​When you should use traditional extrapolative forecasting techniques.

With so much hype around new Machine Learning (ML) and probabilistic forecasting methods, the traditional “extrapolative” or “time series” statistical forecasting methods seem to be getting the cold shoulder.  However, it is worth remembering that these traditional techniques (such as single and double exponential smoothing, linear and simple moving averaging, and Winters models for seasonal items) often work quite well for higher volume data. Every method is good for what it was designed to do.  Just apply each appropriately, as in don’t bring a knife to a gunfight and don’t use a jackhammer when a simple hand hammer will do. 

Extrapolative methods perform well when demand has high volume and is not too granular (i.e., demand is bucketed monthly or quarterly). They are also very fast and do not use as many computing resources as probabilistic and ML methods. This makes them very accessible.

Are the traditional methods as accurate as newer forecasting methods?  Smart has found that extrapolative methods do very poorly when demand is intermittent. However, when demand is higher volume, they only do slightly worse than our new probabilistic methods when demand is bucketed monthly.  Given their accessibility, speed, and the fact you are going to apply forecast overrides based on business knowledge, the baseline accuracy difference here will not be material.

The advantage of more advanced models like Smart’s GEN2 probabilistic methods is when you need to predict patterns using more granular buckets like daily (or even weekly) data.  This is because probabilistic models can simulate day of the week, week of the month, and month of the year patterns that are going to be lost with simpler techniques.  Have you ever tried to predict daily seasonality with a Winter’s model? Here is a hint: It’s not going to work and requires lots of engineering.

Probabilistic methods also provide value beyond the baseline forecast because they generate scenarios to use in stress-testing inventory control models. This makes them more appropriate for assessing, say, how a change in reorder point will impact stockout probabilities, fill rates, and other KPIs. By simulating thousands of possible demands over many lead times (which are themselves presented in scenario form), you’ll have a much better idea of how your current and proposed stocking policies will perform. You can make better decisions on where to make targeted stock increases and decreases.

So, don’t throw out the old for the new just yet. Just know when you need a hammer and when you need a jackhammer.

What’s different about inventory planning for Maintenance, Repair, and Operations (MRO) compared to inventory planning in manufacturing and distribution environments? In short, it’s the nature of the demand patterns combined with the lack of actionable business knowledge.

Demand Patterns

Manufacturers and distributors tend to focus on the top sellers that generate the majority of their revenue. These items typically have high demand that is relatively easy to forecast with traditional time series models that capitalize on predictable trend and/or seasonality.  In contrast, MRO planners almost always deal with intermittent demand, which is more sparse, more random, and harder to forecast.  Furthermore, the fundamental quantities of interest are different. MRO planners ultimately care most about the “when” question:  When will something break? Whereas the others focus on the “how much” question of units sold.

Business Knowledge

Manufacturing and distribution planners can often count on gathering customer and sales feedback, which can be combined with statistical methods to improve forecast accuracy. On the other hand, bearings, gears, consumable parts, and repairable parts are rarely willing to share their opinions. With MRO, business knowledge about which parts will be needed and when just isn’t reliable (excepting planned maintenance when higher-volume consumable parts are replaced). So, MRO inventory planning success goes only as far as their probability models’ ability to predict future usage takes them. And since demand is so intermittent, they can’t get past Go with traditional approaches.

Methods for MRO

In practice, it is common for MRO and asset-intensive businesses to manage inventories by resorting to static Min/Max levels based on subjective multiples of average usage, supplemented by occasional manual overrides based on gut feel. The process becomes a bad mixture of static and reactive, with the result that a lot of time and money is wasted on expediting.

There are alternative planning methods based more on math and data, though this style of planning is less common in MRO than in the other domains. There are two leading approaches to modeling part and machine breakdown: models based on reliability theory and “condition-based maintenance” models based on real-time monitoring.

Reliability Models

Reliability models are the simpler of the two and require less data. They assume that all items of the same type, say a certain spare part, are statistically equivalent. Their key component is a “hazard function”, which describes the risk of failure in the next little interval of time. The hazard function can be translated into something better suited for decision making: the “survival function”, which is the probability that the item is still working after X amount of use (where X might be expressed in days, months, miles, uses, etc.). Figure 1 shows a constant hazard function and its corresponding survival function.

