# The Correct Safety Stock Level is not Simple. Part 3.

Perhaps you have come to this blog because you searched for “simple safety stock formula.” Or you’re just looking for a better, easier safety-stock tool. ”Simple” suggests that ease of use (usually in Excel) is more important than precision, so long as the result is close enough. Albert Einstein advised, “Make everything as simple as possible, but not simpler.” So can a safety-stock calculation be both simple and also close enough?

At what point is a safety-stock calculation simple enough, but not too simple? In two previous blogs, we acknowledged that most common safety stock calculations attempt to address these obvious factors:

• Target service level
• Demand variation

In those blogs, we also discussed how the z factor may cause your safety-stock formula to drive excessive inventory levels. The z factor is simple, but it is not reliably close enough. Likewise, we discussed how safety-stock formulas ignore, or incorrectly address, replenishment interval. Again, a simple safety-stock formula is not close enough.

Now, we’ll consider how the normal-distribution calculations (involving mean and standard deviation) often used in simple safety-stock calculations may not be close enough.

Demand distributions are rarely normal. They are typically right-skewed. Additionally, many demand streams are intermittent, with a lot of zeroes in the demand distribution that increase the right-skewness. This does not keep you from determining a mean and a standard deviation using Excel AVERAGE and STDEV functions. However, it does mean that if you use a safety-stock formula that employs AVERAGE and STDEV, those two parameters do not represent what a right-skewed distribution really looks like.

But will the simple, Excel-friendly AVERAGE and STDEV get us close enough? NO.

The chart below shows a right-skewed demand distribution for a high-volume, non-intermittent item. Its AVERAGE = 100 and its (Excel) STDEV = 70.7. The solid black line is the actual distribution, and the dashed red line is the theoretical normal distribution with AVERAGE 100 and STDEV 70.7. Is this close enough?

Take a closer look at the right tail of the distribution, below. This tail contains the high-demand days that can cause stockouts. The normal distribution (dashed red line) shows virtually zero probability of demand being greater than about 380. But the solid black line shows actual demand activity greater than 380, and even beyond 600 per day. If this is a mission-critical item, then a normal-distribution-based simple safety stock formula may not be close enough.

Granted, Central Limit Theorem (CLT) may come into play – that is, a demand distribution during lead time may eventually behave normally, if the lead time is long enough. But is your lead time long enough to do this? And how would you know?

Can we adjust a simple safety-stock formula for non-normal, right-skewed distributions? Not while keeping it simple. And what right-skewed distribution should we use? Goodness of fit is not an Excel strength, and its right-skewed-distribution functions are limited. Can a simple safety-stock calculation assess whether CLT will allow us to use a normal-distribution-based analysis? Not a chance.

Are you looking for a correct way to set safety stock, so that you achieve your service-level targets without unnecessary inventory?

Nothing could be simpler than sending us your data, and we will send you your correct, comprehensive and optimal safety-stock levels. Contact us for more info on how simple we can help make it for you!

## 2 thoughts on “The Correct Safety Stock Level is not Simple. Part 3.”

• Anthony,

Thanks for your interest! The methodology and resulting analytical capability are fully embedded in a SaaS solution called Right Sized Inventory: http://www.rightsizedinventory.com. As you would expect, it’s proprietary intellectual property. However, the RSI Web site contains a number of the differentiating details. I’ll summarize them here:

Standard academic techniques and formulaic approaches are usually insufficient to produce quality inventory analysis for the following reasons:

• Demand is rarely normally-distributed, so normal-based standard-deviation calculations ignore reality.

• Lead time (LT) is also rarely normally-distributed, so LT variation needs a more sophisticated approach than what you find in typical safety-stock (SS) calculations.

• The common z factor represents a stockout event – more accurately, the probability of no stockout event – but businesses almost universally measure their actual SL performance as a quantity-based fill rate: either unit quantities or order lines filled on time. Of its own accord, the event-based z factor drives an unnecessarily-large multiplier.

• Common sense says that the larger the MOQ, especially when MOQ lasts longer than LT, the less incremental SS is needed. Yet, few formulas even attempt to address this, and the ones that do so aren’t correct. Want proof? A very large MOQ may not require any incremental SS, yet try finding a formula that will come up with an answer of zero.

• Likewise, experience tells us that smaller MOQs drive short replenishment intervals (RIs) and frequent receipts. In turn, these frequent receipts, with multiple receipts inside of a LT cycle, provide a measure of de facto SS. Again, any formula that tries this doesn’t do it optimally.

•A typical deterministic SS formula would provide only 50% confidence. Effective SS analysis needs to enable simple analysis of service-level performance with higher confidence levels.

• Does your unfulfilled demand become disruptive past-due backlog? If so, you know past-due backlog needs more SS. I haven’t found a formula that even tries this one. But you can estimate the probability of demand not fulfilled on time being canceled vs. becoming past-due backlog.

• Each item has a replenishment / reorder interval, or RI. It may be determined by the MOQ, EOQ, lot or package size, etc. Or perhaps your business has a set frequency, replenishing once per week or once per month. RI is not the same as LT. But it is equally critical to the analytical outcome.

• An item’s replenishment method affects its inventory requirements. Many techniques simply use standard formulas to calculate SS or Kanban. But today’s supply chains often embrace demand-driven techniques like Reorder Point or Min-Max. We support 6 different replenishment methods and enable our users to simulate inventory levels with different replenishment methods to find the one that best fits their business.

• A standard formula provides only a single value as an answer. Our analysis uses Monte Carlo simulation to provide a more robust answer and a range of outcomes around that answer. In addition, we provide simple, effective, graphical tools to understand the answer and avoid the “black box” skepticism often associated with optimization answers. Finally, we provide easy-to-use tools to run scenarios and explore the impact that various changes in your supply chain would have on your required inventory.