Operations & Logistics
Periodic Order Quantity (POQ) Time-Supply Interval & Discrete MRP Lot Sizing
Convert fractional Wilson EOQ into an integer MRP order cycle T_POQ = MAX(1, ROUND(EOQ / D_period, 0)) and evaluate discrete Periodic Order Quantity lot size and cycle cost.
Why MRP planners convert continuous EOQ into an integer number of periods (POQ)
Continuous Economic Order Quantity EOQ = SQRT(2 * D * S / h) often recommends awkward fractional intervals—for example, 632.46 units when weekly demand is D = 250 units/week, equivalent to 2.53 weeks of supply! Ordering every 2.53 weeks clashes with weekly MRP buckets, supplier truck schedules, and discrete period requirements.
Periodic Order Quantity (POQ) divides EOQ by average period demand D_period and rounds to the nearest positive integer cycle T_POQ = MAX(1, ROUND(EOQ / D_period, 0)) (here 3 weeks, ordering 3 * 250 = 750 units per release). Because the EOQ total-cost curve is remarkably flat near its minimum, rounding 2.53 weeks to an integer 3-week cycle raises weekly setup-plus-holding cost from theoretical 316.23 to 320.83—just +1.45%—while aligning cleanly with weekly MRP buckets.
| Lot-Sizing Metric (D=250/wk, S=400, h=0.50/wk) | Formula | Result |
|---|---|---|
| Continuous Wilson EOQ | SQRT(2 * 250 * 400 / 0.50) | 632.46 units (2.53 weeks) |
| Integer POQ Cycle T_POQ | MAX(1, ROUND(EOQ / D_wk, 0)) | 3 weeks |
| POQ Release Quantity Q_POQ | T_POQ * D_wk | 750 units |
| Weekly Setup + Holding Cost | (S / T_POQ) + 0.5 * Q_POQ * h_wk | 320.83 (+1.45% vs EOQ optimum 316.23) |
Integer POQ Order Interval T_POQ Formula (Periods)
Compute continuous EOQ inside LET, divide by period demand B2, round to the nearest integer, and floor at 1 period (lot-for-lot).
=LET(eoq_u, SQRT((2 * B2 * B3) / B4), MAX(1, ROUND(eoq_u / B2, 0)))POQ Lot Size & Weekly Total Relevant Cost Formula
Multiply T_POQ (E4) by period demand B2 for steady-state order size, and sum weekly setup cost B3 / E4 plus average cycle holding cost 0.5 * E5 * B4.
=ROUND((B3 / E4) + 0.5 * E5 * B4, 2)Try the example
Use the original values or change them to test your understanding.