ModelRisk Optimizer example · Manufacturing

Inventory Policy Chosen by the Optimizer

Which reorder point and order quantity cost least while keeping the service the customers were promised?

Complexity: ★★★★★
Free Excel workbook (MF-09)
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From the model’s saved run

The Optimizer’s plan against the starting plan

The two policies, and how each performs on the same simulated replenishment cycles.

Decision	Unit	Starting plan	Optimizer’s plan	Change
Reorder point	units	750	832	82
Order quantity	units	940	997	57

Measure	Unit	Starting plan	Optimizer’s plan	Change
Annual cost, mean	US$ a year	7,263	7,374	111
Stock held on average	units	890	1,001	111
Orders a year	orders	15.5	14.6	−0.9
Cycle service level	of cycles	95.9%	98.1%	2.2%	✔ better
Fill rate	of demand	99.59%	99.85%	0.3%	✔ better
Units short a year	units	60	22	−39	✔ better
Cycle service level promised	of cycles	97.5%	97.5%

Fill rate = 1 − units short in a cycle ÷ order quantity. Short a year = short in a cycle × orders a year.

Demand while an order is on its way, against the two reorder points

S-curve (cumulative probability) of Lead-time demand, Starting plan's reorder point, Reorder point in use from the saved simulation.

The business question

A distributor stocks a fast-moving component: about 40 units a day, but some days 20 and some days 70. When its stock falls to a reorder point it orders a fixed quantity, which the supplier usually delivers in five to ten days. About one order in ten is held up for another one to three weeks.

MF-04 compared six reorder points with the economic order quantity and found the cheapest. But the customers have now been promised that 97.5% of cycles end without running out, and the reorder point and the order quantity interact: a larger order means fewer cycles a year, so fewer chances to run out, but more stock on the shelf. Here the ModelRisk Optimizer chooses both together.

Who it is for: Supply-chain and inventory planners, operations managers, buyers.
Main outputs: The Optimizer's reorder point and order quantity against a starting plan (MF-04's cheapest reorder point with the economic order quantity) · for both plans: the annual cost, the cycle service level, the fill rate and the units short a year · the demand during a lead time against both reorder points.

What the Optimizer decides

The Optimizer changes the blue cells. The starting plan is MF-04's cheapest reorder point with the economic order quantity.

Decision	Unit	Starting plan	Optimizer’s plan	Lowest	Highest
Reorder point	units	750	832	300	1,500
Order quantity	units	940	997	400	3,000

Goal: Minimise the mean annual cost
Limit: Cycle service level at least 97.5% (the chance of no shortage in a cycle)
Limit: One order at a time: order quantity above the reorder point, in every plan tried

The Optimizer’s run: Vertex Detector, 109 plans tried, each on 10,000 samples, in 6.3 seconds.

How the model works

Four sheets after this one, read from left to right. Each one feeds the next.

Inputs sheet
The average and spread of daily demand. The supplier's normal lead time (PERT) and the chance and length of a disruption (risk event); the unit cost, holding cost, ordering cost and the cost of a unit short. The cycle service level promised to customers.
Decisions sheet
The two cells the Optimizer changes — the reorder point and the order quantity — with their bounds, the starting plan they are compared with, the goal (the least mean annual cost) and the limits (the service target, and one order at a time).
Inventory sheet
Each iteration draws one lead time — the normal time plus any disruption, in whole days — and adds up that many daily demands (VoseAggregateMC). For each plan, the units short before the order arrives and the cost of a year of such cycles are recorded as outputs.
Results sheet
Both plans on the same simulated cycles: the mean and 90th percentile of the annual cost, the cycle service level, the fill rate and the units short a year, and the demand during a lead time against both reorder points.

ModelRisk techniques

ModelRisk Optimizer: two whole-number decisions
Service level as a probability limit
Lead-time risk VoseRiskEvent
Lead-time demand VoseAggregateMC
Both plans on the same samples

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The results in detail

Demand while an order is on its way

Units demanded during one lead time.

Demand during the lead time — distribution

Histogram of Lead-time demand from the saved simulation.

