

The analysis behind Figure 2 involved making some assumptions that were convenient but not necessary if they were not true. The results came from a method called “Monte Carlo simulation”, in which we start with three units, pick a random demand from the distribution in Figure 1, subtract it from the current stock, and continue until the stock is gone, recording how many days went by before you ran out. Repeating this process 100,000 times produced Figure 2.

Applications of Monte Carlo simulation extend to problems of even larger scope than the “when do we run out” example above. Especially important are Monte Carlo forecasts of future demand. While the usual forecasting result is a set of point forecasts (e.g., expected unit demand over the next twelve months), we know that there are any number of ways that the actual demand could play out. Simulation could be used to produce, say, one thousand possible sets of 365 daily demand demands.

This set of demand scenarios would more fully expose the range of possible situations with which an inventory system would have to cope. This use of simulation is called “stress testing”, because it exposes a system to a range of varied but realistic scenarios, including some nasty ones. Those scenarios are then input to mathematical models of the system to see how well it will cope, as reflected in key performance indicators (KPI’s). For instance, in those thousand simulated years of operation, how many stockouts are there in the worst year? the average year? the best year? In fact, what is the full probability distribution of the number of stockouts in a year, and what is the distribution of their size?

Figures 3 and 4 illustrate probabilistic modeling of an inventory control system that converts stockouts to backorders. The system simulated uses a Min/Max control policy with Min = 10 units and Max = 20 units.

Figure 3 shows one simulated year of daily operations in four plots. The first plot shows a particular pattern of random daily demand in which average demand increases steadily from Monday to Friday but disappears on weekends. The second plot shows the number of units on hand each day. Note that there are a dozen times during this simulated year when inventory goes negative, indicating stockouts. The third plot shows the size and timing of replenishment orders. The fourth plot shows the size and timing of backorders.  The information in these plots can be translated into estimates of inventory investment, average units on hand, holding costs, ordering costs and shortage costs.

Probabilistic demand forecast 3

Figure 3: One simulated year of inventory system operation


Figure 3 shows one of one thousand simulated years. Each year will have different daily demands, resulting in different values of metrics like units on hand and the various components of operating cost. Figure 4 plots the distribution of 1,000 simulated values of four KPI’s. Simulating 1,000 years of imagined operation exposes the range of possible results so that planners can account not just for average results but also see best-case and worst-case values.

Probabilistic demand forecast 4

Figure 4: Distributions of four KPI’s based on 1,000 simulations


Monte Carlo simulation is a low-math/high-results approach to probabilistic forecasting: very practical and easy to explain. Advanced probabilistic forecasting methods employed by Smart Software expand upon standard Monte Carlo simulation, yielding extremely accurate estimates of required inventory levels.


Leave a Comment

Related Posts

Call an Audible to Proactively Counter Supply Chain Noise

Call an Audible to Proactively Counter Supply Chain Noise

You know the situation: You work out the best way to manage each inventory item by computing the proper reorder points and replenishment targets, then average demand increases or decreases, or demand volatility changes, or suppliers’ lead times change, or your own costs change.

Recent Posts

  • Epicor Prophet 21 with Forecasting Inventory PlanningExtend Epicor Prophet 21 with Smart IP&O’s Forecasting & Dynamic Reorder Point Planning
    Smart Inventory Planning & Optimization (Smart IP&O) can help with inventory ordering functionality in Epicor P21, reduce inventory, minimize stockouts and restore your organization’s trust by providing robust predictive analytics, consensus-based forecasting, and what-if scenario planning. […]
  • Supply Chain Math large-scale decision-making analyticsSupply Chain Math: Don’t Bring a Knife to a Gunfight
    Math and the supply chain go hand and hand. As supply chains grow, increasing complexity will drive companies to look for ways to manage large-scale decision-making. Math is a fact of life for anyone in inventory management and demand forecasting who is hoping to remain competitive in the modern world. Read our article to learn more. […]
  • Mature bearded mechanic in uniform examining the machine and repairing it in factoryService Parts Planning: Planning for consumable parts vs. Repairable Parts
    When deciding on the right stocking parameters for spare and replacement parts, it is important to distinguish between consumable and repairable servoce parts. These differences are often overlooked by inventory planning software and can result in incorrect estimates of what to stock. Different approaches are required when planning for consumables vs. repairable service parts. […]
  • Four Common Mistakes when Planning Replenishment TargetsFour Common Mistakes when Planning Replenishment Targets
    How often do you recalibrate your stocking policies? Why? Learn how to avoid key mistakes when planning replenishment targets by automating the process, recalibrating parts, using targeting forecasting methods, and reviewing exceptions. […]
  • Smart Software is pleased to introduce our series of webinars, offered exclusively for Epicor Users.Extend Epicor Kinetic’s Forecasting & Min/Max Planning with Smart IP&O
    Epicor Kinetic can manage replenishment by suggesting what to order and when via reorder point-based inventory policies. The problem is that the ERP system requires that the user either manually specify these reorder points, or use a rudimentary “rule of thumb” approach based on daily averages. In this article, we will review the inventory ordering functionality in Epicor Kinetic, explain its limitations, and summarize how to reduce inventory, and minimize stockouts by providing the robust predictive functionality that is missing in Epicor. […]

    Inventory Optimization for Manufacturers, Distributors, and MRO

    • Blanket Orders Smart Software Demand and Inventory Planning HDBlanket Orders
      Our customers are great teachers who have always helped us bridge the gap between textbook theory and practical application. A prime example happened over twenty years ago, when we were introduced to the phenomenon of intermittent demand, which is common among spare parts but rare among the finished goods managed by our original customers working in sales and marketing. This revelation soon led to our preeminent position as vendors of software for managing inventories of spare parts. Our latest bit of schooling concerns “blanket orders.” […]
    • Hand placing pieces to build an arrowProbabilistic Forecasting for Intermittent Demand
      The New Forecasting Technology derives from Probabilistic Forecasting, a statistical method that accurately forecasts both average product demand per period and customer service level inventory requirements. […]
    • Engineering to Order at Kratos Space – Making Parts Availability a Strategic Advantage
      The Kratos Space group within National Security technology innovator Kratos Defense & Security Solutions, Inc., produces COTS s software and component products for space communications - Making Parts Availability a Strategic Advantage […]
    • wooden-figures-of-people-and-a-magnet-team-management-warehouse inventoryManaging the Inventory of Promoted Items
      In a previous post, I discussed one of the thornier problems demand planners sometimes face: working with product demand data characterized by what statisticians call skewness—a situation that can necessitate costly inventory investments. This sort of problematic data is found in several different scenarios. In at least one, the combination of intermittent demand and very effective sales promotions, the problem lends itself to an effective solution. […]