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Supply Chain Math: Don’t Bring a Knife to a Gunfight

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.

Backing into Safety Stock is the Safe Play

# forecasting and inventory optimization

We frequently encounter confusion about the process of setting safety stock levels. This blog hopes to clarify the issue.

Safety stock is a critical component in any system of inventory management. Indeed, some inventory software treats safety stock as the key decision variable in the quest to balance inventory cost against item availability. Unfortunately, that approach is not the best way to strike the balance.

First, realize that safety stock is part of a general equation:

Inventory Target = Average Lead Time Demand + Safety Stock.

Average Lead Time Demand is defined as the average units demanded multiplied by the average replenishment lead time. Example: If daily demand averages 2 units and the average lead time is 7 days, then the average lead time demand is 2 x 7= 14 units. Keeping 14 units on hand suffices to handle typical demand.

But we all know that demand is random, so keeping enough stock on hand to cover the average lead time demand invites stockouts. As we like to say, “The average is not the answer.” The smart answer is to add in some safety stock to accommodate any random spikes in demand. But how much?

There’s the problem. If you try to guesstimate a number for the safety stock, you are on thin ice. How do you know what the “right” number is?  You may think that you don’t have to worry about that because you have a good-enough answer now, but that answer has a sell-by date. Lead times change. So do demand patterns. So do company priorities. That means today’s good answer may become tomorrow’s blunder.

Some companies try to wing it using a crude rule of thumb approach. For instance, they may say something like “Set safety stock at an additional two weeks of average demand.” This approach is seductive: It only needs simple math, and it is clear.  But for the reasons listed in the previous paragraph, it’s foolish. Better to get a good answer than a convenient answer.

You need a principled, objective way to answer the question that takes account of the mathematics of randomness.  More than that, you need an answer that is linked to the key performance indicators (KPI’s) of the system: inventory cost and item availability.

Simple logic gives you some sense of the answer, but it doesn’t provide the number you need. You know that more safety stock increases both cost and availability, while less safety stock decreases both. But without knowing how much those metrics will change if you change the safety stock, you have no way to align the safety stock decision with management’s intent for striking the balance between cost and availability.

Rather than flying blind, you can back into the choice of safety stock by first finding the right choice for inventory target. Once you’ve done that, the safety stock pops out by a simple subtraction:

Safety Stock = Inventory Target – Average Lead Time Demand.

Often times, companies will state that they don’t carry safety stock because the safety stock field in their ERP system is blank. Nearly always, safety stock is built into the targeted inventory level they have established.  So, using the above formula to “back out” how much safety stock you are building into the plan is quite helpful.  The key is not just to know how much safety stock you are carrying but the link between your inventory target, safety stocks, and its corresponding KPI’s.

For instance, suppose you can tolerate only a 5% chance of stocking out while waiting for replenishment (inventory texts call this interval the “period of risk.”). Software can examine the demand history of each item and work out the odds of stockout based on the thousands of different demand scenarios that can occur during the lead time. Then the right answer for the inventory target is the choice that leads to no more than a 5% stockout risk. Given that target and knowing the average lead time demand, the appropriate safety stock value falls right out by subtraction. You also get to know the average holding, ordering and shortage costs.

That’s what we mean by “backing into the safety stock.” Start with company objectives, determine the appropriate inventory target, then derive the safety stock as the last step. Don’t start with a guess about safety stock and hope for the best.

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