Whether you understand it in detail yourself or rely on trustworthy software, math is a fact of life for anyone in inventory management and demand forecasting who is hoping to remain competitive in the modern world.

At a conference recently, the lead presenter in an inventory management workshop proudly proclaimed that he had no need for “high-fallutin’ math”, which was explained to mean anything beyond sixth-grade math.

Math is not everyone’s first love. But if you really care about doing your job well, you can’t approach the work with a grade school mentality. Supply chain tasks like demand forecasting and inventory management are inherently mathematical. The blog associated with edX, a premier site for online college course material, has a great post on this topic, at https://www.mooc.org/blog/how-is-math-used-in-supply-chain. Let me quote the first bit:

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. They can’t go back to how supply chains were 100 years ago—or even two years ago before the pandemic. Instead, new technologies will help streamline and manage the many moving parts. The logistics skills, optimization technologies, and organizational skills used in supply chain all require mathematics.

Our customers don’t need to be experts in supply chain math, they just need to be able to wield the software that contains the math. Software combines users’ experience and subject matter expertise to produce results that make the difference between success and failure. To do its job, the software can’t stop at sixth-grade math; it needs probability, statistics, and optimization theory.

It’s up to us software vendors to package the math in such a way that what goes into the calculations is all that is relevant, even if complicated; and that what comes out is clear, decision-relevant, and defensible when you must justify your recommendations to higher management.

Sixth-grade math can’t warn you when the way you propose to manage a critical spare part will mean a 70% chance of falling short of your item availability target. It can’t tell you how best to adjust your reorder points when a supplier calls and says, “We have a delivery problem.” It can’t save your skin when there is a surprisingly large order and you have to quickly figure out the best way to set up some expedited special orders without busting the operating budget.

So, respect the folk wisdom and don’t bring a knife to a gunfight.

​If you hear the phrase “regime change” on the news, you immediately think of some fraught geopolitical event. Statisticians use the phrase differently, in a way that has high relevance for demand planning and inventory optimization. This blog is about “regime change” in the statistical sense, meaning a major change in the character of the demand for an inventory item.

An item’s demand history is the fuel that powers demand planners’ forecasting machines. In general, the more fuel the better, giving us a better fix on the average level, the volatility, the size and frequency of any spikes, the shape of any seasonality pattern, and the size and direction of any trend.

But there is one big exception to the rule that “more data is better data.” If there is a major shift in your world and new demand doesn’t look like old demand, then old data become dangerous.

Modern software can make accurate forecasts of item demand and suggest wise choices for inventory parameters like reorder points and order quantities. But the validity of these calculations depends on the relevance of the data used in their calculation. Old data from an old regime no longer reflect current reality, so including them in calculations creates forecast error for demand planners and either excess stock or unacceptable stockout rates for inventory planners.

That said, if you were to endure a recent regime change and throw out the obsolete data, you would have a lot less data to work with. This has its own costs, because all the estimates computed from the data would have greater statistical uncertainty even though they would be less biased. In this case, your calculations would have to rely more heavily on a blend of statistical analysis and your own expert judgement.

At this point, you may ask “How can I know if and when there has been a regime change?” If you’ve been on the job for a while and are comfortable looking at timeplots of item demand, you will generally recognize regime change when you see it, at least if it’s not too subtle. Figure 1 shows some real-world examples that are obvious.

Figure 1: Four examples of regime change in real-world item demand

Unfortunately, less obvious changes can still have significant effects. Moreover, most of our customers are too busy to manually review all the items they manage even once per quarter. When you get beyond, say, 100 items, the task of eyeballing all those time series becomes onerous. Fortunately, software can do a good job of continuously monitoring demand for tens of thousands of items and alerting you to any items that may need your attention. Then too, you can arrange for the software to not only detect regime change but also automatically exclude from its calculations all data collected before the most recent regime change, if any. In other words, you can get both automatic warning of regime change and automatic protection from regime change.

For more on the basics of regime change, see our previous blog on the topic: https://smartcorp.com/blog/demandplanningregimechange/  

An Example with Numbers in It

If you would like to learn more, read on to see a numerical example of how much regime change can alter the calculation of a reorder point for a critical spare part. Here is a scenario to illustrate the point.

Scenario

• Goal: calculate the reorder point needed to control the risk of stockout while waiting for replenishment. Assume the target stockout risk is 5%.
• Assume the item has intermittent daily demand, with many days of zero demand.
• Assume daily demand has a Poisson distribution with an average of 1.0 units per day.
• Assume the replenishment lead time is always 30 days.
• The lead time demand will be random, so it will have a probability distribution and the reorder point will be the 95^th percentile of the distribution.
• Assume the effect of regime change is to either raise or lower the mean daily demand.
• Assume there is one year of daily data available for estimating the mean daily unit demand.

