Supply Chain & Inventory Formula Library
Rigorous mathematical formulas and variable definitions implemented across the AshToolbox client-side calculation engines.
1. Economic Order Quantity (EOQ & EPQ)
Classic Wilson-Harris EOQ:
Q* = sqrt( (2 * D * S) / H )
Where $D$ is annual demand, $S$ is fixed order setup cost, and $H = i \cdot C$ is annual unit holding cost.
Economic Production Quantity (EPQ):
Q_EPQ* = sqrt( (2 * D * S) / (H * (1 - D / P)) )
Where $P > D$ is the finite production rate per year.
2. Safety Stock & Reorder Point (ROP)
Combined Demand & Lead-Time Variability (Independent):
SS = z * sqrt( L_bar * sigma_D^2 + D_bar^2 * sigma_L^2 ) ROP = D_bar * L_bar + SS
Unit Normal Loss Integral for Fill Rate (1 - Beta):
G(z) = phi(z) - z * (1 - Phi(z)) = ((1 - FillRate) * Q) / sigma_DL
3. Bullwhip Effect Analytical Lower Bound (Chen et al. 2000)
Var(Orders) / Var(Demand) >= 1 + (2 * L) / p + (2 * L^2) / p^2
Where $L$ is stage replenishment lead time and $p$ is moving-average forecasting window length.