Anybody doing the job knows that managing inventory can be stressful. Common stressors include: Customers with “special” requests, IT departments with other priorities, balky ERP systems running on inaccurate data, raw material shortages, suppliers with long lead times in far-away countries where production often stops for various reasons and more. This note will address one particular and ever-present source of stress: demand variability.

Everybody Has a Forecasting Problem

Suppose you manage a large fleet of spare parts. These might be surgical equipment for your hospital, or repair parts for your power station. Your mission is to maximize up time. Your enemy is down time. But because breakdowns hit at random, you are constantly in reactive mode. You might hope for rescue from forecasting technologies. But forecasts are inevitably imperfect to some degree: the element of surprise is always present.  You might wait for Internet of Things (IOT) tech to be deployed on your equipment to monitor and detect impending failures, helping you schedule repairs well in advance. But you know you can’t meter up the thousands of small things that can fail and disable a big thing.

So, you decide to combine forecasting with inventory management and build buffers or safety stock to protect against surprise spikes in demand. Now you have to work out how much safety stock to maintain, knowing that too little means vulnerability and too much means bloat.

Suppose you handle finished goods inventories for a make-to-stock company. Your problem is essentially the same as in managing service parts: You have external customers and uncertain demand. But you may also have additional problems in terms of synchronizing multiple suppliers of components that you assemble into finished goods. The suppliers want you to tell them how much of their stuff to make so you can make your stuff, but you don’t know how much of your own stuff you’ll need to make.

Finally, suppose you handle finished goods in a build-to-order company. You might think that you no longer have a forecasting problem, since you don’t build until you are paid to build. But you do have a forecasting problem. Since your finished goods might be assembled from a mixture of components and sub-assemblies, you have to translate some forecast of finished goods demand to work out a forecast of those components. Otherwise, you will go to make your finished goods and discover that you don’t have a required component and have to wait until you can re-actively assemble everything you need. And your customers might not be willing to wait.

So, everybody has a forecasting problem.

What Makes Forecasting Difficult

Forecasting can be quick, easy and dead accurate – as long as the world is simple. If demand for your product is 10 units every week, month after month, you can make very accurate forecasts. But life is not quite like that. If you’re lucky and life is almost like that – maybe weekly demand is more like {10, 9, 10, 8, 12, 10, 10…} — you can still make very accurate forecast and just make minor adjustments around the edges. But if life is as it more often is – maybe weekly demand looks like {0, 0, 7, 0, 0, 0, 23, 0 …} – demand forecasting is difficult indeed. The key distinction is demand variability: it’s the zigging and zagging that creates the pain.

Safety Stock Takes Over Where Forecasting Leaves Off

Statistical forecasting methods are an important part of the solution. They let you squeeze as much advantage as possible from the historical patterns of demand your company has recorded for each item. The job of forecasts is to describe what is typical, which provides the base on which to cope with randomness in demand. Statistical forecasting techniques work by finding “big picture” features in demand records, such as trend and seasonality, then projecting those into the future. They all implicitly assume that whatever patterns exist now will persist, so 5% growth will continue, and July demand will always be 20% higher than February demand. To get to that point, statistical forecasting methods use some form of averaging to smother the “noise” in the demand history.

But then the rest of the job falls on inventory management, because the atypical, random component of future demand will still be a hassle in the future. This inevitable level of uncertainty has to be handled by the “shock-absorber” called safety stock.

The same methods that produce forecasts of trend and/or seasonality can be used to estimate the amount of forecast error. This has to be done carefully using a method called “holdout analysis”.  It works like this. Suppose you have 365 observations of daily demand for Item X, which has a replenishment lead time of 10 days. You want to know how many units will be demanded over some future 10-day period. You might input the first 305 days of demand history into the forecasting technique and get forecasts for the next 10 days, days 306-315.

The answer gives you one estimate of the 10-day total demand. Importantly, it also gives you one estimate of the variability around that forecast, i.e., the forecast error, the difference between what actually happened in days 306-315 and what was forecasted. Now you can repeat the process, this time using the first 306 days to forecast the next 10, the first 307 days to forecast the next 10, etc. You end up with 52 honest estimates of the variability of total demand over a 10-day lead time. Suppose 95% of those estimates are less than 28 units. Then 28 units would be a pretty safe safety stock to add to the forecast, since you will run into shortages only 5% of the time.

Modern statistical software does these calculations automatically. It can ease at least one of the chronic headaches of inventory management by helping you cope with demand variability.

Most demand forecasts are partial or incomplete: They provide only one single number: the most likely value of future demand. This is called a point forecast. Usually, the point forecast estimates the average value of future demand.  Interval forecasts provide an estimate of the possible future range of demand (i.e. demand has a 90% chance of being between 50 – 100 units).  Probabilistic forecasts take it a step further and provide additional information.  Knowing more is always better than knowing less and the probabilistic forecast provides that extra information so crucial for inventory management. This video blog by Dr. Thomas Willemain explains each type of forecast and the advantages of probabilistic forecasting.

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Point forecast (green) shows what is most likely to happen.  The Interval Forecast shows the range (blue) of possibilities.

Probability Forecast shows the probability of each value occurring

Most demand forecasts are partial or incomplete: They provide only one single number: the most likely value of future demand. This is called a point forecast. Usually, the point forecast estimates the average value of future demand.

Much more useful is a forecast of full probability distribution of demand at any future time. This is more commonly referred to as probability forecasting and is much more useful.

The Average is Not the Answer

The one advantage of a point forecast is its simplicity. If your ERP system is also simple, the point forecast fills in the one number needed by the ERP system to do workforce scheduling or raw material purchases.

