Industry
Inventory Simulation: Deterministic vs. Stochastic
October 2026 | Inventory Planning
Every inventory policy is a bet on the future, placed with working capital. APQC’s benchmarking puts the median cost of carrying inventory at 10.0% of inventory value, across a sample of 6,468 companies, so a bet on too much stock is expensive. A bet on too little is expensive too: IHL Group’s 2026 Inventory Distortion Study estimates that stock which doesn’t match demand costs global retail $1.7 trillion a year, about 6.2% of retail sales.
Simulation is how planners test the bet before placing it. But “run a simulation” hides a fork in the road. A deterministic simulation replays one forecast through a policy. A stochastic simulation plays out many randomly generated demand patterns and reports how the policy behaved across all of them. They answer different questions, and confusing the two is how a policy ends up approved because it looked perfect on paper.
01 What Gets Simulated: The Four Policy Families
Most replenishment rules in practice are variations on four policies. The notation comes from inventory theory, and the rules are compact enough to state in one line each.
| Policy | Rule | Review | Where it tends to fit |
|---|---|---|---|
| (s, Q) | When inventory position drops to s, order a fixed quantity Q | Continuous | Items with natural lot sizes; Q often comes from an EOQ calculation |
| (s, S) | When inventory position drops to s, order up to S | Continuous | Higher-value items where order size can flex to restore the target level |
| (R, S) | Every R periods, order up to S | Periodic | Items tied to a supplier or truck schedule, where orders are coordinated |
| (R, s, S) | Every R periods, order up to S only if position is at or below s | Periodic | The general case: fewer, larger orders than (R, S) |
Inventory position means on-hand stock plus open orders, minus backorders. The rules of thumb in MIT’s logistics course notes pair the order-up-to policies (s, S) and (R, s, S) with high-value A items and the periodic (R, S) policy with lower-value B and C items. They are rules of thumb, and the notes say as much.
If theory already says which policy is best, why simulate? Because the strongest result in this area comes with conditions attached. Herbert Scarf’s work on the optimality of (S, s) policies, presented in 1959 and published in 1960, shows that this policy form is optimal in the dynamic inventory problem. The problem it solves is a clean one: a single item, a fixed cost per order, and well-behaved holding and shortage costs. Real networks add minimum order quantities, truck-fill economics, shared capacity, and review calendars that nobody chose for inventory’s sake. Which policy wins on your SKUs is an empirical question, and simulation is the empirical test.
02 Deterministic Simulation: Replaying the Plan
A deterministic simulation takes a fixed demand forecast, one number per period, and runs the policy against it. Nothing in the run is random. Given the same inputs, it produces the same inventory path, the same orders, and the same costs every time.
That makes it the right tool for several jobs. It verifies the mechanics of a policy: whether reorder points trigger when expected, whether orders land in time given the lead time, whether the order-up-to level produces sensible order sizes. It handles demand that is known rather than random, such as a seasonal build-up or a planned promotion. It is cheap to run, so it scales across thousands of SKUs in a single pass. And its output is easy to put in front of finance, because it reads like a plan.
Its weakness is built into the method. If the forecast is treated as exactly right, a sound policy will show no stockouts, because the demand it was sized for is the demand it receives. In 2002 Sam Savage gave this problem a name in Harvard Business Review, the flaw of averages: “plans based on assumptions about average conditions usually go wrong.” A deterministic run answers a narrow question, does this policy work if the forecast is right? It cannot tell you how often the forecast will be wrong or what that costs.
And forecasts are wrong, persistently, at exactly the level where inventory is decided.
Item-level demand resists forecasting
The M5 forecasting competition drew 5,507 teams from 101 countries to forecast 42,840 hierarchical sales series from Walmart. The winning method beat a standard benchmark by 22.4% overall, but the top methods’ advantage over that benchmark averaged only about 3% at the most granular product levels, and sparse, intermittent series were the hardest to forecast. Better models help, but at the SKU and location level, residual uncertainty does not go away.
If uncertainty is a permanent feature of item-level demand, a method that assumes it away has a ceiling on how much it can tell you.
03 Stochastic Simulation: Playing Out the Uncertainty
A stochastic simulation describes demand as a distribution, typically through its average and standard deviation, and then generates many random demand patterns from it. Each pattern is a different version of how the year might unfold. The policy is run against every one, and the results are collected as distributions instead of single numbers.
Three things change when you read the output.
The result is a range, not a point. A deterministic run reports one service level. A stochastic run reports the average fill rate, how bad the bad years get, and how often the policy stocks out at all. The table below shows what that looks like on a single item. It comes from a simple simulation we ran for this article, with the assumptions listed underneath, and it is meant to illustrate the method rather than benchmark any real network.
| Order-up-to level S | Deterministic result | Stochastic: average fill rate | Simulated years with at least one stockout week | Average end-of-week inventory |
|---|---|---|---|---|
| 300 Average demand over the protection interval | No stockouts, 100% fill | 91.0% | 100% | about 33 units |
| 386 Adds safety stock for a 95% service level | No stockouts, 100% fill | 99.3% | 83% | about 93 units |
| 450 | No stockouts, 100% fill | 99.97% | 9% | about 156 units |
Illustrative simulation, not a Log-hub benchmark. One SKU under an (R, S) policy with weekly review (R = 1) and a 2-week lead time. Weekly demand is normally distributed with a mean of 100 and a standard deviation of 30 (floored at zero). Unmet demand is lost. 2,000 simulated years of 52 weeks. The safety stock in the middle row is z × σ × √(R + L) with z = 1.645.
