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.

Are you confused about what is AI and what is machine learning? Are you unsure why knowing more will help you with your job in inventory planning? Don’t despair. You’ll be ok, and we’ll show you how some of whatever-it-is can be useful.

What is and what isn’t

What is AI and how does it differ from ML? Well, what does anybody do these days when they want to know something? They Google it. And when they do, the confusion starts.

One source says that the neural net methodology called deep learning is a subset of machine learning, which is a subset of AI. But another source says that deep learning is already a part of AI because it sort of mimics the way the human mind works, while machine learning doesn’t try to do that.

One source says there are two types of machine learning: supervised and unsupervised. Another says there are four: supervised, unsupervised, semi-supervised and reinforcement.

Some say reinforcement learning is machine learning; others call it AI.

Some of us traditionalists call a lot of it “statistics”, though not all of it is.

In the naming of methods, there is a lot of room for both emotion and salesmanship. If a software vendor thinks you want to hear the phrase “AI”, they may well say it for you just to make you happy.

Better to focus on what comes out at the end

You can avoid some confusing hype if you focus on the end result you get from some analytic technology, regardless of its label. There are several analytical tasks that are relevant to inventory planners and demand planners. These include clustering, anomaly detection, regime change detection, and regression analysis. All four methods are usually, but not always, classified as machine learning methods. But their algorithms can come straight out of classical statistics.

Clustering

Clustering means grouping together things that are similar and distancing them from things that are dissimilar. Sometimes clustering is easy: to separate your customers geographically, simply sort them by state or sales region. When the problem is not so dead obvious, you can use data and clustering algorithms to get the job done automatically even when dealing with massive datasets.

For example, Figure 1 illustrates a cluster of “demand profiles”, which in this case divides all a customer’s items into nine clusters based on the shape of their cumulative demand curves. Cluster 1.1 in the top left contains items whose demand has been petering out, while Cluster 3.1 in the bottom left contains items whose demand has accelerated.  Clustering can also be done on suppliers. The choice of number of clusters is typically left to user judgement, but ML can guide that choice.  For example, a user might instruct the software to “break my parts into 4 clusters” but using ML may reveal that there are really 6 distinct clusters the user should analyze. 

Figure 1: Clustering items based on the shapes of their cumulative demand

Anomaly Detection

Demand forecasting is traditionally done using time series extrapolation. For instance, simple exponential smoothing works to find the “middle” of the demand distribution at any time and project that level forward. However, if there has been a sudden, one-time jump up or down in demand in the recent past, that anomalous value can have a significant but unwelcome effect on the near-term forecast.  Just as serious for inventory planning, the anomaly can have an outsized effect on the estimate of demand variability, which goes directly to the calculation of safety stock requirements.

Planners may prefer to find and remove such anomalies (and maybe do offline follow-up to find out the reason for the weirdness). But nobody with a big job to do will want to visually scan thousands of demand plots to spot outliers, expunge them from the demand history, then recalculate everything. Human intelligence could do that, but human patience would soon fail. Anomaly detection algorithms could do the work automatically using relatively straightforward statistical methods. You could call this “artificial intelligence” if you wish.

Regime Change Detection

Regime change detection is like the big brother of anomaly detection. Regime change is a sustained, rather than temporary, shift in one or more aspects of the character of a time series. While anomaly detection usually focuses on sudden shifts in mean demand, regime change could involve shifts in other features of the demand, such as its volatility or its distributional shape.  

Figure 2 illustrates an extreme example of regime change. The bottom dropped out of demand for this item around day 120. Inventory control policies and demand forecasts based on the older data would be wildly off base at the end of the demand history.

Figure 2: An example of extreme regime change in an item with intermittent demand

Here too, statistical algorithms can be developed to solve this problem, and it would be fair play to call them “machine learning” or “artificial intelligence” if so motivated.  Using ML or AI to identify regime changes in demand history enables demand planning software to automatically use only the relevant history when forecasting instead of having to manually pick the amount of history to introduce to the model. 