Measure	Unit	5th pct	Median	95th pct	Mean
Lead-time demand	units	202	291	720	329

How to read these results

The starting plan — a reorder point of 750 units, MF-04's cheapest, with the economic order quantity of 940 — runs out in about 4% of cycles, so it misses the 97.5% service promised.
The Optimizer raises the reorder point just far enough to keep the promise and orders a little more than the economic order quantity: fewer orders a year mean fewer chances to run out, which is worth more than the extra stock on the shelf.
Keeping the promise costs only a little more a year than the starting plan, and the units short a year fall by almost two-thirds.
Try a 99% promise on the Inputs sheet and run the Optimizer again: the reorder point needed rises steeply, because the disrupted orders decide the safety stock.

Run the Optimizer yourself. Open the workbook, open the Optimizer from the ModelRisk ribbon (the saved task opens with it) and press Start; then simulate to compare the plans.

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Inputs and assumptions

Every assumption in the model, with its uncertainty and where it comes from. The figures are illustrative.

Demand 3 inputs

Assumption	Unit	Value
Average daily demandLast year's sales ÷ selling days.	units a day	40
Standard deviation of daily demandFrom daily sales records.	units a day	15
Selling days a year	days	365

Lead time 3 inputs

Days from placing an order to receiving it.

Assumption	Unit	Uncertainty	Low	Most likely	High
Normal lead timeThe supplier's usual delivery.	days	PERT	5.0	7.0	10.0
Chance of a disruptionAbout one order in ten is held up.	of orders	Fixed	10%
Disruption delayA missed sailing or a customs check: one to three extra weeks.	days	Risk event · PERT	5.0	10.0	20.0

Costs 4 inputs

Assumption	Unit	Value
Unit cost	US$	20
Holding costCapital, storage, obsolescence.	of unit cost a year	25%
Cost of placing an orderPurchasing, freight booking, receiving.	US$	150
Cost of a unit shortLost margin and goodwill.	US$	8

Service promised 1 input

The limit the Optimizer must respect.

Assumption	Unit	Value
Cycle service level promisedThe share of replenishment cycles that must end without running out.	of cycles	97.5%

Units and conventions

Units: Units of the component; money in US$.
Reorder point: The stock level (on hand plus on order) at which a new order is placed.
Order quantity: The units ordered each time; annual demand ÷ order quantity = orders (cycles) a year.
Cycle service level: The chance that stock does not run out before an order arrives.
Fill rate: The share of demand served from stock: 1 − units short ÷ order quantity.

Key assumptions and limitations

Policy: Continuous review: an order of a fixed quantity whenever stock reaches the reorder point. One order outstanding at a time, which the Optimizer is told to keep (order quantity above the reorder point).
Demand: Daily demands are independent Gamma variables; unmet demand is lost.
Lead time: Independent of demand; disruptions affect whole orders.
Optimizer: Each plan the Optimizer tries is judged on the same 10,000 simulated cycles (common random numbers, seed 1) as the simulation on the Results sheet, so plans are compared fairly and the limit the Optimizer met holds on the Results sheet too.
Data: The product and all figures are invented for this example.

How to use it

Enter your demand, your supplier's lead times, your costs and your service target on the Inputs sheet.
On the ModelRisk ribbon, open the Optimizer: the task is saved in this workbook. Press Start. When it finishes, apply the best solution: the reorder point and order quantity on the Decisions sheet change.
Run a simulation from the ModelRisk ribbon (10,000 samples with a fixed seed are set) to compare the new plan with the starting plan on the Results sheet.
To watch the search from the beginning, copy the starting plan onto the Optimizer’s plan first.

ModelRisk functions used

ModelRisk Optimizer: Chooses the reorder point and order quantity: least mean annual cost, cycle service level at least the target, order quantity above the reorder point.
VosePERT, VoseRiskEvent: The normal lead time and the disruption delay.
VoseAggregateMC, VoseGammaObject: The demand during the lead time: a random number of days, each with a Gamma demand.
VoseSimProbability, VoseSimMean, VoseSimPercentile: Service levels, expected shortages and costs of both plans.

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An illustrative example: the figures are invented for teaching and do not describe a real company, project or asset. Last updated 9 October 2026.