OptimalSPARES™ Wiki / Stocking models
Method and tool
Stocking models
Once criticality has set the target service level, inventory theory sizes the stock: how much to order at a time, when to reorder, and how much buffer to carry against uncertainty. The classic formulae, the slow-mover case, and a live calculator.
Economic order quantity
EOQ = √(2 · D · S ÷ H)
D is annual demand, S the cost of placing an order and H the cost of holding one unit for a year. EOQ is the order size that balances ordering too often against holding too much. It is the how-much-to-order half of the policy, and it sets the gap between the min and the max.
Reorder point and safety stock
Safety stock SS = z · σLT
Reorder point ROP = (d · L) + SS
Min = ROP · Max = ROP + order quantity
The reorder point is the level at which a new order is raised. It covers the demand expected during the lead time, d times L, plus a safety stock for the uncertainty in that demand. The safety stock is the buffer, and z is the multiplier set by the target service level.
Service level and z
The service level is the probability of not stocking out during a replenishment cycle, and it maps to the z multiplier on the safety stock. Higher service costs disproportionately more stock, which is why it is spent on the critical parts and saved on the routine ones:
| 90% | z = 1.28 |
|---|---|
| 95% | z = 1.64 |
| 98% | z = 2.05 |
| 99% | z = 2.33 |
Slow movers and insurance spares
Most spare parts are slow, intermittent and discrete, so the normal-demand assumption behind EOQ breaks down. Slow-moving demand is better modelled as a Poisson process, where the variance equals the mean, so the standard deviation over the lead time is the square root of the expected lead-time demand. For very critical or very expensive items, a one-for-one (S−1, S) policy, order one each time one is used, is often right. OptimalSPARES™ picks the model that fits the demand pattern rather than forcing one formula on every part.
Try it: the stocking calculator
Set the demand, the lead time and the service level to see the safety stock and the min and max. Watch how a longer lead time or a higher service level, the mark of a more critical part, raises the stock.
Service level follows criticality: the more critical the part, the higher the target. Slow-moving spares are modelled as Poisson, so the standard deviation is the square root of lead-time demand. Illustrative.
Recommended stocking
Safety stock 3 · demand in lead time 1.8 · z 1.64
Where OptimalSPARES™ fits
OptimalSPARES™ applies these models across the whole catalogue at once: it fits the demand pattern per part, picks normal, Poisson or one-for-one, sizes the safety stock to the criticality-driven service level, and returns the min, max and reorder point ready for the ERP. The maths is applied consistently, not part by part in a spreadsheet.