01 · Purpose and boundaries
Purpose and boundaries
Batch size determines how much work or material is processed or ordered together. Larger batches can spread fixed setup or ordering effort over more units, but increase inventory, waiting, space use, and response delay. The appropriate quantity depends on the decision boundary: purchase lot, production batch, transfer batch, and transport load are different choices.
Begin with the required service and physical constraints. Identify demand pattern, setup effort, available capacity, holding costs, shelf life, packaging multiples, and supplier conditions. Distinguish a genuine fixed cost from an accounting allocation that will not change with batch frequency. A mathematical optimum built from irrelevant costs can recommend operationally harmful inventory.
02 · How the method works
How the method works
For a basic economic order quantity model, let D be annual demand in units/year, S the fixed ordering cost in currency/order, and H the annual holding cost in currency/(unit·year). EOQ is Q* = √(2DS/H). The relevant annual cost is DS/Q + HQ/2, excluding constant purchase cost. At the model optimum, annual ordering and cycle-stock holding costs are equal.
The model assumes reasonably steady known demand, fixed costs, instantaneous full replenishment, no shortages, and no quantity discounts. It treats average cycle stock as Q/2. Lead time affects when to order, while uncertainty and safety stock require additional treatment. These assumptions must be checked before using the result.
Compare feasible container multiples around the result and evaluate service, capacity, storage, and obsolescence. For finite-rate production, the inventory pattern differs and an economic production quantity model may be appropriate. For a warehouse, transfer batches can often be reduced even when the purchase lot remains large.
03 · Worked logistics example
Worked logistics example
Fictional CanalSupply uses 12,000 protective inserts per year. The relevant fixed order-processing cost is £30 per order, and holding cost is £2 per insert per year. EOQ is √(2 × 12,000 × 30 / 2) = 600 inserts. Twenty orders per year cost £600; average cycle stock of 300 inserts costs another £600. Relevant total annual cost is £1,200, excluding purchase cost and safety stock.
At Q = 300, ordering costs are £1,200 and holding costs £300, for £1,500. At Q = 1,200, ordering costs are £300 and holding costs £1,200, again £1,500. The team confirms that a 600-unit order fits storage and supplier packs.
Process simplification reduces fixed order cost from £30 to £7.50. The new EOQ becomes √(2 × 12,000 × 7.50 / 2) = 300. Its ordering and holding components are £300 each. Reducing the setup or order cost by 75% halves the model-optimal quantity because EOQ changes with the square root of S.
04 · Interpretation and decisions
Interpretation and decisions
The initial 600-unit result is a starting point, not a command. If inserts are redesign-sensitive, expected obsolescence may increase H. If demand is seasonal, fixed EOQ timing may produce excess after the peak. If a supplier requires 1,000-unit packs, compare alternatives rather than rounding without review.
A purchase batch of 600 does not require transferring all 600 to a packing bench. Internal delivery in 50-unit containers can improve point-of-use space and response while retaining the purchase policy. Similarly, reducing setup time may permit smaller production batches without proportionally increasing downtime. Judge the combined system, including replenishment labor and constraints.
05 · Common misapplications
Common misapplications
Confusing reorder point with batch quantity leads to stockouts or overstock. EOQ answers how much under its assumptions; demand during lead time and uncertainty influence when to order. Safety stock is not silently included in Q/2.
Avoid inserting hourly demand into an annual-cost model without converting units. Do not treat sunk costs or fixed salaries as automatically avoidable per-order costs. Full truckload discounts, expiration, constrained capacity, and multiple items sharing setups can invalidate the basic model. Large batches may look efficient locally while delaying customer work and hiding defects. A formula should clarify the tradeoff, not suppress these realities.
06 · Advanced adaptation
Advanced adaptation
When setup time constrains capacity, model the feasible number of changes and the product-family schedule together. Sequence-dependent setups, minimum campaign sizes, and shared equipment create interactions that independent EOQs cannot capture. Use observed setup reductions to revisit the policy rather than keeping the old batch by habit.
For volatile demand, consider periodic review, time-phased replenishment, or policies that respond to inventory position. For transport, compare consolidation cost with waiting and service commitments. Include carbon, space, and handling effects when they are material and measurable. Sensitivity analysis around D, S, and H shows whether the decision is robust or depends on one uncertain assumption.
07 · Implementing and sustaining the change
Implementing and sustaining the change
Introduce determination of batch size within a clearly named operating boundary. Identify the product family, shift, equipment, and handoffs affected; record what happens immediately before and after that boundary. A change that improves one task while exporting its delay to another department has not established an improvement. Agree who can stop the trial, who handles exceptions, and which customer commitment takes priority when the normal rule cannot be followed.
Establish a baseline from actual work rather than a single demonstration. Include normal variation in order mix, replenishment timing, staffing, and workload. Keep the denominator visible: minutes per order, defects per shipment, or completed lines per available hour answer different questions. Record the workload and conditions alongside each observation so that a quiet trial period cannot masquerade as better performance. Observe the process with the people who do it; their explanation of interruptions often changes the proposed design.
Start with a reversible pilot large enough to expose handoff problems. Explain the expected mechanism before launch: which action changes, which delay or failure it removes, and which result should respond. Train all affected shifts and support roles using the same operating definition. During the pilot, capture exceptions as information about the design. Do not conceal them through unofficial stock, unrecorded overtime, or a specialist who quietly repairs every failure.
Review customer service, safety, quality, work content, and inventory together. A faster average with more severe late orders may be unacceptable; a lower inventory level with repeated emergency deliveries may have displaced the cost. Investigate variation before declaring success. If the expected mechanism does not appear, revise the design or return to the baseline rather than defending the idea. A promising observation is a reason to test more conditions, not proof that every operating context will behave identically.
After a successful trial, make the new rule part of daily work. Give an accountable owner responsibility for the operating standard, change control, training, and periodic review. Specify the abnormal condition that requires escalation and the person who responds. Check whether the improvement remains effective when a trained colleague is absent or demand changes. Sustain the mechanism through routine management and learning; documentation is useful only when it describes the process people actually follow.
Connections
Related methods and phase use
Placed under Improve because of the outcome it supports. Use the method in other phases when its purpose and assumptions fit the work; the phase list is a guide to selection, not a compulsory sequence.
Sources
Professional foundations and further reading
The explanation and fictional teaching examples are written for LeanTrainingLab. Linked primary sources provide professional foundations; example values and local conventions are stated in the guide. The accepted toolset draws on Six Sigma+Lean Toolset, second edition (Lunau, editor; Springer, 2013). No book text or examples are reproduced here.