Figure 1: Constant hazard function and its survival function

A hazard function that doesn’t change implies that only random accidents will cause a failure. In contrast, a hazard function that increases over time implies that the item is wearing out. And a decreasing hazard function implies that an item is settling in. Figure 2 shows an increasing hazard function and its corresponding survival function.

Figure 2: Increasing hazard function and its survival function

Reliability models are often used for inexpensive parts, such as mechanical fasteners, whose replacement may be neither difficult nor expensive (but still might be essential).

Condition-Based Maintenance

Models based on real-time monitoring are used to support condition-based maintenance (CBM) for expensive items like jet engines. These models use data from sensors embedded in the items themselves. Such data are usually complex and proprietary, as are the probability models supported by the data. The payoff from real-time monitoring is that you can see trouble coming, i.e., the deterioration is made visible, and forecasts can predict when the item will hit its red line and therefore need to be taken off the field of play. This allows individualized, pro-active maintenance or replacement of the item.

Figure 3 illustrates the kind of data used in CBM. Each time the system is used, there is a contribution to its cumulative wear and tear. (However, note that sometimes use can improve the condition of the unit, as when rain helps keep a piece of machinery cool). You can see the general trend upward toward a red line after which the unit will require maintenance. You can extrapolate the cumulative wear to estimate when it will hit the red line and plan accordingly.

Figure 3: Illustrating real-time monitoring for condition-based maintenance

To my knowledge, nobody makes such models of their finished goods customers to predict when and how much they will next order, perhaps because the customers would object to wearing brain monitors all the time. But CBM, with its complex monitoring and modeling, is gaining in popularity for can’t-fail systems like jet engines. Meanwhile, classical reliability models still have a lot of value for managing large fleets of cheaper but still essential items.

Smart’s approach
The above condition-based maintenance and reliability approaches require an excessive data collection and cleansing burden that many MRO companies are unable to manage. For those companies, Smart offers an approach that does not require development of reliability models. Instead, it exploits usage data in a different way. It leverages probability-based models of both usage and supplier lead times to simulate thousands of possible scenarios for replenishment lead times and demand.  The result is an accurate distribution of demand and lead times for each consumable part that can be exploited to determine optimal stocking parameters.   Figure 4 shows a simulation that begins with a scenario for spare part demand (upper plot) then produces a scenario of on-hand supply for particular choices of Min/Max values (lower line). Key Performance Indicators (KPIs) can be estimated by averaging the results of many such simulations.

Figure 4: An example of a simulation of spare part demand and on-hand inventory

You can read about Smart’s approach to forecasting spare parts here: https://smartcorp.com/wp-content/uploads/2019/10/Probabilistic-Forecasting-for-Intermittent-Demand.pdf

Probabilistic scenarios are sequences of data points generated to represent potential real-world situations. Unlike scenarios in war games or other simulations, these are synthetic time series used as inputs to system models or as intuition-builders for decision-makers.

For instance, scenarios of future item demand can be fed into Monte Carlo simulation models of inventory control systems, thereby creating a virtual laboratory in which to explore the consequences of management decisions, such as changing reorder points and/or order quantities. In addition, plots of metrics like on-hand inventory or stockouts can help inventory planners deepen their “feel” for the randomness inherent in their operations.

Figure 1 shows daily demand scenarios generated from a single observed demand series recorded over one year. Note that the same data generating process can “look quite different” in detail from sample to sample. This mimics real life.

Figure 1: An observed demand sequence and demand scenarios derived from it.

Figure 2 shows two demand scenarios and their consequences for stock on hand in a particular inventory control system. The difference between the two inventory plots illustrates the degree to which randomness in demand dominates the problem. The top plot shows two episodes of stockout, while the bottom plot shows nine. Averaging over many scenarios will clarify the typical values of Key Performance Metrics (KPIs) such as the average number of stockouts associated with any choice of Reorder Point and Order Quantity (which are 10 and 25, respectively, in Figure 2.)

Figure 2: Two demand scenarios and their consequences for on-hand inventory

In this note, we’ll describe techniques for creating scenarios and list criteria for evaluating scenario generators.

