How long does inventory need to last? Lead time, review period, and the horizon you choose

The guide on order economics answers how much stock to hold against a horizon $H$. This piece answers the question underneath it: how long does the stock actually need to last, and who decides?

The short answer is that an order has to last until the next order arrives. That window has two parts. One is mostly set by your supplier. The other is a choice you make, usually without noticing, every time you decide how often to order.

The window an order has to cover

Suppose you order every two weeks and the supplier takes three weeks to deliver. You place an order today. It lands in three weeks. Your next chance to order is in two weeks, and that order also takes three weeks, so it lands in five. Nothing you do after today can put stock on the shelf before week five.

So the stock you have, plus what is already on its way, plus today’s order, must cover demand for the next five weeks:

This is the protection interval. It is the horizon in the order-economics guide, and it is the window the forecast distribution has to describe. Drag the sliders and watch it move.

Two things follow immediately.

1. The window is not the time between orders. Ordering every week with a six-week lead time still means each order protects seven weeks. Teams that size orders to “cover until next order” under-protect by the whole lead time.
2. The two parts are controlled differently. Lead time is mostly given: it belongs to the supplier, the transport mode and the distance. The review period is yours. That makes it the cheapest lever on the window, and one that most planning systems leave on a default.

The review period is a decision with its own economics

Ordering more often shrinks the window, which means less stock to protect against less uncertainty. But each order has a cost: freight, receiving, admin, and often a minimum order you have to meet. Ordering less often saves those costs and lengthens the window. So there is a trade-off, and for each SKU it has a best answer.

Three costs move against each other as the review period $R$ grows:

1. Ordering falls as $K / R$, where $K$ is the cost of one order.
2. Holding and ageing rise, because each order covers a longer window and the cycle stock grows.
3. Shortages shift too, because a longer window is more uncertain, and because the critical ratio itself falls. A unit left over at the end of a cycle waits one more review period, so the overage cost is $hR$ and

The longer you wait between orders, the more each leftover costs, and the lower the percentile the economics will pay to protect. This is the same effect as in the horizon section of the order-economics guide, now driven by a choice instead of a given.

Set the costs and the chart finds the cadence. Each bar is the expected weekly cost of ordering every $R$ weeks, with the order-up-to level re-optimized for that cadence.

What the examples show

All four examples share the same demand (100 a week, CV 0.5) and a two-week lead time. Only the economics differ.

Four lessons come out of this table.

1. The best cadence varies by a factor of three or more across SKUs with identical demand. A single company-wide ordering rhythm is right for, at most, the SKUs whose economics happen to match it.
2. Stock that ages wants short cycles. The cost of a long window falls hardest on items that lose value while they wait, so they should be ordered often, in small amounts, even at a higher ordering cost.
3. Expensive stockouts raise the level, not the cadence. The “stockout is costly” SKU keeps roughly the same review period as the cheap one and simply orders up to a higher level. Protection and cadence are separate decisions answering separate questions.
4. The bottom is flat. In every case several cadences cost within 5% of the best. That is good news: the review period can follow supplier delivery days, truck schedules or a shared ordering calendar at almost no cost, as long as it is in the right range.

There is also a useful shortcut. The economic order quantity cycle, $\sqrt{2DK/h}\,/\,D$, is close to the best review period in all four examples: 5.2 weeks for the cheap SKU, 2.3 for the ageing one, 10 for the expensive-to-order one. EOQ ignores uncertainty, but because the cost curve is flat it is usually a good first guess for the cadence. The uncertainty then sets how far above or below the window’s expected demand to order.

Lead time is sometimes a choice too

Where there is a real choice of supplier or transport mode, such as sea versus air, a local versus an offshore source, or paying for expedited production, the same logic applies to $L$. A shorter lead time shrinks the window without adding orders. For stock that ages, it also raises the critical ratio. Whether it is worth paying for comes down to a direct comparison: the price premium per unit against the holding, ageing and shortage cost it removes. Neither “always the cheapest landed cost” nor “always the fastest” is a policy; both are guesses about that comparison.

