More Truth About Inventory Management Theory

Last month I demonstrated that the classic ‘saw tooth’ diagram associated with inventory management and control is sometimes not at all representative of reality for engineering materials and spare parts. Today, I am going to expand on this to show just how much it can cost your company if you fall into the trap of classic inventory management theory.

You will recall the diagram from last time that showed an actual component profile, shown here as Figure 1.

Figure 1: Actual Component Demand/Supply Chart

Falling into the trap of classic inventory management theory can happen when we use software to calculate the holding requirements without checking on the logic or results. (See also The Optimization Trap) It is easy to see how this happens when you consider that people are often under pressure to review their inventory holdings and they have, say, 10,000 line items to review. Or if you have a ‘built in’ calculator that gets used in a matter-of-fact way.

However, blindly applying software could cost your company millions in unnecessary inventory purchases. Let’s use the above component as an example. Here are some key data points for this component:

Average issue quantity: 22
Average issue frequency: 12 months
Maximum no. issued: 96
Minimum no. issued: 1
Lead time for supply: 8 weeks

The first thing to recognize is that the above chart does not reflect the data that the maximum number issued is 96 items. This is because, on those occasions, the receipt and issue happened in the same week. The chart plot uses a weekly value (rather than daily) so this volatility is in the data but not in the chart. Your computer software would not miss this the way that the chart plot does.

Now, let’s calculate the max-min holding levels using different inventory management approaches.

1. Poisson Function
Anecdotally, the item issues in lots of 10, so it might seem that a Poisson analysis is appropriate. Using a standard Poisson function, and seeking 99.9% coverage, suggests a reorder point (ROP)of 20. If we expect to issue 10 at a time we would most likely set the reorder quantity at 10. This gives a maximum holding of 30.

2. Gaussian Function
If we recognize, however, that the maximum number issued is 96 and the minimum 1, it is clear that the item is not issued in standard lots of 10. We then might apply a Gaussian, or Normal, function to work out the ROP and use the standard formula for the reorder quantity (ROQ).

For the ROQ, let’s use an item cost of $300, an order cost of $100 and a holding cost of 25%. These values yield an ROQ of 8. This is the economic order quantity, given the quantity used per year, the cost of ordering, and the cost of holding the stock.

To calculate the ROP I am going to use a Mean Average Deviation (MAD) rather than a standard deviation. This simplifies the calculation with little impact on the result. In this case we calculate the ROP using the formula:

ROP = (D x LT) + (csf x MAD x Sqrt(LT))

Where:
D = demand in units per week
LT = lead time in weeks
csf = customer service factor (determined from standard tables)
MAD = Mean Average Deviation
Sqrt = square root

Due to the high volatility in the demand for this item (maximum issued 96, minimum 1) the MAD is 24.3, which is very high. Assuming a required availability of 98% leads to a csf of 2.56.

Putting these and the other known values into the formula calculates a ROP of 180.
That’s right 180!

3. Logic and Understanding
What the data doesn’t tell us is that this company makes sure that all orders of catalogued items go through their storeroom and the usage of this item (which is a catalogued item) is forecast and planned. This is why, using logic, the original max-min was set at 10-0 and the larger quantities are ordered when needed.

Conclusion
Let’s compare the results of these three approaches:
1. Poisson: maximum holding 30 – cost to company $9,000
2. Gaussian: maximum holding 188 – cost to company $56,400
3. Logic: maximum holding 10 – cost to company $3,000

This clearly shows that applying the wrong approach can easily cost you tens of thousands of dollars per item! Conversely, applying the correct approach to existing inventory could save you 95% of the value invested (that means real money).

The message from this should be obvious: do not rely on software to recalculate your inventory holdings if you do not understand the algorithm being used and the relevance of its application. It’s not difficult to apply the correct approach, you just need to think about it in advance.

The Truth About Inventory Management Theory

The classic ‘saw tooth’ diagram demonstrates the theory associated with inventory management and control. The saw tooth diagram shows the available quantity of an SKU over time. Figure 1 is an example of this diagram. Here the x-axis represents elapsed time and the y-axis represents the quantity on hand. This figure also includes reference to some of the common terms and definitions as they relate to the classic saw tooth representation. The key simplifying attributes of the theoretical model are the assumptions of linear demand (that is, average demand is constant over time) and instant and complete replenishment.

Figure 1: The Classic Theoretical Saw Tooth Diagram

The problem is, of course, that reality almost never looks like this. The truth is that for engineering and spare parts, the chart in Figure 2 is far more likely to be representative. This graph has four characteristics that separate it from the theoretical profile.

Figure 2: Actual Component Demand/Supply Chart

First, for this particular component the initial parameter was to set a ROP of zero. That is, there is no safety stock. This level is more common for engineering materials and spare parts than many people realize.

Second, in this specific case the ROQ was set to 10; hence, the theoretical maximum is 10 (ROQ + Safety Stock), however, for the majority of the elapsed time the actual holdings are much higher than 10. Thus, a traditional or theoretical review of the ROP and ROQ would provide no improved understanding of how to manage this item because process and behavioral elements of inventory management have a far greater impact on the result than just the basic ROP and ROQ settings.

Third, this item has long periods of no movement followed by short periods of multiple movements. Compare this to the theoretical model that assumes a constant and linear usage of items. As a result the ‘average demand value’ (so often used in theory) varies enormously depending upon the period in the timeline; it is not constant or linear.

Fourth, the large spike in holdings on the right hand side (at the end of the timeline) is not a result of additional purchasing, but results from a massive and sudden return to store of items previously removed. Thus the apparent cycle of usage at point C was not usage at all (although someone did remove the items from the storeroom) and the purchases made to replace these items were not actually necessary. (However, those doing the purchasing did not know this at the time, they were following their process.) The problem was that the maintenance people who removed the items did not use them and did not advise anyone of this. So, when they eventually had a cleanup and returned the items to the store the item became overstocked, compared to the theoretical maximum, by 21 items or 210%!

This example shows that the theoretical model and the actual situation can be sufficiently different so as to make the application of simplistic solutions not only pointless, but also even dangerous to operational goals and company finances. A smart inventory solution is to ensure that the influence, impact, and complicating factors of all the elements of materials and inventory management are considered.

This blog is an extract from the upcoming second edition of the book Smart Inventory Solutions. To find out more or to preorder your copy of this new book visit Industrial Press or Amazon