Read the first row against the deterministic column. A policy sized to exactly the average demand over its protection interval looks flawless in the deterministic run and stocks out in 17 of 52 weeks on average once demand is allowed to vary. The middle row carries a 95% service-level buffer and still produces at least one stockout week in 83% of simulated years, because a service level measured per replenishment cycle compounds over 52 weeks of cycles. The bottom row shows the price of chasing the last points: roughly 67% more average inventory than the middle row for under one additional point of fill rate.
The price of service is nonlinear. That last result is not a quirk of this example. Under the standard safety stock formula, z × σ × √(R + L), the buffer scales directly with the service-level factor z, the matching point on the normal distribution: 1.28 for a 90% service level, 1.65 for 95%, and 2.33 for 99%. Holding demand variability and the protection interval constant, moving from 90% to 95% raises safety stock by about 28%, and moving from 95% to 99% raises it by another 41%. A deterministic run can’t show you this curve. A stochastic run lets you compare policies at several service levels and see where the cost starts to outrun the benefit.
The number of runs matters. If the quantity you are estimating is a probability near 95%, such as the chance a policy gets through a year without stocking out, the 95% margin of error from ten simulation runs is about ±13.5 percentage points. At 100 runs it is about ±4.3 points, and at 1,000 runs about ±1.4 points. Ten runs is a useful sanity check on whether a policy is in the right range. Reading tail risk off ten runs is not.
What Goes In Determines What Comes Out
A stochastic simulation is only as good as its demand parameters, and three habits make them better.
Calibrate at the stocking point, not the end customer. Variability tends to amplify as orders move upstream, which Hau Lee, V. Padmanabhan, and Seungjin Whang described in their work on the bullwhip effect. A standard deviation measured at the shelf understates the variability a distribution center actually sees.
Treat irregular items separately. Mean and standard deviation describe a smooth, bell-shaped demand pattern well. For intermittent items, where many periods have no demand at all, they can mislead, which is why the M5 results above single those series out as the hardest case. How often demand occurs is as important an input as how large it is.
Use scenarios for the uncertainties that aren’t statistical. Randomness around a stable average is one kind of risk. A supplier whose lead time moves from 2 weeks to 4 is another, and it is better tested as a what-if than as a random draw. Recent tariff swings are a live example of lead times and demand assumptions shifting at the same time; our analysis of why manufacturers kept stockpiling covers the market side of that story.
04 Deterministic or Stochastic? How to Choose
The two methods are complements. Each is blind to something the other sees.
| Deterministic | Stochastic | |
|---|---|---|
| Question it answers | Does this policy work if the forecast is right? | How often will this policy fail, and what does the buffer cost? |
| Demand input | One value per period (the forecast) | Average, standard deviation, and how often demand occurs |
| Runs per SKU | One | Many, each with a different random demand pattern |
| Output | One inventory, order, and cost path | Distributions of service level, lost sales, inventory, and cost |
| Best for | Planned demand, validating policy mechanics, large SKU portfolios, communicating the plan | Sizing buffers, setting service targets, volatile or irregular SKUs, comparing policies under risk |
| Watch out for | Blind to variability: every sound policy looks perfect | Only as good as the demand parameters; too few runs gives noisy tails |
In practice a workable sequence has three steps.
Segment first. Stable, predictable items with reliable forecasts don’t need the same treatment as volatile or intermittent ones. An ABC-XYZ split, which crosses value with demand variability, is the usual way to decide where the effort goes.
Match the method to the segment. Use deterministic runs to validate mechanics and confirm that a policy produces the order pattern the plan expects. Use stochastic runs to size buffers and set service targets, especially on the volatile and irregular segments, where a fixed forecast tells you the least.
Stress-test the winner. Take the policy that looks best and change the inputs: a longer lead time, a higher standard deviation, a different review period. A policy that stays acceptable across those changes is worth more than one that is optimal for a single set of assumptions.
05 Five Ways Simulation Results Mislead
Most bad simulation decisions come from a handful of repeat mistakes.
Reading a deterministic pass as a risk assessment. A clean deterministic run shows the policy is mechanically sound. It says nothing about how it performs when demand deviates from the forecast.
Stopping at ten runs. Few runs are fine for exploration. They are not enough to estimate the tails, and the tails are where the stockouts live.
Comparing policies at different service levels. A policy with 97% fill and higher cost against one with 93% fill and lower cost is not a comparison. Compare policies at the same service level, or plot cost against service for each, so that the differences reflect policy design rather than where each one happened to land.
Using one standard deviation for everything. Variability differs by item, by location, and by where in the network demand is measured. A single assumption applied across a portfolio will be too generous for some SKUs and too tight for others.
Ignoring the review period. Under a periodic policy, the buffer has to cover demand over the review period plus the lead time. MIT’s inventory notes give safety stock as zσ√(R + L). With a 2-week lead time, moving from weekly to four-weekly review stretches that interval from 3 weeks to 6 and raises the required safety stock by a factor of √2, about 41%, with nothing else changed. Review frequency is a cost lever, and a simulation can price it.
06 Conclusion
A deterministic simulation tells you whether the plan works. A stochastic simulation tells you how often reality will break it, and what it costs to make that happen less often. Used alone, the first flatters every sound policy, and the second can be noisy if it is under-run or fed careless parameters. Used together, one to validate the mechanics and the other to size the buffers, they give planning, sales, and finance a shared answer to the question that inventory policy exists to settle: how much stock is enough, and how sure are we?
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