Reorder Point & Safety Stock Lab (2D)

Demand

Mean daily demand (μ) 20 units

Demand model

Poisson (σ = √μ, discrete units) Gaussian (adjustable σ)

Demand variability σ (CV) 0.30

Replenishment

Lead time (L) 5 days

Target service level (z)

Order sizing

Fixed order quantity Economic Order Quantity (EOQ)

Order quantity (Q) 280 units

Ordering cost (K) $50/PO

Holding cost (h) $0.05/unit/day

Speed 3

Live Readout

Day

Stock on hand

—

Reorder point

—

Safety stock

—

Order qty in use

—

σ demand (rolling)

—

Fill rate (actual)

—

Target service level

95.0%

Stockout days

Stockout rate

0.0%

Avg inventory

—

Total cost

How it works

Every simulated day, a random demand is drawn either from a Poisson distribution (variance always equals the mean, μ — the standard model for discrete, independently arriving unit demand) or a Gaussian distribution with adjustable coefficient of variation (mean × CV = σ). Stock decrements by units actually sold; unmet demand is a stockout and does not carry over.

σ (rolling, 30-day window, sample st.dev.)
SS  = z · σ · √L              (safety stock)
ROP = μ̂ · L + SS              (reorder point)
EOQ = √(2 · D · K / h)         D = μ̂ × 365 (annual demand)

μ̂ and σ are re-estimated every day from a trailing 30-day demand window (not the slider's theoretical values), so the reorder point adapts the way a real inventory system's forecast would. A purchase order fires the moment stock crosses the current ROP and has none already in transit; it arrives exactly L days later. Raising the service level (z) or the lead time (L) both widen the safety-stock buffer — √L growth means doubling lead time only multiplies safety stock by ≈1.41×, but it also doubles the deterministic μ̂·L term, so total buffer needed still grows noticeably.

Orange band — the safety-stock cushion between (ROP − SS) and ROP.
Red columns — days a stockout occurred (demand exceeded stock on hand).
Green dot — a purchase order arriving; orange triangle — a purchase order being placed.

Stock level Reorder point Safety-stock band Order arrived Stockout day