Reorder Point & Inventory Shrinkage Detection

The Trigger: Defining the Reorder Point

The reorder point is a simple yet powerful concept: it is the inventory level that ensures you don't run out of stock while waiting for a new shipment to arrive. This waiting period is known as the lead time.

In a perfectly predictable world, you would simply calculate the number of items you expect to sell during the lead time and place a new order when your inventory hits that exact number. However, the world of commerce—much like the world of crime—is fraught with uncertainty. Customer demand can spike unexpectedly, or suppliers can face delays. To guard against these risks, a prudent manager holds safety stock.

Therefore, the reorder point is composed of two key elements: the expected demand during the lead time, and a buffer of safety stock to handle unpredictability.

The Basic Calculation

Let's begin with the simplest scenario, where demand and lead time are constant. A brief video segment will illustrate this fundamental formula.

For our case, let's establish the known facts. The annual demand (D) is 1,200 sets. Assuming the boutique operates 300 days a year, the average daily demand is:

Our intelligence suggests the supplier for "Midnight Seraph" has a consistent lead time (LT) of 5 days.

Without considering any variability, the demand during lead time would be:

So, in a perfect world, the reorder point would be 20 units. But we must prepare for the unexpected.

Accounting for Uncertainty with Safety Stock

To protect against stockouts from fluctuating demand, we need to add safety stock. This is where your statistical expertise becomes invaluable. While there are crude ways to estimate safety stock, a more rigorous approach uses probability distributions.

This next video segment introduces the concept of safety stock and its role in achieving a desired service level (i.e., the probability of not stocking out).

The most common and robust method for calculating safety stock assumes that demand is variable and can be modeled by a normal distribution. We need to decide on a service level—let's aim for a 95% service level for this high-end product line, meaning we accept a 5% chance of a stockout during any given order cycle.

The formula for safety stock (SS) in this context is:

Where:

• Z is the Z-score corresponding to our desired service level.
• ${\sigma }_d$ is the standard deviation of daily demand.
• LT is the lead time in days.

Our investigation has uncovered the following data from the boutique's records: while the average daily demand is 4 units, its standard deviation (${\sigma }_d$) is 1.5 units. For a 95% service level, the Z-score is approximately 1.645.

Now, we can calculate the required safety stock:

Since we can't hold a fraction of a lingerie set, we round up to 6 units of safety stock.

The article "Safety Stock Formula & Calculation" provides an excellent overview of this method among others.

Establishing the Final Reorder Point

We now have all the components to establish the official reorder point for the "Midnight Seraph" line.

ROP = (Average Daily Demand × Lead Time) + Safety Stock

This is our critical trigger. When the inventory on hand for "Midnight Seraph" drops to 26 sets, a new order for 60 sets (the EOQ) must be placed.

The following video provides a final, clear example of this complete calculation, solidifying the procedure.

Pinpointing the Shrinkage

With the correct reorder point established at 26 units, we can now scrutinize the boutique's inventory logs. We're looking for order cycles where the inventory dropped below the safety stock level of 6 units upon the new shipment's arrival, without corresponding sales to explain the discrepancy.

Let's examine a cycle from last May:

• May 12: Inventory level hits 26 units. An order for 60 units is correctly placed.
• Lead Time: 5 days (delivery expected on May 17).
• Expected state on May 17:
  • Expected sales during lead time: $4\times 5=20$ units.
  • Expected inventory upon delivery: $26-20=6$ units (our safety stock level).
• Actual state on May 17:
  • The delivery of 60 units arrives.
  • The inventory log shows only 1 unit on hand just before the new stock was added.
  • Sales records for May 12-16 show 22 units were sold.

Here is our clue. The inventory level should have been $26-22=4$ units. But it was only 1.

Three sets of "Midnight Seraph" have vanished. They were not sold, yet they are gone. This is unaccounted-for shrinkage—our first solid piece of evidence of theft. By applying this analysis across all order cycles, we can trace back to the first month this anomaly appeared, thereby pinpointing when the heist likely began.

An Advanced Perspective: Modeling Shrinkage Directly

Our current method detects shrinkage by looking for deviations from a standard model. A more sophisticated approach, fitting for your background in Operations Research, would be to build a model that anticipates shrinkage.

A fascinating academic paper does just this. It introduces parameters to represent the proportion of items that are lost or misplaced—in our case, stolen.

This advanced model adjusts the reorder point itself to account for expected theft, aiming to maintain a desired service level even in a compromised environment. While we won't apply it now, it's a valuable tool to keep in your arsenal for more complex cases.

Conclusion

Today, we have sharpened our investigative toolkit significantly. We moved from knowing how much to order to knowing precisely when to order by calculating the reorder point. We saw that this calculation must account for real-world uncertainty through the use of statistically determined safety stock.

Most importantly, we transformed this operational metric into a forensic tool. By comparing the boutique's actual inventory levels against the correctly calculated reorder point and safety stock buffer, we uncovered a discrepancy that points directly to theft.

Key Takeaways:

• The Reorder Point (ROP) is the inventory level that triggers a new order.
• ROP = Demand during Lead Time + Safety Stock.
• Safety Stock is a buffer to protect against variability in demand and/or lead time and is calculated based on a desired service level.
• For the "Midnight Seraph" line, the ROP is 26 units.
• By comparing expected inventory levels at the time of replenishment with actual levels, we can identify and quantify inventory shrinkage.

Preview of the Next Lesson

We have now established the three pillars of an optimal inventory policy for L'Atelier Secret: the Economic Order Quantity (Q* = 60), the minimum annual cost ($3,000), and the Reorder Point (ROP = 26). We've also found evidence of theft. The next logical step is to quantify the financial damage. In our next session, we will perform a sensitivity analysis to determine how changes in demand—whether from legitimate market shifts or from the distorted figures caused by theft—impact the total cost and reveal the true scale of the inventory manipulation.