Does a shorter horizon cause stockouts?

A familiar argument runs like this: shorten the horizon and weeks of cover goes down, so stockouts go up; if the business wants higher availability, it should plan over a longer horizon. The arithmetic in the first half is correct. The conclusion is not, and for stock that ages it points in exactly the wrong direction. It helps to separate four claims.

1. Cover falls, but availability does not have to

Take the SKU that ages quickly from Exhibit 2 and let the economics set the level each time. Shortening either part of the window cuts cover sharply, and the share of demand served goes up, not down.

Two different mechanisms are at work. A shorter lead time leaves less uncertainty to protect against, so the same critical ratio needs far less stock and still loses fewer units. A shorter review period does that and more: a leftover now waits one week instead of twelve, so the critical ratio rises from 0.31 to 0.84 and the economics choose to protect a higher percentile. Weeks of cover falls by two thirds in both cases. As a scoreboard for availability, it is simply the wrong instrument.

2. What does rise is the number of stockout occasions

The last column is the honest catch. With more cycles per year there are more moments at which stock can run out, so the count of cycles that end in a stockout rises, from 3.0 to 8.2 a year in the table, even though each one is smaller and fewer units are lost overall. A team that measures availability as “days with a stockout” or “number of stockout events” will see a shorter horizon as worse; a team that measures lost units or lost margin will see it as better.

Neither metric is wrong, but they answer different questions. If what really hurts is the occasion, for example a customer who walks away the first time the shelf is empty, then that is a cost per stockout event, not per unit, and it belongs in the model as such. Lengthening the horizon to have fewer, larger cycles is a very indirect and expensive way to price it.

3. When the model holds less, it is making a price decision

At the economic optimum, the probability of getting through a cycle without a stockout equals the critical ratio, by construction. So when the model accepts a 64% chance of getting through a cycle rather than 95%, it is not under-forecasting or being careless. It has compared the cost of the stock needed to prevent the remaining stockouts with the margin those stockouts lose, and found the stock more expensive. For stock that ages, that comparison gets worse the longer each unit has to wait, which is why the ratio falls as the horizon grows.

This is the core of the argument. The stockouts that remain at the optimum are the ones not worth preventing. Shortening the horizon does not create them; it changes their price, and usually makes protection cheaper.

4. Buying availability: the horizon is the expensive lever

Suppose the business still wants more availability than the economics choose. There are two ways to buy it: raise the order-up-to level at the economic cadence, or order less often so that each order covers a longer window. Exhibit 3 prices both. Each thin curve is a fixed cadence; the thick curve is the cheapest way to reach each fill rate.

The results depend on the SKU, and that is the point.

1. Cheap to hold. The economics already serve 97.8% of demand at $216 a week. Reaching 99% costs $4 a week more at the same five-week cadence, by raising the level. Getting there with a twelve-week cadence costs $289 a week, nearly a third more. The horizon is a poor lever, but a cheap mistake.
2. Ages quickly. The economics serve 90.9% at $533 a week. The cheapest route to 99% is a shorter cycle, ordering every two weeks, at $610 a week, 14% more. Getting there by ordering every eight weeks costs $966 a week, and every twelve weeks $1,278: 58% and 110% more than the cheapest route. The cost does not rise in a straight line, because every extra week adds holding on a larger pile of stock that is also losing value, so each additional point of availability bought this way costs more than the last.
3. Expensive to order. Here the economics already pick a long, ten-week cycle because orders are costly, and the curves for long cadences sit close together. A longer horizon is the natural route in this case, but because ordering is expensive, not because the horizon buys availability.

So “plan over a longer horizon to raise availability” is roughly right only for SKUs that are cheap to hold, where it is wasteful but harmless, and for SKUs where orders are expensive anyway. For high-overage stock, which is exactly where people most want to avoid write-offs, it is the most expensive route and runs opposite to the cheapest one.

Competing objectives are one objective, once priced

The last readout in Exhibit 3 is the most useful number in a service-level debate. A 99% fill-rate target for the ageing SKU is only optimal if each unit short costs about $59. The real figure in the example is $8. For the cheap-to-hold SKU, 99% implies about $17 per unit short.