Regression analysis

Regression analysis relates one variable to another through an equation. For example, sales of window frames in one month may be predicted from building permits issued a few months earlier. Regression analysis has been considered a part of statistics for over a century, but we can say it is “machine learning” since an algorithm works out the precise way to convert knowledge of one variable into a prediction of the value of another.

Summary

It is reasonable to be interested in what’s going on in the areas of machine learning and artificial intelligence. While the attention given to ChatGPT and its competitors is interesting, it is not relevant to the numerical side of demand planning or inventory management. The numerical aspects of ML and AI are potentially relevant, but you should try to see through the cloud of hype surrounding these methods and focus on what they can do.  If you can get the job done with classical statistical methods, you might just do that, then exercise your option to stick the ML label on anything that moves.

Forecasting inventory requirements is a specialized variant of forecasting that focuses on the high end of the range of possible future demand.

For simplicity, consider the problem of forecasting inventory requirements for just one period ahead, say one day ahead. Usually, the forecasting job is to estimate the most likely or average level of product demand. However, if available inventory equals the average demand, there is about a 50% chance that demand will exceed inventory and result in lost sales and/or lost good will. Setting the inventory level at, say, ten times the average demand will probably eliminate the problem of stockouts, but will just as surely result in bloated inventory costs.

The trick of inventory optimization is to find a satisfactory balance between having enough inventory to meet most demand without tying up too many resources in the process. Usually, the solution is a blend of business judgment and statistics. The judgmental part is to define an acceptable inventory service level, such as meeting 95% of demand immediately from stock. The statistical part is to estimate the 95th percentile of demand.

When not dealing with intermittent demand, you can often estimate the required inventory level by assuming a bell-shaped (Normal) curve of demand, estimating both the middle and the width of the bell curve, then using a standard statistical formula to estimate the desired percentile. The difference between the desired inventory level and the average level of demand is called the “safety stock” because it protects against the possibility of stockouts.

When dealing with intermittent demand, the bell-shaped curve is a very poor approximation to the statistical distribution of demand. In this special case, Smart leverages patented technology for intermittent demand that is designed to accurately forecast the ranges and produce a better estimate of the safety stock needed to achieve the required inventory service level.

A forecast is a prediction about the value of a time series variable at some time in the future. For instance, one might want to estimate next month’s sales or demand for a product item. A time series is a sequence of numbers recorded at equally spaced time intervals; for example, unit sales recorded every month.

The objectives you pursue when you forecast depend on the nature of your job and your business. Every forecast is uncertain; in fact, there is a range of possible values for any variable you forecast. Values near the middle of this range have a higher likelihood of actually occurring, while values at the extremes of the range are less likely to occur. The following figure illustrates a typical distribution of forecast values.

Illustrating a forecast distribution of forecast values

Point forecasts

The most common use of forecasts is to estimate a sequence of numbers representing the most likely future values of the variable of interest. For instance, suppose you are developing a sales and marketing plan for your company. You may need to fill in 12 cells in a financial spreadsheet with estimates of your company’s total revenues over the next 12 months. Such estimates are called point forecasts because you want a single number (data point) for each forecast period. Smart Demand Planner’ Automatic forecasting feature provides you with these point forecasts automatically.

Interval forecasts

Although point forecasts are convenient, you will often benefit more from interval forecasts. Interval forecasts show the most likely range (interval) of values that might arise in the future. These are usually more useful than point forecasts because they convey the amount of uncertainty or risk involved in a forecast. The forecast interval percentage can be specified in the various forecasting dialog boxes in the Demand Planning Software.  Each of the many forecasting methods (automatic, moving average, exponential smoothing and so on) available in Smart Demand Planner allow you to set a forecast interval.

The default configuration in Smart Demand Planner provides 90% forecast intervals. Interpret these intervals as the range within which the actual values will fall 90% of the time. If the intervals are wide, then there is a great deal of uncertainty associated with the point forecasts. If the intervals are narrow, you can be more confident. If you are performing a planning function and want best case and worst case values for the variables of interest at several times in the future, you can use the upper and lower limits of the forecast intervals for that purpose, with the single point estimate providing the most likely value. In the previous figure, the 90% forecast interval extends from 3.36 to 6.64.

