There’s a stale old joke: “There are two types of people – those who believe there are two types of people, and those who don’t.” We can modify that joke: “There are two types of people – those who know there are three types of supply chain analytics, and those who haven’t yet read this blog.”

The three types of supply chain analytics are “descriptive”, “predictive”, and “prescriptive.” Each plays a different role in helping you manage your inventory. Modern supply chain software lets you exploit all three.

Descriptive Analytics

Descriptive Analytics are the stuff of dashboards. They tell you “what’s happenin’ now.” Included in this category are such summary numbers as dollars currently invested in inventory, current customer service level and fill rate, and average supplier lead times. These statistics are useful for keeping track of your operations, especially when you track changes in them from month to month. You will rely on them every day. They require accurate corporate databases, processed statistically.

Predictive Analytics

Predictive Analytics most commonly manifest as forecasts of demand, often broken down by product and location and sometimes also by customer. These statistics provide early warning so you can gear up production, staffing and raw material procurement to satisfy demand. They also provide predictions of the effect of changes in operating policies, e.g., what happens if we increase our order quantity for Product X from 20 to 25 units? You might rely on Predictive Analytics periodically, perhaps weekly or monthly, when you look up from what’s happening now to see what will happen next. Predictive Analytics uses Descriptive Analytics as a foundation but adds more capability. Predictive Analytics for demand forecasting requires advanced statistical processing to detect and estimate such features of product demand as trend, seasonality and regime change.  Predictive Analytics for inventory management uses forecasts of demand as inputs into models of the operation of inventory policies, which in turn provide estimates of key performance metrics such as service levels, fill rates, and operating costs.

Prescriptive Analytics

Prescriptive Analytics are not about what is happening now, or what will happen next, but about what you should do next, i.e., they recommend decisions aimed at maximizing inventory system performance. You might rely on Prescriptive Analytics to best posture your entire inventory policy. Prescriptive Analytics uses Predictive Analytics as a foundation then adds optimization capability. For instance, Prescriptive Analytics software can automatically work out the best choices for future values of Min’s and Max’s for thousands of inventory items. Here, “best” might mean the values of Min and Max for each item that minimize operating cost (the sum of holding, ordering, and shortage costs) while maintaining a 90% floor on item fill rate.

Example

The figure below shows how supply chain analytics can help the inventory manager. The columns show three predicted Key Performance Indicators (KPI’s): service level, inventory investment, and operating costs (holding costs + ordering costs + shortage costs).

 Figure 1: The three types of analytics used to evaluate planning scenarios

The rows show four alternative inventory policies, expressed as scenarios. The “Live” scenario reports on the values of the KPI’s on July 1, 2018. The “99% All” scenario changes the current policy by raising the service level of all items to 99%. The “75 floor/99 ceiling” scenario raises service levels that are too low up to 75% and lowers very high (i.e., expensive) service levels down to 95%. The “Optimization” scenario prescribes item specific service levels that minimizes total operating costs.

The “Live 07-01-2018” scenario is an example of Descriptive Analytics. It shows the current baseline performance. The software then allows the user to try out changes in inventory policy by creating new “What If” scenarios that might then be converted to named scenarios for further consideration. The next two scenarios are examples of Predictive Analytics. They both assess the consequences of their recommended inventory control policies, i.e., recommended values of Min and Max for all items. The “Optimization” scenario is an example of Prescriptive Analytics because it recommends a best compromise policy.

Consider how the three alternative scenarios compare to the baseline “Live” scenario. The “99% All” scenario raises the item availability metrics, increasing service level from 88% to 99%. However, doing so increases the total inventory investment from $3 million to about $4 million. In contrast, the “75 floor/99 ceiling” scenario increases both service level and reduces the cash tied up in inventory by about $300,000. Finally, the “Optimization” scenario achieves an 80% service level, a reduction from the current 88%, but it cuts more than $2 million from the inventory value and reduces operating costs by more than $400,000 annually. From here, managers could try further options, such as giving back some of the $2 million savings to achieve a higher average service level.

Summary

Modern software packages for inventory planning and inventory optimization should offer three kinds of supply chain analytics: Descriptive, Predictive, and Prescriptive. Their combination lets inventory managers track their operations (Descriptive), forecast where their operations will be in the future (Predictive), and optimize their inventory policies in response in anticipation of future conditions (Prescriptive).

