Supply Chain Industry Presets
Select an operational preset to prefill daily demand distribution, supplier transit windows, and service targets.
Step 1: Operational Demand & Lead Time Variables
Inventory Parameters & Volatility Metrics
Step 2: Replenishment Thresholds & Buffer Breakdown
Reorder Point & Safety Stock Summary
| Replenishment Component | Units / Days | Capital Value ($) | Operational Function & Significance |
|---|---|---|---|
| Deterministic Lead Time Demand ($\bar{d} \times \bar{L}$) | 1,680 units | $58,800 | Expected unit consumption while waiting for supplier arrival (120 units/day $\times$ 14 days). |
| Demand Uncertainty Contribution ($\bar{L} \times \sigma_D^2$) | 8,750 variance | — | Variance arising from daily sales fluctuations during the 14-day transit window. |
| Lead Time Uncertainty Contribution ($\bar{d}^2 \times \sigma_L^2$) | 129,600 variance | — | Variance arising from vendor shipping delays ($\pm 3$ days supplier standard deviation). |
| Total Standard Deviation of Lead Time Demand ($\sigma_{LTD}$) | 370.0 units | — | Joint combined standard deviation: $\sqrt{\bar{L}\sigma_D^2 + \bar{d}^2\sigma_L^2}$. |
| Required Statistical Safety Stock ($\text{SS} = Z \times \sigma_{LTD}$) | 609 units | $21,315 | Buffer absorbing 95.0% of all peak surges and port customs delays. |
| Total Recommended Reorder Point (ROP) | 2,289 units | $80,115 | Total inventory position (on-hand + on-order) trigger point. |
| Annual Safety Stock Carrying Cost Drag | — | $4,689 / yr | Working capital cost to hold 609 safety stock units at 22.0% annual holding rate. |
Step 3: Multi-Variable Inventory Risk Sensitivity Matrices
Service Level ($Z$) vs. Supplier Lead Time & Demand Volatility Stress Tests
Reorder Point (ROP Units): Service Level vs. Supplier Lead Time ($\bar{L}$)
ROP trigger levels across service levels (columns) and average lead time in days (rows).
Annual Safety Stock Holding Cost ($): Service Level vs. Lead Time Std Dev ($\sigma_L$)
Annual carrying cost drag across service levels (columns) and vendor delay volatility (rows).
Supply Chain Operations Methodology
Reorder Point Mathematical Formulations & Volatility Decomposition
1. Classical vs. Joint Variable Reorder Point
In elementary textbook models, lead time is assumed constant ($\sigma_L = 0$). In modern global supply chains, supplier transit variability often creates far more stockout risk than customer demand swings:
Key Insight: The second term inside the radical, $\bar{d}^2\sigma_L^2$, scales with the square of daily demand. High-volume SKUs sourced from unreliable suppliers demand massive safety stocks unless lead times are compressed.
2. The Economics of Service Levels
Cycle Service Level (CSL) corresponds to the cumulative distribution function (CDF) of the standard normal distribution curve:
Exponential Curve: Increasing service levels from 95% ($Z=1.645$) to 99.5% ($Z=2.576$) increases safety stock by over 56%, directly inflating working capital requirements. Inventory managers must balance this carrying cost against the gross margin penalty of lost customer sales.
Frequently Asked Questions