A SEASONAL ORDER UNDER UNCERTAINTY

How much upside is worth the downside?

Learn why the order that maximizes expected contribution can differ from the order that fits a loss limit.

A fictional store’s picnic-tote launch. Synthetic assumptions; no institutional affiliation.

Edit assumptions and rerun the experiment

Change inputs together, then run 10,000 shared scenarios. Results stay labeled as the last completed run until you rerun. Reload resets the example; copy your completed assumptions from the model details before leaving.

YOUR ASSUMPTIONS

Set the season.

01 · Demand forecast

Underlying mean, unitsStandard deviation, units

Normal demand, conditioned to be nonnegative, then rounded to whole units. The realized mean can differ from your input.

Preparing the demand preview…

02 · Product economics

Selling price, USDLeftover recovery, USDUnit cost min, USDUnit cost max, USD

Fixed launch cost, USD

Landed unit cost is uniform across the range, independent of demand. One cost applies to the entire order in each scenario.

03 · Comparisons & risk limit

Option A, unitsOption B, unitsOption C, units

Maximum chance of loss, %

We screen every whole order from 1–5,000 units. A small sampling cushion must fit inside this limit.

04 · Reproduce the experimentRandom seed

10,000 shared demand/cost draws per run. Identical assumptions and seed reproduce the same outcomes.

Default scenario is ready.

Certainty: demand 500, deviation 0 and unit cost $21. Hand-check all three order choices.

Preparing the fonts and 10,000 shared scenarios…

THE QUANTITY DECISION

Find the peak, then apply the risk limit.

Primary comparison · expected contribution is analytic; loss share is simulated
Order	Units	Expected contribution	Loss estimate	Screen

Inspect downside and inventory

Contribution and inventory

Inspect order

Model, statistical checks and reproducibility

Contribution = full-price sales × price + leftovers × recovery − ordered units × landed cost − fixed launch cost. It excludes headquarters costs, tax and financing. Missed demand disappears; every leftover is cleared. The launch cost is incurred for every allowed order; choosing not to launch is outside this comparison.

The expected-profit curve enumerates all whole quantities from 1–5,000. Demand is a normal distribution conditioned above zero and rounded to units; cost is independently uniform and rounded to cents. Expected profit uses the midpoint cost. This is a model benchmark, not a forecast of real demand.

The critical ratio is (price − mean cost) / (price − recovery), when price > mean cost > recovery. It identifies the unconstrained continuous demand quantile; the marker uses the exact best allowed integer under rounded demand. Fixed launch cost does not shift that peak.

Loss means contribution below zero. We reuse 10,000 seeded demand/cost draws across every quantity. The screen uses the upper endpoint of a 95% Wilson loss-probability interval, a conservative sampling cushion. This controls sampling noise, not model uncertainty. Certainty cases use their exact loss rate. Among eligible quantities, the highest analytic expected contribution wins; ties favor fewer units.

One world, different orders

Inspect a shared scenario

Same demand and landed cost for every compared order
Ordered units	Demand units	Cost per unit	Contribution

Paired worlds isolate the effect of changing quantity. Redrawing an independent world for each order would mix that change with additional simulation noise.

Monte Carlo cross-check for the three editable comparisons
Units	Simulated mean	Exact expected	Mean sampling interval	Loss interval

Reload resets the example. Copy the completed assumptions before leaving if you need to retain this experiment.