Lot size

Lot size is the quantity of units produced, purchased, or processed as a single batch in manufacturing and inventory management, representing a fundamental decision that balances setup costs against holding costs (Stevenson W.J. 2018, p.543)^[1]. Produce too few units per batch and you waste time and money on frequent setups. Produce too many and capital sits frozen in inventory while storage costs mount. Somewhere between those extremes lies an optimal quantity—the lot size that minimizes total costs.

The concept dates to 1913, when Ford W. Harris published his economic order quantity formula in Factory magazine. Over a century later, lot sizing remains central to operations management. Modern enterprise resource planning systems calculate lot sizes automatically, but the underlying trade-offs haven't changed. Whether you're ordering components from a supplier or scheduling production runs, lot size decisions shape efficiency, cash flow, and customer responsiveness.

Economic order quantity (EOQ)

The classic lot sizing model:

The Harris-Wilson formula

Basic EOQ. The economic order quantity formula is EOQ = √(2DS/H), where D represents annual demand, S is the cost per order or setup, and H is the annual holding cost per unit^[2].

Balancing costs. EOQ occurs where annual ordering costs equal annual holding costs. At smaller lot sizes, you order more frequently (high ordering costs, low inventory). At larger lot sizes, you order less frequently (low ordering costs, high inventory).

Square root relationship. Because of the square root, EOQ increases less than proportionally with demand. If demand quadruples, optimal lot size only doubles.

Assumptions

Constant demand. The basic model assumes steady, predictable demand throughout the year.

Instantaneous replenishment. Orders arrive all at once, not gradually.

No stockouts. The model assumes you always meet demand without shortages.

Fixed costs. Order and holding costs remain constant regardless of quantity or timing^[3].

Extensions

Quantity discounts. When suppliers offer price breaks at volume thresholds, the analysis must compare total costs at EOQ versus costs at discount quantities. Sometimes ordering more than EOQ saves money.

Non-instantaneous receipt. When production occurs over time rather than arriving all at once, the economic production quantity (EPQ) model applies, yielding larger optimal lot sizes.

Planned shortages. If backorders are acceptable and incur known costs, models can incorporate intentional stockouts.

Lot sizing in MRP systems

Material requirements planning uses various approaches:

Lot-for-lot

Exact requirements. Lot-for-lot ordering produces or orders exactly what's needed each period. No more, no less.

Minimum inventory. This approach minimizes holding costs but may increase setup frequency.

JIT compatibility. Lot-for-lot aligns with just-in-time philosophies that treat inventory as waste^[4].

Fixed order quantity

Predetermined amount. Orders are always the same size, regardless of actual requirements. May result in inventory accumulation when requirements vary.

Standard containers. Physical constraints (pallets, containers, packaging) sometimes dictate fixed lot sizes.

Period order quantity

Coverage periods. Orders cover a fixed number of periods' requirements (e.g., always order four weeks' worth). Lot size varies based on forecasted demand.

Balancing act. POQ attempts to achieve EOQ benefits while handling variable demand.

Part-period balancing

Dynamic approach. This heuristic increases lot size until cumulative holding costs approximately equal setup costs.

Period-by-period. The calculation recurs each period, adapting to changing requirements^[5].

Manufacturing considerations

Lot size interacts with production realities:

Setup time and cost

Changeover burden. Setup involves cleaning equipment, changing tools, adjusting settings, loading programs, and running test pieces. These activities produce no output while consuming time and resources.

SMED revolution. Single-minute exchange of dies and other quick-changeover techniques dramatically reduce setup times. Lower setup costs shift optimal lot sizes downward, enabling smaller batches.

Flexibility benefits. Shorter setups enable more frequent changeovers, improving responsiveness and reducing lead times.

Quality implications

Defect exposure. Large lots mean more units at risk if quality problems emerge. A defect discovered after producing 10,000 units has worse consequences than one found after 100 units.

Feedback delay. Small lots provide faster feedback on quality issues, enabling quicker correction^[6].

Capacity constraints

Machine availability. Limited capacity may force larger lot sizes to ensure sufficient production during available time.

Bottleneck management. At bottleneck resources, lot sizes affect system throughput. Lost setup time at bottlenecks is lost system capacity.

Inventory and financial impacts

Lot size decisions have broad effects:

Working capital

Inventory investment. Average inventory equals approximately half the lot size (in the basic model). Larger lots tie up more capital.

Cash flow timing. Larger lots mean larger but less frequent payments to suppliers, affecting cash flow patterns^[7].

Storage requirements

Space costs. Larger lots require more warehouse space, handling equipment, and management attention.

Obsolescence risk. Items held longer have greater risk of becoming obsolete, expiring, or suffering damage.

Customer service

Availability. Larger lot sizes mean more stock on hand, potentially improving fill rates.

Response time. Smaller lots with more frequent production can improve responsiveness to customer orders.

Beyond simple models

Real-world lot sizing involves complexity:

Multiple items. Joint replenishment of related items, shared setups, and coordinated ordering complicate single-item EOQ logic.

Stochastic demand. Variable, uncertain demand requires safety stock and more sophisticated lot sizing approaches.

Rolling schedules. Lot sizing recurs continuously as new information arrives and forecasts update^[8].

System integration. Modern ERP and advanced planning systems optimize lot sizes across entire supply chains, considering interactions that simple formulas ignore.

Lot size — recommended articles

Inventory management — Operations management — Production planning — Supply chain management

References

• Stevenson W.J. (2018), Operations Management, 13th Edition, McGraw-Hill.
• Harris F.W. (1913), How Many Parts to Make at Once, Factory, The Magazine of Management, 10(2), pp.135-136.
• Heizer J., Render B., Munson C. (2020), Operations Management, 13th Edition, Pearson.
• Hopp W.J., Spearman M.L. (2011), Factory Physics, 3rd Edition, Waveland Press.

Footnotes

1. ↑ Stevenson W.J. (2018), Operations Management, p.543
2. ↑ Harris F.W. (1913), How Many Parts to Make at Once, pp.135-136
3. ↑ Heizer J., Render B., Munson C. (2020), Operations Management, pp.498-512
4. ↑ Hopp W.J., Spearman M.L. (2011), Factory Physics, pp.234-256
5. ↑ Stevenson W.J. (2018), Operations Management, pp.567-578
6. ↑ Hopp W.J., Spearman M.L. (2011), Factory Physics, pp.278-294
7. ↑ Heizer J., Render B., Munson C. (2020), Operations Management, pp.523-534
8. ↑ Stevenson W.J. (2018), Operations Management, pp.589-602

Author: Sławomir Wawak