Upper percentiles

In inventory control, your goal may be to make good estimates of a high percentile of the demand for a product item. These estimates help you cope with the tradeoff between, on the one hand, minimizing the costs of holding and ordering stock, and, on the other hand, minimizing the number of lost or back-ordered sales due to a stock out. For this reason, you may wish to know the 99th percentile or service level of demand, since the chance of exceeding that level is only 1%.

When forecasting individual variables with features like Automatic forecasting, note that the upper limit of a 90% forecast interval represents the 95th percentile of the predicted distribution of the demand for that variable. (Subtracting the 5th percentile from the 95th percentile leaves an interval containing 95%-5% = 90% of the possible values.) This means you can estimate upper percentiles by changing the value of the forecast interval. In the figure, “Illustrating a forecast distribution”, the 95th percentile is 6.64.

To optimize stocking policies at the desired service level or to let the system recommend which stocking policy and service level generates the best return, consider using Smart Inventory Optimization.   It is designed to support what-if scenarios that show predicted tradeoffs of varying inventory polices including different service level targets.

Lower percentiles

Sometimes you may be concerned with the lower end of the predicted distribution for a variable. Such cases often arise in financial applications, where a low percentile of a revenue estimate represents a contingency requiring financial reserves. You can use Smart Demand Planner in this case in a way analogous to the case of forecasting upper percentiles. In the figure, “Illustrating a forecast distribution” , the 5th percentile is 3.36.

In conclusion, forecasting involves predicting future values, with point forecasts offering single estimates and interval forecasts providing likely value ranges. Smart Demand Planner automates point forecasts and allows users to set intervals, aiding in uncertainty assessment. For inventory control, the tool facilitates understanding upper (e.g., 99th percentile) and lower (e.g., 5th percentile) percentiles. To optimize stocking policies and service levels, Smart Inventory Optimization supports what-if scenarios, ensuring effective decision-making on how much to stock given the risk of stock out you are willing to accept.

Belmont, MA, June 2023 – Smart Software, Inc., provider of industry-leading demand forecasting, planning, and inventory optimization solutions, today announced the award of US Patent 11,656,887, “SYSTEM AND METHOD TO SIMULATE DEMAND AND OPTIMIZE CONTROL PARAMETERS FOR A TECHNOLOGY PLATFORM.”

The patent directs “technical solutions for analyzing historical demand data of resources in a technology platform to facilitate management of an automated process in the platform.” One important application is optimization of parts inventories.

Aspects of the invention include: an advanced bootstrap process that converts a single observed time series of item demand into an unlimited number of realistic demand scenarios; a performance prediction process that executes Monte Carlo simulations of a proposed inventory control policy to assess its performance; and a performance improvement process that uses the performance prediction process to automatically explore the space of alternative system designs to identify optimal control parameter values, selecting ones that minimize operating cost while guaranteeing a target level of item availability.

The new analytic technology described in the patent will form the basis for the upcoming release of the next generation (“Gen2”) of Smart Demand Planner™ and Smart IP&O™. Current customers and resellers can preview Gen2 by contacting their Smart Software sales representative.

Research underlying the patent was self-funded by Smart, supplemented by competitive Small Business Innovation Research grants from the US National Science Foundation.

About Smart Software, Inc.
Founded in 1981, Smart Software, Inc. is a leader in providing businesses with enterprise-wide demand forecasting, planning, and inventory optimization solutions.  Smart Software’s demand forecasting and inventory optimization solutions have helped thousands of users worldwide, including customers such as Disney, Arizona Public Service, Ameren, and The American Red Cross.  Smart’s Inventory Planning & Optimization Platform, Smart IP&O gives demand planners the tools to handle sales seasonality, promotions, new and aging products, multi-dimensional hierarchies, and intermittently demanded service parts and capital goods items.  It also provides inventory managers with accurate estimates of the optimal inventory and safety stock required to meet future orders and achieve desired service levels.  Smart Software is headquartered in Belmont, Massachusetts, and our website is www.smartcorp.com.