That turns “availability versus cost” from a negotiation into a question of fact. If a stockout really costs $59, through lost customers, contract penalties or line stoppages, put $59 into the shortage cost and the model will find the cheapest way to deliver the availability that justifies, usually a higher level and often a shorter cycle. If it does not, the target is buying availability at a loss, and no choice of horizon makes that loss go away.

Three things that are all called “the horizon”

Much of the confusion in practice comes from one word doing three jobs.

The last row deserves a note. A planning system’s look-ahead is not a decision with an optimum. It is a truncation of a problem that has no natural end. In a rolling plan, only today’s orders are executed and the rest is recomputed next time. So the look-ahead needs to reach far enough to see the consequences of today’s decision, typically at least a few protection intervals, and beyond that point extending it changes nothing except the amount of unreliable forecast it depends on.

In Python

from statistics import NormalDist

N = NormalDist()

def periodic_review(mu, sd, L, R, K, h, p):
    """Weekly cost of ordering every R weeks, up to the economic level for L + R weeks."""
    H = L + R
    m, s = mu * H, sd * H ** 0.5
    cr = p / (p + h * R)                    # a leftover waits one more review period
    S = m + N.inv_cdf(cr) * s
    z = (S - m) / s
    short = s * (N.pdf(z) - z * (1 - N.cdf(z)))   # expected units short per cycle
    ordering = K / R
    holding = h * (S - mu * L - mu * R / 2 + short)
    shortage = p * short / R
    return ordering + holding + shortage, S, cr

for name, K, h, p in [("cheap to hold", 400, 0.3, 8), ("ages quickly", 400, 1.5, 8),
                      ("expensive to order", 1500, 0.3, 8), ("stockout is costly", 400, 0.3, 60)]:
    best = min(range(1, 13), key=lambda R: periodic_review(100, 50, 2, R, K, h, p)[0])
    cost, S, cr = periodic_review(100, 50, 2, best, K, h, p)
    print(f"{name:19s} order every {best:2d} wk, stock lasts {2 + best:2d} wk, "
          f"up to {S:,.0f} (CR {cr:.2f}), ${cost:,.0f}/wk")

The normal approximation is fine for choosing a cadence because the cost curve is flat near its minimum. For the order-up-to level itself, especially for slow movers or skewed demand, sample the forecast over $L + R$ weeks and take the critical-ratio quantile, as in the order-economics guide.

Common mistakes

• Covering until the next order instead of the next delivery. The window is lead time plus review period. Leaving out the lead time is one of the most common causes of chronic stockouts.
• One ordering rhythm for every SKU. Cadence has its own economics. A weekly cycle that suits fast, cheap items is expensive for slow, bulky ones, and a monthly cycle that suits durable stock is expensive for anything that ages.
• Treating the review period as a fact. Supplier days and system defaults are often inherited, not chosen. They should be checked against the cost curve, which usually leaves room to align with logistics without losing money.
• Judging a shorter horizon by its weeks of cover. Less cover from a shorter window usually means higher availability at lower cost. Measure lost units or lost margin, and count stockout occasions only if occasions are what actually cost money.
• Lengthening the horizon to raise availability. It is the most expensive lever for stock that ages and runs opposite to the cheapest one. If availability is worth more, raise the shortage cost and let the level and the cadence follow.
• Optimizing the planning system’s look-ahead. It needs to be long enough, not optimal. Time spent tuning it is usually time not spent on the review period, which actually drives cost.
• Setting weeks of cover as a target. Cover is what comes out once the window and the economics are right.

Where to go next

• Where should the next dollar of inventory go? allocates a limited budget across SKUs by expected return per dollar.
• How much to order explains the critical ratio, EOQ and why weeks of cover is the wrong question.
• The Critical Ratio Explorer lets you set the two costs for a single decision.
• When many SKUs share a supplier and a truck, the cadence becomes a shared decision: the fixed cost of an order is split across items with different holding costs. That is the joint replenishment problem, one of the next patterns in the inventory section of the library.