Figure 2 Example of change in mean demand and sample of random daily demand

Figure 2 shows one form of this scenario. The top panel shows that the average daily demand increases from 1.0 to 1.5 after 270 days. The bottom panel shows one way that a year’s worth of daily demand might appear. (At this point, you may be feeling that calculating all this stuff is complicated, even for what turns out to be a simplified scenario. That is why we have software!)

Analysis

Successful calculation of the proper reorder point will depend on when regime change happens and how big a change occurs. We simulated regime changes of various sizes at various times within a 365 day period. Around a base demand of 1.0 units per day, we studied shifts in demand (“shift”) of ±25% and ±50% as well as a no change reference case. We located the time of the change (“t.break”) at 90, 180, and 270 days. In each case, we computed two estimates of the reorder point: The “ideal” value given perfect knowledge of the average demand in the new regime (“ROP.true”), and the estimated value of mean demand computed by ignoring the regime change and using all the demand data for the past year (“ROP.all”).

Table 1 shows the estimates of the reorder point computed over 100 simulations. The center block is the reference case, in which there is no change in the daily demand, which remains fixed at 1 unit per day. The colored block at the bottom is the most extreme increasing scenario, with demand increasing to 1.5 units/day either one-third, one-half, or two-thirds of the way through the year.

We can draw several conclusions from these simulations.

ROP.true: The correct choice for reorder point increases or decreases according to the change in mean demand after the regime change. The relationship is not a simple linear one: the table spans a 600% range of demand levels (0.25 to 1.50) but a 467% range of reorder points (from 12 to 56).

ROP.all: Ignoring the regime change can lead to gross overestimates of the reorder point when demand drops and gross underestimates when demand increases.  As we would expect, the later the regime change, the worse the error. For example, if demand increases from 1.0 to 1.5 units per day two-thirds of the way through the year without being noticed, the calculated reorder point of 43 units would fall 13 units short of where it should be.

A word of caution: Table 1 shows that basing the calculations of reorder points using only data from after a regime change will usually get the right answer. What it doesn’t show is that the estimates can be unstable if there is very little demand history after the change. Therefore, in practice, you should wait to react to the regime change until a decent number of observations have accumulated in the new regime. This might mean using all the demand history, both pre- and post-change, until, say, 60 or 90 days of history have accumulated before ignoring pre-change data.

Table 1 Correct and Estimated Reorder Points for different regime change scenarios

Why Scenario-based planning helps planners better manage risk and create better outcomes.

If you are reading this, you are probably a supply chain professional with responsibilities for demand forecasting, inventory management or both. If you live in the 21^st century, you use software of some kind to help you do your job. But what, fundamentally, does your software do for you?

Traditionally, software has served as a delivery vehicle for equations. Even if you decided early on in life that you and equations don’t get along, they can still do something for you, and you can live with them—provided some software keeps all that math at a safe distance away.

This is fine, as far as it goes. But we at Smart Software think you would do better by trading in your equations for scenarios. Most often, the point of an equation is to give “the answer”, typically in the form of a number, as in “next month’s demand for SKUxxx will be 105 units.” Results like these are helpful, but incomplete.

Forecasting can be thought of as a computing problem, but it is more helpful to think of it as an exercise in risk management. The equation’s forecast of 105 units does not include any indication of the uncertainty in the forecast, though there is always some. It does not help you think about plausible contingencies: what if demand is for more than 105 units? What if it’s for fewer than 105? Could it get as high as 130 or as low as 80? Is 80 even remotely likely?

This is where scenario-based analysis shows its advantage. One definition of “scenario” is “a postulated sequence of events.” Our definition is more extensive: a scenario is “a postulated sequence of events and their associated probabilities of happening.” Scenarios are the ultimate what-if planning tool. Forecasting by equation will predict a demand for 105 units. Scenario forecasting produces a bundle of possible demand figures, some more likely and others less so. If there are few or no scenarios as low as 80, you can let that contingency go.

Plus-or-Minus How Much?

Those who are better versed in equation-based forecasting might protest that equation-based software sometimes provides indications of the “plus or minus” of a forecast, complete with a bell-shaped curve indicating the relative likelihood of various contingencies. However, when you see a perfect bell-shaped distribution, you know you are being asked to rely on a theoretical assumption that is only sometimes valid.