A new metric we call the “Attention Index” will help forecasters identify situations where “data behaving badly” can distort automatic statistical forecasts (see adjacent poem). It quickly identifies those items most likely to require forecast overrides—providing a more efficient way to put business experience and other human intelligence to work maximizing the accuracy of forecasts. How does it work?

Classical forecasting methods, such as the various flavors of exponential smoothing and moving averages, insist on a leap of faith. They require that we trust present conditions to persist into the future. If present conditions do persist, then it is sensible to use these extrapolative methods—methods which quantify the current level, trend, seasonality and “noise” of a time series and project them into the future.

But if they do not persist, extrapolative methods can get us into trouble. What had been going up might suddenly be going down. What used to be centered around one level might suddenly jump to another. Or something really odd might happen that is entirely out of pattern. In these surprising circumstances, forecast accuracy deteriorates, inventory calculations go wrong and general unhappiness ensues.

One way to cope with this problem is to rely on more complex forecasting models that account for external factors that drive the variable being forecasted. For instance, sales promotions attempt to disrupt buying patterns and move them in a positive direction, so including promotion activity in the forecasting process can improve sales forecasting. Sometimes macroeconomic indicators, such as housing starts or inflation rates, can be used to improve forecast accuracy. But more complex models require more data and more expertise, and they may not be useful for some problems—such as managing parts or subsystems, rather than finished goods.

If one is stuck using simple extrapolative methods, it is useful to have a way to flag items that will be difficult to forecast. This is the Attention Index. As the name suggests, items to be forecast with a high Attention Index require special handling—at least a review, and usually some sort of forecast adjustment.

The Attention Index detects three types of problems:

An outlier in the demand history of an item.
An abrupt change in the level of an item.
An abrupt change in the trend of an item.
Using software like SmartForecasts™, the forecaster can deal with an outlier by replacing it with a more typical value.

An abrupt change in level or trend can be dealt with by omitting, from the forecasting calculations, all data from before the “rupture” in the demand pattern—assuming that the item has switched into a new regime that renders the older data irrelevant.

While no index is perfect, the Attention Index does a good job of focusing attention on the most problematic demand histories. This is demonstrated in the two figures below, which were produced with data from the M3 Competition, well known in the forecasting world. Figure 1 shows the 20 items (out of the contest’s 3,003) with the highest Attention Index scores; all of these have grotesque outliers and ruptures. Figure 2 shows the 20 items with the lowest Attention Index scores; most (but not all) of the items with low scores have relatively benign patterns.

If you have thousands of items to forecast, the new Attention Index will be very useful for focusing your attention on those items most likely to be problematic.

Thomas Willemain, PhD, co-founded Smart Software and currently serves as Senior Vice President for Research. Dr. Willemain also serves as Professor Emeritus of Industrial and Systems Engineering at Rensselaer Polytechnic Institute and as a member of the research staff at the Center for Computing Sciences, Institute for Defense Analyses.

A readable, well-organized textbook could be invaluable to “help corporate forecasters-in-training understand the basics of time series forecasting,” as Tom Willemain notes in the conclusion to this review, originally published in Foresight: The International Journal of Applied Forecasting. Principally written for an academic audience, the review also serves inexperienced demand planning professionals by pointing them to an in-depth resource.

This neat little book aims to “introduce the reader to quantitative forecasting of time series in a practical, hands-on fashion.” For a certain kind of reader, it will doubtless succeed, and do so in a stylish way.

The author, Dr. Galit Shmueli, is the SRITNE Chaired Professor of Data Analytics and Associate Professor of Statistics and Information Systems at the Indian School of Business, Hyderabad. She has authored or coauthored several other books on applied statistics and business analytics.

The book is meant to be a text for a “mini-semester” course for graduate or upper-level undergraduate students. I think it would be a stretch to believe there is enough technical material here to serve as the basis for a graduate course, but I could see it working well for undergraduates in industrial engineering or management who have had a prior statistics course (and therefore will indeed be able to “recall that a 95% prediction interval for normally distributed errors is…”).

There are end-of-chapter exercises of appropriate size and even setups for three real-world semester projects, so instructors could use the book as envisioned by the author. The book illustrates its points using XLMiner, an Excel add-in, and students can use the free demo version for almost all the exercises. Text datasets are available from the book’s web site, which also provides a free time series analysis “dashboard” application. The author notes that other software can be used in place of XLMiner and mentions Minitab, JMP, and Rob Hyndman’s forecast library in R.

While reading this book, I was delighted by its clarity. Having spent time recently correcting the technical prose of two otherwise good graduate students, I found the writing in this book to be a refreshing contrast, making technical concepts understandable.

