Calculate safety stock, reorder point (ROP), and expected backorders using Poisson demand.
Why use a Poisson inventory model instead of Normal distribution for MRO spares?
Standard safety stock formulas assume normally distributed continuous demand. Critical maintenance spares (motors, turbines, pumps) have slow-moving, discrete Poisson failure arrivals (e.g. 0 to 3 failures per year). Using Normal distributions severely under-stocks or distorts stocking levels for slow-moving parts.
| Stock Level (s) | Cycle Service Level P(K ≤ s) | Recommendation |
|---|---|---|
| 0 units | 36.79% | Risk of Stockout |
| 1 units | 73.58% | Risk of Stockout |
| 2 units | 91.97% | ★ Optimal Stocking Point |
| 3 units | 98.10% | Acceptable (Higher Holding Cost) |
| 4 units | 99.63% | Acceptable (Higher Holding Cost) |
| 5 units | 99.94% | Acceptable (Higher Holding Cost) |
For slow-moving insurance and capital spares, demand across lead time L follows a Poisson distribution with parameter θ = λ · L. The optimal inventory level s* is the smallest non-negative integer satisfying: Σk=0^s [ e-θ · θ^k / k! ] ≥ CSL.
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