Criteria for Scenarios

As we’ll see below, there are several ways to create scenarios. No matter the source, what criteria define a “good” scenario? There are four main criteria: fidelity, variety, quantity, and cost. Fidelity summarizes how accurately a scenario imitates real-world situations. High fidelity means the scenarios mirror actual events closely, providing a solid foundation for analysis and decision-making. Variety describes the diversity of scenarios a generator can create. A versatile generator can simulate a wide range of potential situations, allowing for a thorough exploration of possibilities and risks. Quantity refers to how many scenarios a generator can produce. A generator that can create a large number of scenarios provides ample data for analysis. Cost considers both the computational and human resources required to produce the scenarios. An efficient scenario generator balances quality with resource usage, ensuring the effort is justified by the value and accuracy of the outcomes.

Scenario Generation

Again, think of a scenario as a time series. How are scenarios created?

1. Geppetto’s Workshop: This approach involves hand-crafting scenarios manually by experts. While it can yield high fidelity (realism), it is very resource-intensive and cannot easily generate variety, which requires a large number of scenarios.
2. Groundhog Day: This method involves repeatedly using a single real-world situation as input. While it’s realistic by definition and cost-effective (no resources are used beyond recording the data), this approach lacks variety and so cannot accurately reflect the diversity of real-world scenarios.
3. Parametric Models: Examples of parametric models are the classics studied in Statistics 101 classes: the Normal, exponential, Poisson, etc. The demand plots in Figure 2 are generated parametrically, being the squares of Poisson random variables. These models generate an unlimited number of low cost scenarios having good variety, but they may not always capture the complexity of real-world data, potentially compromising fidelity. When reality is more complicated, these models generate over-simplified scenarios.
4. Non-Parametric Time Series Bootstraps: This approach can score well on all criteria: fidelity, variety, quantity, and cost. It’s a versatile method that excels in creating massive numbers of realistic scenarios. The synthetic demand histories in Figure 1 are simple bootstrap samples based on the observed values in the top graph. (For some nitty-gritty details about generating scenarios, see the links below.)

Exploiting Scenarios

Scenarios prove their worth in two ways: As inputs to decision making and as intuition-builders. For instance, when demand scenarios are used as inputs to simulation models, they enable stress testing and performance estimation for system design. Scenarios can also serve as intuition-builders for decision-makers or system operators. Their visual representation aids in developing insight into and appreciation for the risks involved in making operational decisions, be they for demand forecasting or inventory management.

Scenario-based analysis is very computer intensive, especially when the scenarios are generated by bootstrapping. At Smart Software, computation happens in the cloud. Imagine the computational load involved in determining reorder points and order quantities for each of tens of thousands of inventory items using hundreds or thousands of demand simulations for each item. Further imagine the software not only evaluating a specific proposed reorder point/order quantity pair but roaming over the entire “design space” of pairs to find the best pair of control parameters for each item. To make this practical, we take advantage of the parallel processing power of the cloud. Essentially, each inventory item is assigned its own computer to use in the calculations, so that all that computing can happen simultaneously rather than sequentially. Now we can cut loose and really get you the results you need.

Learning More

Those interested in further technical details and references can find more information here.

What Makes a Probabilistic Forecast?

Probabilistic Forecasting for Intermittent Demand

People new to the jobs of “demand planner” or “supply planner” are likely to have questions about the various forecasting terms and methods used in their jobs. This note may help by explaining these terms and showing how they relate.

Demand Planning

Demand planning is about how much of what you have to sell will go out the door in the future, e.g., how many what-nots you will sell next quarter. Here are six methodologies often used in demand planning.

• Statistical Forecasting
  • These methods use demand history to forecast future values. The two most common methods are curve fitting and data smoothing.
  • Curve fitting matches a simple mathematical function, like the equation for a straight line (y= a +b∙t) or an interest-rate type curve (y=a∙b^t), to the demand history. Then it extends that line or curve forward in time as the forecast.
  • In contrast, data smoothing does not result in an equation. Instead it sweeps through the demand history, averaging values along the way, to create a smoother version of the history. These methods are called exponential smoothing and moving average. In the simplest case (i.e., in the absence of trend or seasonality, for which variants exist), the goal is to estimate the current average level of demand and use that as the forecast.
  • These methods produce “point forecasts”, which are single-number estimates for each future time period (e.g., “Sales in March will be 218 units”). Sometimes they come with estimates of potential forecast error bolted on using separate models of demand variability (“Sales in March will be 218 ± 120 units”).

