Business & Operations
Part-Period Balancing (EPP) & Groff's Marginal Lot-Sizing Heuristic in MRP
Determine discrete MRP production batch horizons under lumpy time-varying demand using Economic Part-Period EPP = S / h and Groff's marginal rule D_{t+n} * n * (n + 1) <= 2*S / h.
Replace static EOQ when weekly MRP net requirements jump up and down!
Classic EOQ = SQRT(2*D*S / h) assumes flat, continuous demand—a poor fit for lumpy MRP schedules where weekly net requirements swing from 50 units to 0 to 90 units! Part-Period Balancing (PPB) converts setup cost S ($180) and per-unit per-period holding cost h ($1.50/unit-week) into the Economic Part-Period EPP = S / h = 120 unit-periods: holding 120 units for 1 week (or 60 units for 2 weeks) costs the exact same $180 as triggering a new setup! You batch future periods n = 1, 2, ... until cumulative part-periods SUM(n * D_{t+n}) match EPP as closely as possible.
Gene K. Groff improved on PPB by equating marginal setup savings against marginal holding cost, yielding Groff's clean marginal stopping test: include period t + n in the current batch as long as D_{t+n} * n * (n + 1) <= (2 * S) / h (= 240)! For demands D1 = 80 (n=0), D2 = 50 (n=1: 50*1*2 = 100 <= 240 -> Batch!), D3 = 35 (n=2: 35*2*3 = 210 <= 240 -> Batch!), and D4 = 40 (n=3: 40*3*4 = 480 > 240 -> Stop & Start New Lot!), Groff cleanly batches Weeks 1–3 (165 units, cumulative part-periods = 50*1 + 35*2 = 120 = exact EPP)!
| Period Offset n | Net Demand D_{t+n} | Cumulative Part-Periods (EPP = 120) | Groff Test D*n*(n+1) <= 240 |
|---|---|---|---|
| Week 1 (n = 0, Setup Week) | 80 units | 0 part-periods | 0 <= 240 -> Include |
| Week 2 (n = 1 week held) | 50 units | 50 * 1 = 50 | 50 * 1 * 2 = 100 <= 240 -> Include |
| Week 3 (n = 2 weeks held) | 35 units | 50 + (35 * 2) = 120 (= EPP!) | 35 * 2 * 3 = 210 <= 240 -> Include |
| Week 4 (n = 3 weeks held) | 40 units | 120 + (40 * 3) = 240 (> EPP) | 40 * 3 * 4 = 480 > 240 -> STOP (New Lot!) |
Economic Part-Period Threshold EPP = S / h (Unit-Periods)
Divides setup/ordering cost S (F2) by per-unit per-period holding cost h (F3).
=IF(OR(F2 <= 0, F3 <= 0), "Invalid Cost Inputs", ROUND(F2 / F3, 2))Groff Marginal Lot-Sizing Decision for Period Offset n
Tests D_{t+n} * n * (n + 1) <= (2 * S) / h to decide whether to append period t+n to the current production lot.
=IF(B5 * A5 * (A5 + 1) <= (2 * $F$2) / $F$3, "Add to Current Lot", "Start New Setup")Try the example
Use the original values or change them to test your understanding.