Another virtue of this book is its selection of topics. The technical ones are reasonably standard (smoothing methods, regression using polynomial trends, and dummy variables) but also range a bit toward the more exotic (logistic regression, neural nets, a bit of ARIMA). More impressive is the inclusion of what might be called “meta-topics” relevant to forecasting: performance assessment, an overview of alternative technical approaches, and one on the forecasting process, from definition of goals to ways to gear reports differently for managerial and technical audiences. This is the kind of forecasting wisdom we find in Chris Chatfield’s book (2004), though presented rather less tartly and with less mathematical exposition. I typically recommend Chatfield’s introductory book for more technical readers interested in getting into time series; I would recommend Shmueli’s book for a more general audience.

No review is complete without quibbles. Here are a few—too few to undo my very positive view of this impressive little book:

• The text makes a good case for “well formatted and easily readable” charts (p. 179). But I found many of the screen shots to be poorly printed and difficult to see. The book is otherwise so visually pleasing that these defects seem very out of character. It uses luxurious amounts of white space and whimsical marginal art to great effect, producing a very “light” feel that must surely help comprehension.

• The author claims (p. 115) that smoothing methods (e.g., moving averages, exponential smoothing) cannot be fully automated because “the user must specify smoothing constants.” Of course, this is not so, since there are several software packages that do this, and the text later contradicts itself on this point on page 127.

• The otherwise good discussion of autocorrelation misleads when it claims (p. 88) that negative lag-1 autocorrelation means that “high values are immediately followed by low values and vice versa.” Well, usually, but not always.

When I finished reading this book, I realized immediately that there is another target audience outside the classroom. My company often conducts training sessions on the use of our software, and these include some general background on forecasting methods and processes. If we could excise the material on XLMiner, and even if we couldn’t, this text would make a wonderful “leave behind” to help corporate forecasters-in-training understand the basics of time series forecasting. The book is so well written, well organized and well designed that it might even be read. We can certainly use it to help our new programmers understand the applications they are developing. And this book might even serve as guilty reading for a graduate student who wants to really “get” what’s going on in Box, Jenkins and Reinsel (2008).

Thomas Willemain, PhD, co-founded Smart Software and currently serves as Senior Vice President for Research. Dr. Willemain also serves as Professor Emeritus of Industrial and Systems Engineering at Rensselaer Polytechnic Institute and as a member of the research staff at the Center for Computing Sciences, Institute for Defense Analyses.

Most statistical forecasting works in one direct flow from past data to forecast. Forecasting with leading indicators works a different way. A leading indicator is a second variable that may influence the one being forecasted. Applying testable human knowledge about the predictive power in the relationship between these different sets of data will sometimes provide superior accuracy.

Most of the time, a forecast is based solely on the past history of the item being forecast. Let’s assume that the forecaster’s problem is to predict future unit sales of an important product. The process begins with gathering data on the product’s past sales. (Gregory Hartunian shares some practical advice on choosing the best available data in a previous post to the Smart Forecaster.) This data flows into forecasting software, which analyzes the sales record to measure the level of random variability and exploit any predictable aspects, such as trend or regular patterns of seasonal variability. The forecast is based entirely on the past behavior of the item being forecasted. Nothing that might have caused the wiggles and jiggles in the product’s sales graph is explicitly accounted for. This approach is fast, simple, self-contained and scalable, because software can zip through a huge number of forecasts automatically.

But sometimes the forecaster can do better, at the cost of more work. If the forecaster can peer through the fog of randomness and identify a second variable that influences the one being forecasted, a leading indicator, more accurate predictions are possible.

For example, suppose the product is window glass for houses. It may well be that increases or decreases in the number of construction permits for new houses will be reflected in corresponding increases or decreases in the number of sheets of glass ordered several months later. If the forecaster can distill this “lagged” or delayed relationship into an equation, that equation can be used to forecast glass sales several months hence using known values of the leading indicator. This equation is called a “regression equation” and has a form something like:

Sales of glass in 3 months = 210.9 + 26.7 × Number of housing starts this month.

Forecasting software can take the housing start and glass sales data and convert them into such a regression equation.

Graph displaying a relationship between example figures for time-shifted building permits and demand for glass
Leading indicators demonstrated
However, unlike automatic statistical forecasting based on a product’s past sales, forecasting with a leading indicator faces the same problem as the proverbial recipe for rabbit stew: “First catch a rabbit”. Here the forecaster’s subject matter expertise is critical to success. The forecaster must be able to nominate one or more candidates for the job of leading indicator. After this crucial step, based on the forecaster’s knowledge, experience and intuition, then software can be used to verify that there really is a predictive, time-delayed relationship between the candidate leading indicator and the variable to be forecasted.

