The best inventory planning processes rely on statistical analysis to uncover relevant facts about the data. For instance:

1. The range of demand values and supplier lead times to expect.
2. The most likely values of item demand and supplier lead time.
3. The full probability distributions of item demand and supplier lead time.

If you reach the third level, you have the facts required to answer important operational questions, additional questions such as:

1. Exactly how much extra stock is needed to improve service levels by 5%?
2. What will happen to on-time-delivery if inventory is reduced by 5%?
3. Will either of the above changes generate a positive financial return?
4. More generally, what service level target and associated inventory level is most profitable?

When you have the facts and add your business knowledge, you can make more informed stocking decisions that will generate significant returns. You’ll also set proper expectations with internal and external stakeholders, ensuring there are fewer unwelcome surprises.

Why Days of Supply Targets Don’t Work when Computing Safety Stocks

CFOs tell us they need to spend less on inventory without impacting sales.  One way to do that is to move away from using targeted day of supply to determine reorder points and safety stock buffers.   Here is how a days of supply model works:

1. Compute average demand per day and multiply the demand per day by supplier lead time in days to get lead time demand
2. Pick a days of supply buffer (i.e., 15, 30, 45 days, etc.). Use larger buffers being used for more important items and smaller buffers for less important items.
3. Add the desired days of supply buffer to demand over the lead time to get the reorder point. Order more when on hand inventory falls below the reorder point

Here is what is wrong with this approach:

1. The average doesn’t account for seasonality and trend – you’ll miss obvious patterns unless you spend lots of time manually adjusting for it.
2. The average doesn’t consider how predictable an item is – you’ll overstock predictable items and understock less predictable ones. This is because the same days of supply for different items yields a very different stock out risk.
3. The average doesn’t tell a planner how stock out risk is impacted by the level of inventory – you’ll have no idea whether you are understocked, overstocked, or have just enough. You are essentially planning with blinders on.

There are many other “rule of thumb” approaches that are equally problematic.  You can learn more about them in this post. 

A better way to plan the right amount of safety stock is to leverage probability models that identify exactly how much stock is needed given the risk of stock-out you are willing to accept.   Below is a screenshot of Smart Inventory Optimization that does exactly that.  First, it details the predicted service levels (probability of not stocking out) associated with the current days of supply logic.  The planner can now see the parts where predicted service level is too low or too costly.  They can then make immediate corrections by targeting the desired service levels and level of inventory investment. Without this information, a planner isn’t going to know whether the targeted days of safety stock is too much, too little, or just right resulting in overstocks and shortages that cost market share and revenue. 

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

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.

You may remember the story of Goldilocks from your long-ago youth. Sometimes the porridge was too hot, sometimes it was too cold, but just once it was just right. Now that we are adults, we can translate that fairy tale into a professional principle for inventory planning: There can be too little or too much inventory, and there is some Goldilocks level that is “just right.” This blog is about finding that sweet spot.

To illustrate our supply chain fable, consider this example. Imagine that you sell service parts to keep your customers systems up and running. You offer a particular service part that costs you $100 to make but sells for a 20% markup. You can make $20 on each unit you sell, but you don’t get to keep the whole $20 because of the inventory operating costs you bear to be able to sell the part. There are holding costs to keep the part in good repair while in stock and ordering costs to replenish units you sell. Finally, sometimes you lose revenue from lost sales due to stockouts.  

These operating costs can be directly related to the way you manage the part in inventory. For our example, assume you use a (Q,R) inventory policy, where Q is the replenishment order quantity and R is the reorder point. Assume further that the reason you are not making $30 per unit is that you have competitors, and customers will get the part from them if they can’t get it from you.

Both your revenue and your costs depend in complex ways on your choices for Q and R. These will determine how much you order, when and therefore how often you order, how often you stock out and therefore how many sales you lose, and how much cash you tie up in inventory. It is impossible to cost out these relationships by guesswork, but modern software can make the relationships visible and calculate the dollar figures you need to guide your choice of values for Q and R. It does this by running detailed, fact-based, probabilistic simulations that predict costs and performance by averaging over a large number of realistic demand scenarios.  

With these results in hand, you can work out the margin associated with (Q,R) values using the simple formula

Margin = (Demand – Lost Sales) x Profit per unit sold – Ordering Costs – Holding Costs.

In this formula, Lost Sales, Ordering Costs and Holding Costs are dependent on reorder point R and order quantity Q.

Figure 1 shows the result of simulations that fixed Q at 25 units and varied R from 10 to 30 in steps of 5. While the curve is rather flat on top, you would make the most money by keeping on-hand inventory around 25 units (which corresponds to setting R = 20). More inventory, despite a higher service level and fewer lost sales, would make a little less money (and ties up a lot more cash), and less inventory would make a lot less.

Figure 1: Showing that there can be too little or too much inventory on hand

Without relying on the inventory simulation software, we would not be able to discover

• a) that it is possible to carry too little and too much inventory
• b) what the best level of inventory is
• c) how to get there by proper choices of reorder point R and order quantity Q.

Without an explicit understanding of the above, companies will make daily inventory decisions relying on gut feel and averaging based rule of thumb methods. The tradeoffs described here are not exposed and the resulting mix of inventory yields a far lower return forfeiting hundreds of thousands to millions per year in lost profits.  So be like Goldilocks.  With the right systems and software tools, you too can get it just right!