• Probabilistic Forecasting
  • This approach keys on the randomness of demand and works hard to estimate forecast uncertainty. It regards forecasting less as an exercise in cranking out specific numbers and more as an exercise in risk management.
  • It explicitly models the variability in demand and uses that to present results in the form of large numbers of scenarios constructed to show the full range of possible demand sequences. These are especially useful in tactical supply planning tasks, such as setting reorder points and order quantities.

• Causal Forecasting
  • Statistical forecasting models use as inputs only the past demand history of the item in question. They regard the up-and-down wiggles in the demand plot as the end result of myriad unnamed factors (interest rates, the price of tea in China, phases of the moon, whatever). Causal forecasting explicitly identifies one or more influences (interest rates, advertising spend, competitors’ prices, …) that could plausibly influence sales. Then it builds an equation relating the numerical values of these “drivers” or “causal factors” to item sales. The equation’s coefficients are estimated by “regression analysis”.

• Judgemental Forecasting
  • Golden Gut. Despite the general availability of gobs of data, some companies pay little attention to the numbers and give greater weight to the subjective judgements of an executive deemed to have a “Golden Gut”, which allows him or her to use “gut feel” to predict what future demand will be. If that person has great experience, has spent a career actually looking at the numbers, and is not prone to wishful thinking or other forms of cognitive bias, the Golden Gut can be a cheap, fast way to plan. But there is good evidence from studies of companies run this way that relying on the Golden Gut is risky.
  • Group Consensus. More common is a process that uses a periodic meeting to create a group consensus forecast. The group will have access to shared objective data and forecasts, but members will also have knowledge of factors that may not be measured well or at all, such as consumer sentiment or the stories relayed by sales reps. It is helpful to have a shared, objective starting point for these discussions consisting of some sort of objective statistical analysis. Then the group can consider adjusting the statistical forecast. This process anchors the forecast in objective reality but exploits all the other information available outside the forecasting database.
  • Scenario Generation. Sometimes several people will meet and discuss “strategic what-if” questions. “What if we lose our Australian customers?” “What if our new product roll-out is delayed by six months?” “What if our sales manager for the mid-west jumps to a competitor?” These bigger-picture questions can have implications for item-specific forecasts and might be added to any group-consensus forecasting meeting.

• New product forecasting
  • New products, by definition, have no sales history to support statistical, probability, or causal forecasting. Subjective forecasting methods can always be used here, but these often rely on a dangerous ratio of hopes to facts. Fortunately, there is at least partial support for objective forecasting in the form of curve fitting.
  • A graph of the cumulative sales of an item often describes some sort of “S-curve”, i.e., a graph that starts at zero, builds up, then levels off to a final lifetime total sales. The curve gets its name because it looks like a letter S somehow smeared and stretched to the right. Now there are an infinite number of S-curves, so forecasters typically pick an equation and subjectively specify some key parameter values, like when sales will hit 25%, 50% and 75% of total lifetime sales and what that final level will be. This is also overtly subjective, but it produces detailed period-by-period forecasts that can be updated as experience builds up. Finally, S-curves are sometimes shaped to match the known history of a similar, predecessor product (“Sales for our last gizmo looked like this, so let’s use that as a template.”).

Supply Planning

Demand planning feeds into supply planning by predicting future sales (e.g., for finished goods) or usage (e.g., for spare parts). Then it is up to supply planning to make sure the items in question will be available to sell or to use.

• Dependent demand
  • Dependent demand is demand that can be determined by its relationship to demand for another item. For instance, a bill of materials may show that a little red wagon consists of a body, a pull bar, four wheels, two axles, and various fasteners to keep the wheels on the axles and connect the pull bar to the body. So if you hope to sell 10 little red wagons, you’d better make 10, which means you need 10×2 = 20 axles, 10×4 = 40 wheels, etc. Dependent demand governs raw materials purchasing, component and subsystems purchasing, even personnel hiring (10 wagons need one high-school kid to put them together over a 1 hour shift).
  • If you have multiple products with partially overlapping bills of materials, you have a choice of two forecasting approaches. Suppose you sell not only little red wagons but little blue baby carriages and that both use the same axles. To predict the number of axles you need you could (1) predict the dependent demand for axles from each product and add the forecasts or (2) observe the total demand history for axles as its own time series and forecast that separately. Which works better is an empirical question that can be tested.

