Operations & Analytics
Peterson-Silver Variability Coefficient (V): EOQ vs. Dynamic Lot Sizing
Calculate Rein Peterson and Edward Silver’s squared-CV demand variability index V = (N * SUM(D^2)) / (SUM(D)^2) - 1 to decide when steady Economic Order Quantity (V < 0.25) beats Silver-Meal or Wagner-Whitin dynamic lot sizing (V >= 0.25).
Stop applying constant-demand EOQ to lumpy seasonal or MRP demand schedules!
Classic Wilson Economic Order Quantity (EOQ) assumes smooth, stationary demand across every planning bucket—so feeding lumpy promotional or MRP component schedules like [20, 260, 40, 80] into EOQ triggers either stockouts during demand spikes or bloated remnant inventory across quiet weeks!
Rein Peterson and Edward Silver (1979) established the industry-standard Operations Research decision test using the dimensionless Variability Coefficient V = (N * SUM(D_t^2)) / (SUM(D_t)^2) - 1 (equal to the population squared coefficient of variation (sigma / mu)^2 across N periods)! When V < 0.25 (for example, steady weekly demand [110, 95, 105, 90] -> V = 0.0063), simple fixed EOQ / POQ performs within ~1% of optimal cost; when V >= 0.25 (lumpy schedule [20, 260, 40, 80] -> V = 0.9000), planners must switch to time-phased Silver-Meal heuristic or exact Wagner-Whitin dynamic programming!
| 4-Period MRP Demand Schedule (Total = 400 Units) | Sum of Squared Demands | Variability Index V | Recommended Lot-Sizing Policy |
|---|---|---|---|
| Smooth Demand [110, 95, 105, 90] | 40,250 | 0.0063 (< 0.25) | Stationary EOQ / Fixed Order Quantity |
| Lumpy Promotional [20, 260, 40, 80] | 76,000 | 0.9000 (>= 0.25) | Dynamic Lot Sizing (Silver-Meal / Wagner-Whitin) |
| Zero Total Demand Across Horizon | 0 | Division Guard | "Zero Demand Horizon" |
Peterson-Silver Demand Variability Coefficient V = (N * SUM(D^2)) / (SUM(D)^2) - 1
Uses ROWS(B2:B5) for N and SUMPRODUCT(B2:B5, B2:B5) for sum of squared period demands.
=IF(SUM(B2:B5) <= 0, "Zero Demand Horizon", ROUND((ROWS(B2:B5) * SUMPRODUCT(B2:B5, B2:B5)) / (SUM(B2:B5) ^ 2) - 1, 4))Automated EOQ vs. Dynamic Lot-Sizing Policy Selector (V = 0.25 Cutoff)
Recommends Fixed EOQ when V < 0.25 and Dynamic Lot Sizing (Silver-Meal / Wagner-Whitin) when V >= 0.25.
=IF(SUM(B2:B5) <= 0, "Zero Demand Horizon", IF(((ROWS(B2:B5) * SUMPRODUCT(B2:B5, B2:B5)) / (SUM(B2:B5) ^ 2) - 1) < 0.25, "Use Stationary EOQ (V < 0.25)", "Use Dynamic Lot Sizing: Silver-Meal / Wagner-Whitin (V >= 0.25)"))Try the example
Use the original values or change them to test your understanding.