# Safety Stock and Quantity On Hand with Fixed Interval Variable Quantity Replenishment

QOH = ROQ / 2 + SS.
Average inventory quantity on hand = 50% of reorder quantity + safety stock. This formula is both fundamental and satisfyingly intuitive. On average, half of the reorder quantity is on hand: 100% just after receipt, and virtually none just prior to the next receipt. And since safety stock is “extra” inventory, it is, on average, on hand.

But is this formula always true? Well, if you reorder on an ROP fixed interval variable quantity system, or FIVQ, no.

First, let’s define FIVQ: placing orders of varying sizes, at regular intervals, to replenish inventory up to a specified or target inventory level, as driven by ROP. This is as opposed to a fixed quantity variable interval (FQVI) system.

Now, let’s use Item XYZ as an example:

XYZ’s calculated average QOH is:

1650 = 1000 Avg ROQ / 2 + 1150 SS.

But XYZ’s actual average QOH = 700, which is 950 less than the calculated level!

Indeed, with FIVQ, the ROQ / 2 part of the QOH calculation does apply. For XYZ, half of the average ROQ, or 500, is on hand. But why is the remaining 200, or 700-500, less than the safety stock of 1150?

The difference is about 10 day’s worth of demand, since the fixed reorder interval is 10 days. With FIVQ, the ROQ is only enough to bring the total on-hand and on-order back up to the ROP  (or perhaps more if the item also has a MOQ and/or order multiple > 1). The next day after a reorder, any demand consumption greater than zero theoretically triggers ROP again.

However, the delay between when ROP theoretically triggers the replenishment and when this is noticed during reorder review is nearly 10 days. So about one fixed interval’s worth, or about 950 of the 1150 safety stock, is regularly consumed by this delay.

In the perpetual-inventory excerpt above, XYZ’s ROP theoretically triggers on Day 21. However, the demand consumption for Days 20-29 is not reordered until Day 30. Safety stock must cover the demand for Days 20-29, since lead time does not.

We could argue that this delay is part of lead time. Practically, though, FIVQ replenishment lead time starts at reorder review and ends when the received quantity is available for consumption.

With FIVQ, then, ongoing demand, not just demand spikes, regularly consumes safety stock. So this portion of safety stock is not on hand, on average. Also, if the FIVQ item also has an MOQ and/or order multiple, this can provide some de facto safety stock. FIVQ, combined with MOQ and/or order multiple, means the fundamental, intuitive QOH = ROQ / 2 + SS is not likely to give a correct result.

As a general rule, here’s how to estimate average QOH for FIVQ, and it depends on the average replenishment-interval equivalent of the average MOQ, or average MOQ / average daily demand:

• IF average replenishment interval <= fixed reorder interval THEN

QOH ≈ ROQ / 2 + SS – (average daily demand * fixed reorder interval)

• IF replenishment interval > reorder interval THEN

QOH ≈ ROQ / 2 + SS – (average daily demand * fixed reorder interval / 2)

As another nuance, when replenishment interval and fixed reorder interval are very close to the same but not the same, QOH is somewhere in between these two calculations. (When there is no MOQ and/or order multiple constraint, replenishment interval = fixed reorder interval.)

FIVQ increases both safety stock and ROP. In fact, FIVQ would require safety stock even if there was no demand and lead-time variation. From an inventory-performance perspective, FIVQ isn’t quite as efficient as fixed quantity variable interval. This is because FIVQ requires safety stock not just for variations during lead time, but also during the reorder-review interval. Nonetheless, many businesses, and their suppliers, prefer FIVQ because it provides regular, predictable reorder timing.