Inventory policy Discrete-event simulation Runs in your browser

Inventory Stress Lab

Two reorder policies, one demand stream. A continuous (r, Q) rule and a periodic order-up-to rule face exactly the same seeded demand and lead times, day for day, so the difference you see between them comes from the policies rather than from luck. Unmet demand walks away rather than waiting in a backlog.

The model, stated plainly

What happens on a day

Anything scheduled to arrive today arrives and joins on-hand stock.
The policy reviews. The continuous rule looks every day; the periodic rule looks only on its review days.
If the rule says to order, the order is placed and scheduled to arrive after its lead time. Lead time is at least one day, so nothing ever arrives the same day it is ordered.
Demand arrives. Whatever is on the shelf is sold. Whatever is not on the shelf is lost — there is no backlog and no back-order queue, so a customer turned away today does not return tomorrow.
Closing on-hand stock is charged holding cost.

Inventory position

Both rules review the actual inventory position: on-hand stock plus everything already ordered and still in transit. Tracking only on-hand stock is the classic way to over-order, because the same shortfall gets covered again on every review until the first shipment lands.

The two rules

Continuous (r, Q). Reviewed daily. When the inventory position falls to r or below, order whole lots of Q until the position sits above r. Ordering in lot multiples matters when a large day of demand drops the position far below r at once; a single lot would leave it short.
Periodic order-up-to (R, S). Reviewed every R days. When the inventory position is below S, order the gap so the position lands exactly on S. Between reviews the rule does nothing, whatever happens.

How the two are made comparable

For each replication the lab draws one demand series and one lead-time series, then runs both policies against those same numbers. The lead time for an order placed on day t is the same draw for both policies, so when both order on the same day both wait the same number of days. This is common random numbers: it strips out the shared noise and leaves a much cleaner paired comparison than running the two policies on separate random streams.

Demand and lead times come from separate streams, so switching the demand distribution leaves the lead-time draws untouched and vice versa.

Where the model is thin

The continuous rule is reviewed once a day, not truly continuously. On a daily clock that is the closest it gets.
Orders may cross: with variable lead times a later order can arrive before an earlier one. The lab allows this rather than forcing arrivals into sequence, which is the more realistic of the two choices but makes some textbook formulas inapplicable.
Each policy starts full at its own target — the continuous rule at r plus Q, the periodic rule at S. The 30-day warmup exists to let that starting choice wash out, but it does not erase it completely.
No capacity limits, no minimum order quantities, no quantity discounts, no perishability, no supplier failures.

Set up the scenario

Demand

Daily demand distribution

Mean daily demand

Demand standard deviation

Only used by the normal option. Poisson fixes the variance at the mean.

Lead time

Shortest lead time (days)

Whole days. One is the smallest the model allows.

Longest lead time (days)

Set it equal to the shortest for a fixed lead time. Otherwise every whole number in the range is equally likely.

Policies

Continuous: reorder point r (units)

Continuous: lot size Q (units)

Periodic: review every R days

Periodic: order-up-to level S (units)

Costs

Holding, per unit per day

Ordering, per order placed

Lost sale, per unit turned away

Run

Seed

Any text. The same seed and settings give identical results every time.

Fixed for every run: 30 warmup days that are simulated but not scored, 180 measured days, and 100 replications.

Results

The P10 to P90 columns are spread, not confidence intervals. They say that 80 of the 100 simulated 180-day runs landed between those two numbers — that is how much a single season varies. A confidence interval would describe how precisely the lab has pinned down the average, and it shrinks as you add replications. These bands do not shrink; they describe the business risk, and running more replications only measures them more sharply.

For the average, use the standard error reported with the paired difference below. That one does shrink with more replications, and it is the right number for asking whether one policy really beats the other.

Per-policy results over the 180 measured days, averaged across 100 replications.
Measure	Continuous (r, Q)	Periodic (R, S)	Reading it

Paired difference, periodic minus continuous

Because both policies see the same demand and lead times in each replication, the two can be subtracted replication by replication. That pairing removes the shared randomness and is far more sensitive than comparing the two averages on their own.

Positive numbers mean the periodic policy cost more or served worse.
Measure	Mean difference	Standard error of that mean	P10 to P90 of the difference

Each bar spans P10 to P90 of total cost across the 100 replications. The notch is the median; the dot is the mean.

Continuous (r, Q) Periodic (R, S)

Closing on-hand stock for replication 1. The shaded block on the left is the 30-day warmup, which is simulated but excluded from every number above. A line touching zero is a day that ended with nothing on the shelf.

Continuous (r, Q) Periodic (R, S)

Replication 1, day by day, as a table

Every day of replication 1 for both policies.
Policy	Day	Phase	Received	Position at review	Ordered	Lead	Demand	Sold	Lost	On hand, close

Export

Every export repeats the seed and the full scenario, so a file can be traced back to the run that made it.

Self-tests

A simulation is easy to get subtly wrong, and a wrong one still produces confident-looking averages. These checks run the same simulation code and confirm the accounting closes: units are conserved, stock never goes negative, orders fire only when the rule says they should, and the same seed reproduces the same numbers. The values in the table are computed when you press the button.

Also callable from the console as window.runToolTests().

Things worth trying

Widen the lead time without changing its mean. Move from 4 to 4 days up to 1 to 7 days. The average wait is unchanged; the fill rate usually is not. Variability, not the average, is what a buffer has to absorb.
Stretch the review interval. Push R from 7 to 14 days with S unchanged and watch the periodic policy give ground. The periodic rule is blind between reviews, so it has to carry cover for the review interval plus the lead time, while the continuous rule only covers the lead time.
Raise the lost-sale penalty. Physical flows do not move at all — the same units are sold and the same units are lost — but the ranking of the two policies can flip, because the penalty reprices the same outcome.
Take Q down and watch ordering cost climb. Small lots hold less stock and order far more often. Where those two lines cross is the practical version of the economic order quantity, found by simulation rather than by the square-root formula, and with lost sales in the picture the two answers do not have to agree.