Scenario forecasts do not rely on that assumption.  In fact, they need not rely on any pre-conceived mathematical assumption whose main selling point is that it simplifies analysis. You don’t need a simplified analysis–you need a realistic analysis based on facts.

Cutting-edge software produces scenario forecasts, not just for demand planning but also for inventory management. Demand is a key input to inventory software, along with supplier behavior as reflected in replenishment lead times. Both demand and supply need to be forecasted if you want to see the consequences of, for instance, choosing a reorder point of 15 and an order quantity of 25.

Inventory systems are what is called “path sensitive”, meaning that any particular sequence of demand values will yield different performance than the same demand values in a different order. For example, if all your highest demand periods come bunched up, one after another, you’ll have much more difficulty keeping stocked than if the same high demand periods are spaced apart with time to restock in between. Scenarios reflect these differences in sufficient detail to yield average performance metrics reflective of the various contingencies inherent in uncertain demand.

Figure 1 illustrates the difference between an equation-based forecast and forecast scenarios.  The green cells hold 10 months of demand for a spare part. The blue cells hold an equation-based forecast that calls for average demand of 1.5 units in months 11, 12 and 13. The pistachio-colored cells hold eight scenario forecasts, though in practice our software would generate tens of thousands of scenarios. Now, the scenarios also average out to 1.5 units per month, but they go further and display the wide variety of ways that the next three months could play out. For instance, reading vertically, the monthly demand could range from 0 to 3. Reading horizontally, the three-month totals could range from 0 to 6, compared to the equation-based estimate of 4.5. Continuing with this toy example, if you have 5 units on hand and the replenishment lead time is greater than 3 months, the equation-based model says you will be ok over the next 3 months, but the scenario-based results say you have 1 chance in 8 (12.5%) chance of stocking out. Equivalently, you have an 87.5% service level. If the part is critical and you are aiming for a 95% service level, you are at risk of missing your item availability goal.

Figure 1: Comparing equation-based and scenario-based forecasts

Summary

Remember, equation-based forecasting gives you information, but shallow information. Scenario-based forecasting can tell you not just what result is most likely but also how reliable any of a variety of predictions are—and this allows you to bring your judgment to bear on balancing risk and stocking expenses—all automated to scale to a vast catalog of items.

In Smart Software’s forty-plus years of providing forecasting software, we’ve met many people who find themselves, perhaps surprisingly, becoming demand forecasters. This blog is aimed primarily at those fortunate individuals who are about to start this adventure (though seasoned pros may enjoy the refresher).

Welcome to the field! Good forecasting can make a big difference to your company’s performance, whether you are forecasting to support sales, marketing, production, inventory, or finance.

There is a lot of math and statistics underlying demand forecasting methods, so your assignment suggests that you are not one of those math-phobic people who would rather be poets. Luckily, if you are feeling a bit shaky and not yet healed from your high school geometry class, a lot of the math is built into forecasting software, so your first job is to leave the math for later while you get a view of the big picture. It is indeed a big picture, but let’s isolate few of the ideas that will most help you succeed.

1. Demand Forecasting is a team sport. Even in a small company, the demand planner is part of a team, with some folks bringing the data, some bringing the tech, and some bringing the business judgment. In a well-run business, your job will never be to simply feed some data into a program and send out a forecast report. Many companies have adopted a process called Sales and Operations Planning (S&OP) in which your forecast will be used to kick off a meeting to make certain judgments (e.g., Should we assume this trend will continue? Will it be worse to under-forecast or over-forecast?) and to blend extra information into the final forecast (e.g., sales force input, business intelligence on competitors’ moves, promotions). The implication for you is that your skills at listening and communicating will be important to your success.

2. Statistical Forecasting engines need good fuel. Historical data is the fuel used by statistical forecasting programs, so bad or missing or delayed data can degrade your work product. Your job will implicitly include a quality control aspect, and you must keep a keen eye on the data that are supplied to you. Along the way, it is a good idea to make the IT people your friends.

3. Your name is on your forecasts. Like it or not, if I send forecasts up the chain of command, they get labeled as “Tom’s forecasts.” I must be prepared to own those numbers. To earn my seat at the table, I must be able to explain what data my forecasts were based on, how they were calculated, why I used Method A instead of Method B to do the calculations, and especially how firm or squishy they are. Here honesty is important. No forecast can reasonably be expected to be perfectly accurate, but not all managers can be expected to be perfectly reasonable. If you’re unlucky, your management will think that your reports of forecast uncertainty suggest either ignorance or incompetence. In truth, they indicate professionalism. I have no useful advice about how best to manage such managers, but I can warn you about them. It’s up to you to educate those who use your forecasts. The best managers will appreciate that.

