MRP Lot Sizing: Lot for Lot, POQ and EOQ With Example

What an MRP lot sizing policy is

An MRP lot sizing policy is the rule that decides how much to order or produce, and in which weeks, from the net requirements calculated by MRP. The most common rules are lot-for-lot (L4L), fixed order quantity (EOQ) and periodic order quantity (POQ), and the choice changes the number of orders and the inventory.

MRP tells you what is needed and when. The lot sizing policy tells you how to group those requirements into orders: ordering small and often raises setup or ordering cost; ordering large and rarely raises inventory.

Visual map of lot sizing rules

The map compares the three rules on the same data and shows the total cost of each.

The three rules and when each one fits

EOQ = √(2 × D × S ÷ H)   |   T = EOQ ÷ D (periods)   |   POQ covers T periods

D is average demand per period, S is the cost per order or setup, and H is the cost of holding one unit for one period. For manufactured items with a finite production rate, see the economic production quantity (EPQ). Reorder point and economic order quantity logic is in inventory management; here the focus is demand that changes week by week.

Example: eight weeks of requirements for one component

Fictional example. Net requirements: 35, 30, 40, 0, 10, 40, 30 and 0 units, total 185, average D = 185 ÷ 8 = 23.125 per week. Order cost S = $100, holding cost H = $1 per unit per week, charged on each week’s ending inventory. Starting inventory is zero and lead time is ignored for simplicity (afterwards, offset the orders by the lead time).

EOQ = √(2 × 23.125 × 100 ÷ 1) = √4,625 ≈ 68 units; T = 68 ÷ 23.125 ≈ 2.94, so 3 periods

Lot-for-lot

Six orders (in the weeks with a requirement) and no inventory: 6 × 100 + 0 = $600.

Fixed quantity of 68 (EOQ)

Three orders of 68 and summed ending inventory of 206 unit-weeks: 3 × 100 + 206 × 1 = $506.

Periodic order, T = 3 (POQ)

Three orders (105 for weeks 1 to 3, 50 for weeks 4 to 6, and 30 for weeks 7 and 8) and summed inventory of 200: 3 × 100 + 200 × 1 = $500.

Comparing the results

Three points show how to read the table:

• Lot-for-lot has the highest cost here only because setup is expensive relative to inventory. If S were $10, it would be the best.
• T = 3 comes from rounding the formula and does not guarantee the minimum: T = 4 costs $410 and T = 2 costs $470. Test the neighboring periods before fixing T.
• For reference, the optimal plan for this case (Wagner-Whitin algorithm) costs $380, with orders of 65, 50 and 70 units. The simple rules land close to the optimum without heavy computation.

The EOQ cost also includes 19 units left over at the end of the horizon. In a rolling plan, that surplus would be used in week 9.

How to choose the lot sizing policy

1. Classify the items. Use the ABC curve: A items deserve lot-for-lot or a short POQ; C items accept a large fixed lot.
2. Compare S and H. Expensive setup favors larger lots; expensive inventory favors lot-for-lot.
3. Look at demand variability. Stable demand accepts a fixed lot; lumpy demand calls for POQ or lot-for-lot.
4. Respect constraints. Packaging multiples, supplier minimum quantities and line capacity (see capacity planning).
5. Release the orders. Planned orders become production orders or purchase orders.

Lot size also interacts with safety stock, which MRP handles separately, and with the higher-level plan in the MPS.

Common mistakes and limitations

• Using an average-demand EOQ on lumpy demand. A fixed lot calculated for the average leaves excess in slow weeks and shortages in busy ones.
• Estimating S and H carelessly. Setup cost should include real lost time; H should include cost of capital, space and obsolescence.
• Ignoring lead time. The rules set quantities by requirement week; the release date comes from offsetting by lead time.
• Applying one rule to every item. Each item has its own S, H and demand profile.
• Never reviewing. Revisit the policy when setup changes. Setup reduction (SMED) makes lot-for-lot viable. Also check the effect on inventory turnover.

Frequently asked questions

What is lot-for-lot in MRP?

It is the rule that creates one order per requirement, in the exact quantity, leaving inventory close to zero.

What is the EOQ formula?

EOQ = √(2 × D × S ÷ H). In the example: √(2 × 23.125 × 100 ÷ 1) ≈ 68 units.

What is POQ?

Periodic order quantity: each order covers the requirements of T periods, with T = EOQ ÷ D rounded.

Which lot sizing rule is best?

It depends on S, H and demand. In the example, POQ with T = 3 cost $500, against $600 for lot-for-lot and $506 for fixed EOQ.

Does a fixed lot suit lumpy demand?

Poorly: it creates excess and shortages. Prefer POQ or lot-for-lot.

Does MRP choose the policy by itself?

No. You set a rule per item, and MRP applies it when calculating planned orders.

About the author

Vagner Soares

Lean Manufacturing & Behavioral Management Specialist

Over 20 years in the automotive and metalworking industries (GM and Dana), Lean Manufacturing practitioner since 2006. SENAI instructor and mentor in Brazil’s Brasil Mais Produtivo program, delivering consulting, training and audits for 50+ companies, combining quality, productivity and people development.

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