• Inventory management
  • Inventory management entails many different tasks. These include setting inventory control parameters such as reorder points and order quantities, reacting to contingencies such as stockouts and order expediting, setting staffing levels, and selecting suppliers.

• Forecasting plays a role in the first three. The number of replenishment orders that will be made in a year for each product determines how many people are needed to cut PO’s. The number and severity of stockouts in a year determines the number of contingencies that must be handled. The number of PO’s and stockouts in a year will be random but be governed by the choices of inventory control parameters. The implications of any such choices can be modeled by inventory simulations. These simulations will be driven by detailed demand scenarios generated by probabilistic forecasts.

​

Dealing with the day-to-day of inventory management can keep you busy. There’s the usual rhythm of ordering, receiving, forecasting and planning, and moving things around in the warehouse. Then there are the frenetic times – shortages, expedites, last-minute calls to find new suppliers.

All this activity works against taking a moment to see how you’re doing. But you know you have to get your head up now and then to see where you’re heading. For that, your inventory software should show you metrics – and not just one, but a full set of metrics or KPI’s – Key Performance Indicators.

Multiple Metrics

Depending on your role in your organization, different metrics will have different salience. If you are on the finance side of the house, inventory investment may be top of mind: how much cash is tied up in inventory? If you’re on the sales side, item availability may be top of mind: what’s the chance that I can say “yes” to an order? If you’re responsible for replenishment, how many PO’s will your people have to cut in the next quarter?

Availability Metrics

Let’s circle back to item availability. How do you put a number on that? The two most used availability metrics are “service level” and “fill rate.” What’s the difference? It’s the difference between saying “We had an earthquake yesterday” and saying, “We had an earthquake yesterday, and it was a 6.4 on the Richter scale.” Service level records the frequency of stockouts no matter their size; fill rate reflects their severity. The two can seem to point in opposite directions, which causes some confusion. You can have a good service level, say 90%, but have an embarrassing fill rate, say 50%. Or vice versa. What makes them different is the distribution of demand sizes. For instance, if the distribution is very skewed, so most demands are small but some are huge, you might get the 90%/50% split mentioned above. If your focus is on how often you have to backorder, service level is more relevant. If your worry is how big an overnight expedite can get, the fill rate is more relevant.

One Graph to Rule them All

A graph of on-hand inventory can provide the basis for calculating multiple KPI’s. Consider Figure 1, which plots on-hand each day for a year. This plot has information needed to calculate multiple metrics: inventory investment, service level, fill rate, reorder rate and other metrics.

Inventory investment: The average height of the graph when above zero, when multiplied by unit cost of the inventory item, gives quarterly dollar value.

Service level: The fraction of inventory cycles that end above zero is the service level. Inventory cycles are marked by the up movements occasioned by the arrival of replenishment orders.

Fill rate: The amount by which inventory drops below zero and how long it stays there combine to determine fill rate.

In this case, the average number of units on hand was 10.74, the service level was 54%, and the fill rate was 91%.

KPI’s and KPP’s

In the over forty years since we founded Smart Software, I have never seen a customer produce a plot like Figure 1.  Those who are further along in their development do produce and pay attention to reports listing their KPI’s in tabular form, but they don’t look at such a graph. Nevertheless, that graph has value for developing insight into the random rhythms of inventory as it rises and falls.

Where it is especially useful is prospectively. Given market volatility, key variables like supplier lead times, average demand, and demand variability all shift over time. This implies that key control parameters like reorder points and order quantities must adjust to these shifts. For instance, if a supplier says they’ll have to increase their average lead time by 2 days, this will impact your metrics negatively, and you may need to increase your reorder point to compensate. But increase it by how much?

Here is where modern inventory software comes in. It will let you propose an adjustment and then see how things will play out. Plots like Figure 1 let you see and get a feel for the new regime. And the plots can be analyzed to compute KPP’s – Key Performance Predictions.

KPP’s help take the guesswork out of adjustments. You can simulate what will happen to your KPI’s if you change them in response to changes in your operating environment – and how bad things will get if you make no changes.