4. Leave your spreadsheets behind. It’s not uncommon for someone to be promoted to forecaster because they were great with Excel. Unless you are with an unusually small company, the scale of modern corporate forecasting overwhelms what you can handle with spreadsheets. The increasing speed of business compounds the problem: the sleepy tempo of annual and quarterly planning meetings is rapidly giving way to weekly or even daily re-forecasts as conditions change. So, be prepared to lean on a professional vendor of modern, scalable cloud-based demand planning and statistical forecasting software for training and support.

5. Think visually. It will be very useful, both in deciding how to generate demand forecasts and in presenting them to management, so take advantage of the visualization capabilities built into forecasting software. As I noted above, in today’s high-frequency business world, the data you work with can change rapidly, so what you did last month may not be the right thing to do this month. Literally keep an eye on your data by making simple plots, like “timeplots” that show things like trend or seasonality or (especially) changes in trend or seasonality or anomalies that must be dealt with. Similarly, supplementing tables of forecasts with graphs comparing current forecasts to prior forecasts to actuals can be very helpful in an S&OP process. For example, timeplots showing past values, forecasted values, and “forecast intervals” indicating the objective uncertainty in the forecasts provide a solid basis for your team to fully appreciate the message in your forecasts.

That’s enough for now. As a person who’s taught in universities for half a century, I’m inclined to start into the statistical side of forecasting, but I’ll save that for another time. The five tips above should be helpful to you as you grow into a key part of your corporate planning team. Welcome to the game!

1. Blaming Shortages on Lead Time Variability
Suppliers will often be late, sometimes by a lot. Lead time delays and supply variability are supply chain facts of life, yet inventory carrying organizations are often caught by surprise when a supplier is late.  An effective inventory planning process embraces these facts of life and develops policies that effectively account for this uncertainty.  Sure, there will be times when lead time delays come out of nowhere.  But most often the stocking policies like reorder points, safety stocks, and Min/Max levels aren’t recalibrated often enough to catch changes in the lead time over time.  Many companies only review the reorder point after it has been breached, instead of recalibrating after each new lead time receipt.  We’ve observed situations where the Min/Max settings are only recalibrated annually or are even entirely manual.  If you have a mountain of parts using old Min/Max levels and associated lead times that were relevant a year ago, it should be no surprise that you don’t have enough inventory to hold you until the next order arrives.

2. Blaming Excess on Bad Sales/Customer Forecasts
Forecasts from your customers or your sales team are often intentionally over-estimated to ensure supply, in response to past inventory shortages where they were left out to dry. Or, the demand forecasts are inaccurate simply because the sales team doesn’t really know what their customer demand is going to be but are forced to give a number. Demand Variability is another supply chain fact of life, so planning processes need to do a better job account for it.  Why should rely on sales teams to forecast when they best serve the company by selling? Why bother playing the game of feigning acceptance of customer forecasts when both sides know it is often nothing more than a WAG?  A better way is to accept the uncertainty and agree on a degree of stockout risk that is acceptable across groups of items.  Once the stockout risk is agreed to, you can generate an accurate estimate of the safety stock needed to counter the demand variability.  The catch is getting buy-in, since you may not be able to afford super high service levels across all items.  Customers must be willing to pay a higher price per unit for you to deliver extremely high service levels.  Sales people must accept that certain items are more likely to have backorders if they prioritize inventory investment on other items.  Using a consensus safety stock process ensures you are properly buffering and setting the right expectations.  When you do this, you free all parties from having to play the prediction game they were not equipped to play in the first place.

3. Blaming Problems on Bad Data
“Garbage In/Garbage Out” is a common excuse for why now is not the right time to invest in planning software. Of course, it is true that if you feed bad data into a model, you won’t get good results, but here’s the thing:  someone, somewhere in the organization is planning inventory, building a forecast, and making decisions on what to purchase. Are they doing this blindly, or are they using data they have curated in a spreadsheet to help them make inventory planning decisions? Hopefully, the latter.  Combine that internal knowledge with software, automating data import from the ERP, and data cleansing.  Once harmonized, your planning software will provide continually updated, well-structured demand and lead time signals that now make effective demand forecasting and inventory optimization possible.  Smart Software cofounder Tom Willemain wrote in an IBF newsletter that “many data problems derive from data having been neglected until a forecasting project made them important.” So, start that forecasting project, because step one is making sure that “what goes in” is a pristine, documented, and accurate demand signal.