Vose SoftwareModelRisk example · Manufacturing
Inventory Policy under Uncertain Demand and Lead Time
When should we reorder? Demand while an order is on its way, the service level it buys, and the cost.
From the model’s saved run
Demand while an order is on its way
Units demanded during one lead time: simulated, and the Normal formula's view.
| Measure | Unit | 5th pct | Median | 95th pct | Mean |
|---|---|---|---|---|---|
| Lead-time demand, simulated | units | 202 | 291 | 720 | 329 |
| Lead time | days | 6 | 7 | 18 | 8 |
| Measure | Unit | Value |
|---|---|---|
| Standard deviation, simulated | units | 146 |
| Mean, Normal formula | units | 330 |
| Standard deviation, Normal formula | units | 146 |
S-curve (cumulative probability) of Lead-time demand from the saved simulation.
Histogram of Lead-time demand 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 the economic quantity, which the supplier usually delivers in five to ten days.
About one order in ten, though, is held up — a missed sailing, a customs check — for another one to three weeks, and the stock must last until it arrives. The textbook reorder point adds a safety stock based on a Normal distribution.
The model simulates the demand during the lead time as it really is, compares six reorder points on service and cost, and shows how far the Normal formula falls short.
- Who it is for
- Supply-chain and inventory planners, operations managers, buyers.
- Main outputs
- The demand during the lead time, simulated and by the textbook Normal formula · for six reorder points: the cycle service level, the fill rate, the units short a year and the annual cost · the reorder point that 95% and 99% service really need.
How the model works
Three 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 reorder points to compare.
Inventory sheet
The order quantity is the economic order quantity. 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 reorder point, the units short in that replenishment cycle and the cost of a year of such cycles are recorded as outputs.
Results sheet
The cycle service level (the chance of no shortage in a cycle), the fill rate (the share of demand served from stock), the units short a year and the annual cost of each reorder point. The reorder point that 95% and 99% service need, against the Normal formula.
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The results in detail
Which reorder point?
Service and cost of each reorder point, with the economic order quantity.
| Reorder point (units) | Cycle service | Fill rate | Short units a year | Cost US$ a year | Lowest cost |
|---|---|---|---|---|---|
| 350 | 78.3% | 95.72% | 624 | 9,774 | |
| 450 | 90.0% | 97.16% | 415 | 8,602 | |
| 550 | 91.1% | 98.16% | 269 | 7,931 | |
| 650 | 93.2% | 99.00% | 146 | 7,449 | |
| 750 | 95.8% | 99.59% | 60 | 7,263 | ✔ lowest |
| 850 | 98.4% | 99.88% | 18 | 7,425 |
Fill rate = 1 − units short in a cycle ÷ order quantity. Short a year = short in a cycle × orders a year.
The Normal formula against the simulation
The reorder point each service target needs, and the service the Normal formula really delivers.
| Cycle service target | Needed units, simulated | Normal formula, units | Delivers really |
|---|---|---|---|
| 95% | 720 | 571 | 91.5% |
| 99% | 893 | 670 | 93.6% |
How to read these results
- Demand during a lead time averages about 330 units but has two humps: most orders arrive within about a week and see 200 to 400 units of demand, while the one order in ten that is disrupted waits two to four weeks and sees 500 to 1,000. The Normal formula has the right mean and standard deviation, but not this shape.
- The Normal formula's reorder point for 95% service (571 units) runs out in about 9% of cycles, and its 99% point (670) delivers about 94%. Reaching 95% really takes about 720 units, and 99% about 900: the disrupted orders decide the safety stock.
- Weighing the cost of holding stock (US$5 a unit a year) against running out (US$8 a unit short), a reorder point of about 750 is cheapest here, at about US$7,300 a year. It serves 96% of cycles, and 99.6% of demand, from stock.
- The fill rate is much higher than the cycle service level: when stock runs out, it is usually for a few days at the end of a long delay, so most demand is still served. Choose the measure that matches what customers notice.
- Fewer disruptions may beat more stock: try a 5% chance of disruption on the Inputs sheet.
See it move. Open the workbook, change an input on the Inputs sheet and run the simulation: every table and chart on this page updates in Excel.
Inputs and assumptions
Every assumption in the model, with its uncertainty and where it comes from. The figures are illustrative.
Demand 3 inputs
| Assumption | Unit | Value |
|---|---|---|
| Average daily demandLast year's sales ÷ selling days. | units a day | 40 |
| Standard deviation of daily demandFrom daily sales records. | units a day | 15 |
| Selling days a year | days | 365 |
Lead time 3 inputs
Days from placing an order to receiving it.
| Assumption | Unit | Uncertainty | Low | Most likely | High |
|---|---|---|---|---|---|
| Normal lead timeThe supplier's usual delivery. | days | PERT | 5.0 | 7.0 | 10.0 |
| Chance of a disruptionAbout one order in ten is held up. | of orders | Fixed | 10% | ||
| Disruption delayA missed sailing or a customs check: one to three extra weeks. | days | Risk event · PERT | 5.0 | 10.0 | 20.0 |
Costs 4 inputs
| Assumption | Unit | Value |
|---|---|---|
| Unit cost | US$ | 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 |
Reorder points to compare 2 inputs
| Assumption | Unit | Value |
|---|---|---|
| Lowest reorder pointSix are compared. | units | 350 |
| Step between reorder points | units | 100 |
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.
- 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.
- Safety stock
- Reorder point − average demand during the lead time.
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.
- Demand
- Daily demands are independent Gamma variables; unmet demand is lost.
- Lead time
- Independent of demand; disruptions affect whole orders.
- Data
- The product and all figures are invented for this example.
How to use it
- Enter your demand, your supplier's lead times and the chance of a disruption.
- Enter your costs and the range of reorder points to compare.
- Run a simulation from the ModelRisk ribbon (10,000 samples with a fixed seed are set).
- Choose the reorder point with the lowest cost, or the one that meets your service target.
ModelRisk functions used
- 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.
- VoseVariance, VosePERTObject, VoseRiskEventObject
- The variance of the normal lead time and of the disruption delay, for the Normal formula.
- VoseSimProbability, VoseSimMean, VoseSimPercentile
- Service levels, expected shortages and costs, and the reorder points that targets need.
Further reading
- Monte Carlo simulation explained (Vose guide)
- Silver, E. A., Pyke, D. F. & Thomas, D. J. (2017). Inventory and Production Management in Supply Chains, 4th edition. CRC Press.
- Vose, D. (2008). Risk Analysis: A Quantitative Guide, 3rd edition. Wiley — aggregate distributions.
Download the workbook and run it yourself. It opens in Excel with ModelRisk. The free trial runs every example model.
Related example models
- ModelRiskOptimizer★★★★★Inventory Policy Chosen by the OptimizerWhich reorder point and order quantity cost least while keeping the service the customers were promised?Demand over a random lead time as an aggregate; the reorder point and order quantity chosen together by the Optimizer for a service target.
- ModelRisk★★★★★Reliability and Availability of a Production LineHow often will the line stop, what does it cost, and is a standby machine worth it?Four machines in series, each failing and being repaired at random through the year; one fitted to its failure records.
- ModelRisk★★★★★Capacity Expansion DecisionHow many presses should we add?Sixty months of seasonal, uncertain demand against four capacity options with overtime, subcontracting and lost sales.
An illustrative example: the figures are invented for teaching and do not describe a real company, project or asset. Last updated 9 October 2026.