The disadvantage of a point forecast is that it is too simple. It ignores additional information in an item’s demand history that can give you a more complete picture of how demand might unfold: a probability forecast.

Going Beyond the Average: Probability Forecasting

While the point forecast provides limited information, e.g., “The most likely demand next month is 15 units”, the probability forecast adds crucial information, e.g., “There is a 20% chance that demand will exceed 28 units and a 10% chance that it will be less than 5 units”.

This information lets you do risk assessment and contingency planning. Contingency planning is necessary because the point forecast usually has only a small chance of actually being correct. A probability forecast may also say “The chance of demand being 15 units is only 10%, even though it is the single most likely value.” In other words, there is a 90% chance that the point forecast is wrong. This kind of error is not a mistake in the forecasting calculations: it is the reality of dealing with demand volatility. It might better be called an “uncertainty” than an “error”.

An operations manager can use the extra information in a probability forecast in both informal and formal ways. Informally, even if an ERP system requires a single-number forecast as input, a wise manager will want to have some clue about the risks associated with that point forecast, i.e., its margin of error. So a forecast of 15 ± 1 unit is a lot safer than a forecast of 15 ± 10. The ± part is a compression of a probabilistic forecast. Figure 1 below shows an item’s demand history (red line), point forecasts for the next 12 months (green line) and their margins of error (cyan lines). The lowest forecast of about 3,300 units occurs in June, but the actual demand might be as much as 800 units higher or lower.

Bonus: Application to Inventory Management

Inventory management requires that you balance item availability against the inventory cost. It turns out that knowing the full probability distribution of demand over a replenishment lead time is essential for setting reorder points (also called mins) on a rational, scientific basis. Figure 2 shows a probability forecast of total demand during the 33 week replenishment lead time for a certain spare part. While the average lead time demand is 3 units, the most likely demand is zero, and a reorder point of 14 is needed to insure that the chance of stocking out is only 1%. Once again, the average is not the answer.

Knowing more is always better than knowing less and the probability forecast provides that extra bit of crucial information. Software has been able to supply a point forecast for over 40 years, but modern software can do better and provide the whole picture.

Figure 1: The red line shows the demand history of a finished good. The green line shows the point forecasts for the next 12 months. The blue lines indicate the margins of error in the 12 point forecasts.

Figure 2: A probabilistic forecast of demand for a spare part over a 33 week replenishment lead time. The most likely demand is zero, the average demand is 3, but a reorder point of 14 units is required to have only a 1% chance of stock out.

Demand planning takes time and effort. It’s worth the effort to the extent that it actually helps you make what you need when you need it.

But the job can be done well or poorly. We see many manufacturers stopping at the first level when they could easily go to the second level. And with a little more effort, they could go all the way to the third level, utilizing probabilistic modeling to convert demand planning results into an inventory optimization process.

The First Level

The first level is making a demand forecast using statistical methods. Figure 1 shows a first level effort: an item’s demand history (red line) and its expected 12-month forecast (green line).

The forecast is bare bones. It only projects expected demand ignoring that demand is volatile and will inevitably create forecast error. (This is another example of an important maxim: “The Average is Not the Answer”). The forecast is as likely to be too high as it is to be too low, and there is no indication of forecast uncertainty accompanying the forecast. This means the planner has no estimate of the risk associated with committing to the forecast. Still, this forecast does provide a rational basis for production planning, personal scheduling, and raw materials purchase. So, it’s much better than guessing.

The Second Level

The second level takes explicit account of forecast uncertainty. Figure 2 shows a second level effort, known as a “percentile forecast”.

Now we see an explicit indication of forecast uncertainty. The cyan line above the green forecast line represents the projected 90th percentile of monthly demand. That is, the demand in each future month has a 90% chance of falling at or below the cyan line. Put another way, there is a 10% chance of demand exceeding the cyan line in each month.

This analysis is much more useful because it supports risk management. If it is important to assure sufficient supply of this item, then it makes sense to produce to the 90th percentile instead of to the expected forecast. After all, it’s a coin flip as to whether the expected forecast will result in enough production to meet monthly demand. This second level forecast is, in effect, a rough substitute for a careful inventory management process.

Figure 2. A percentile forecast, where the cyan line estimates the 90th percentiles of monthly demand.

Going All the Way to the Third Level

Best practice is the Third Level, which uses demand planning as a foundation for completing a second task: explicit inventory optimization. Figure 3 shows the fundamental plot for the efficient management of our finished good, assuming it has a 1 month production lead time.

Figure 3 shows the utilization of probabilistic forecasting and how much draw-down in finished good inventory might take place over a one month production lead time. The uncertainty in demand is apparent in the spread of the possible demand, from a low of 0 to a high of 35, with 15 units being the most likely value. The vertical red line at 22 indicates the “reorder point“ (or “min” or “trigger value”) corresponding to keeping the chance of stocking out while waiting for replenishment to a low 5%. When inventory drops to 22 or below, it is time to order more. The Third Level uses probabilistic demand forecasting with full exposure of forecast uncertainty to efficiently manage the stock of the finished product.

To Sum Up

Forecasting the most likely demand for an item is a useful first step. It gets you halfway to where you want to be. But it provides an incomplete guide to planning because it ignores demand volatility and the forecast uncertainty that it creates. Adding a cushion to the demand forecast gets you further along, because it lessen the risk that a jump in demand will leave you short of product. This cushion can be calculated by probabilistic forecasting approaches that forecasts a high percentile of the distribution of future demand. And if you want to take one step further, you can feed forecasts of the demand distribution over a lead time to calculate reorder points (mins) to ensure that you have an acceptably low level of stock-out risk.

Given what modern forecasting technology can do for you, why would you want to stop halfway to your goal?