This verification step is done using a “cross-correlation” analysis. The software essentially takes as input a sequence of values of the variable to be forecasted and another sequence of values of the supposed leading indicator. Then it slides the data from the forecast variable ahead by, successively, one, two, three, etc. time periods. At each slip in time (called a “lag”, because the leading indicator is lagging further and further behind the forecast variable), the software checks for a pattern of association between the two variables. If it finds a pattern that is too strong to be explained as a statistical accident, the forecaster’s hunch is confirmed.

Obviously, forecasting with leading indicators is more work than forecasting using only an item’s own past values. The forecaster has to identify a leading indicator, starting with a list suggested by the forecaster’s subject matter expertise. This is a “hand-crafting” process that is not suited to mass production of forecasts. But it can be a successful approach for a smaller number of important items that are worth the extra effort. The role of forecasting software, such as our SmartForecasts system, is to help the forecaster authenticate the leading indicator and then exploit it.

Thomas Willemain, PhD, co-founded Smart Software and currently serves as Senior Vice President for Research. Dr. Willemain also serves as Professor Emeritus of Industrial and Systems Engineering at Rensselaer Polytechnic Institute and as a member of the research staff at the Center for Computing Sciences, Institute for Defense Analyses.

Fluctuations in an inventory supply chain are inevitable. Randomness, which can be a source of confusion and frustration, guarantees it. A ship carrying goods from China may be delayed by a storm at sea. A sudden upswing in demand one day can wipe out inventory in a single day, leaving you unable to meet the next day’s demand. Randomness creates frictions that make it hard to do your job.

At first blush, it sometimes seems best to respond to randomness with the ostrich approach: head buried in the sand. You can settle on a prediction and proceed on the assumption that the prediction will always be spot on. The flaw in that approach is that it ignores statistical methods that allow us to make use of a wealth of knowledge about our knowledge itself—how confident we can be in our predictions, and what breadth of possibilities confront us. The efficient approach to tackling the problems that stem from randomness is not to ignore uncertainty, but to embrace it with eyes open.

As a fundamental tenet of Smart Software’s approach to forecasting, we will always provide you with an assessment of the level of uncertainty in forecasts. If you are expecting nothing more than an absolute figure—the demand for widgets in February will be 120 units—you may dismiss the added element of uncertainty as a negative, or lose faith in a forecast you had hoped would be definite. But we argue for what we consider the adult approach; you need to know what you are risking when you commit to a forecast and premise your decision-making upon it.

Your forecasts can have big consequences that go beyond inventory stocking levels. They can determine your raw materials needs or staffing levels—forecasts drive many important resource allocation decisions. If you have too much faith in the most likely outcome, without also specifically considering just how likely it is, you aren’t really understanding the risks you face, and you may put yourself in a precarious position.

The need to make fully informed decisions forces us to see, in a forecast, the plus/minus range of results with a certain likelihood of occurring. In the specific case of forecasts that are going into inventory systems, this is an important part of deliberately planning for contingencies. This is how you determine not only the inventory you need to maintain in order to satisfy typical demand, but also the additional inventory you need on hand to deal with most unexpected outcomes.

This importance only increases when you are trying to maintain a reliable store of critical spare parts. Between the cost of stocking additional inventory, and accounting for the degree of reliability in your forecasts, there is a balance that crystallizes when an airplane that you need in the air is grounded—because you don’t have the replacement for a damaged part.

(While stocking extra inventory relies on the high end of the uncertainty range, if cash flow is tight, it’s the low end of the range that becomes important. Treasury-minded users find value in this other side of uncertainty in scenarios where even minimal overstocking can be more of a problem than a missed sales opportunity, for example. Reliable information about the lowest likely outcomes pays off at this time.)

Inventory theory says that you need to think about the outer ends of likely possibilities and prepare to cope with more scenarios than just what is most likely. Randomness is a reality that can’t be ignored. The average is not the answer.

Thomas Willemain, PhD, co-founded Smart Software and currently serves as Senior Vice President for Research. Dr. Willemain also serves as Professor Emeritus of Industrial and Systems Engineering at Rensselaer Polytechnic Institute and as a member of the research staff at the Center for Computing Sciences, Institute for Defense Analyses.