KEVOS® MAKEOS · Inventory

Economic Production Quantity Check (Batch Size, Run Length, Peak Stock, Cost against Current Batch)

When I make a part in batches while it is also being used, what batch size gives the lowest set-up plus holding cost, how long is each run, and how much does my current batch size cost me extra?

Economic production quantity for a part made at a finite rate while demand continues: daily demand, the batch size with the lowest yearly set-up and holding cost (the economic order quantity adjusted for stock building only at the production rate less the demand rate), run length, cycle length, peak stock, runs per year and production days used, and the yearly cost of your current batch size against the optimum, against the extra cost you accept.

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How this tool works

Inputs, units and where to find them

InputUnitTypical source
Annual demandunits/yearUnits used or sold per year.
Production rate while runningunits/dayUnits the process makes per working day while it is running this part.
Working days per yeardaysDays a year the plant works.
Set-up cost per runAUDCost of one changeover: set-up labour, scrap, first-off inspection and lost output where the machine is a bottleneck.
Holding cost per unit per yearAUDCost of holding one unit for a year: capital, storage, handling, obsolescence (often a share of unit cost).
Current practice
Current batch sizeunitsBatch size you make now.
Extra cost accepted over the optimum%How far above the lowest cost you are prepared to run.

What each input means

Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.

What this means: Annual demand
Illustration: Annual demandA row of identical items being counted; Annual demand is how many there are.DExample: 24000 units/yearAnnual demand
What it is
The number of units used or sold each year, which sets how often batches must be made.
Units and format
Enter a number in units/year: units/year. The form accepts 0.000001 units/year or more. Required: the tool does not calculate until every input is valid.
Example
The form opens with 24000 units/year as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
The economic batch rises with the square root of demand.
Get it right
Use a forecast for the coming year; seasonal demand may need different batch sizes in different seasons.
What this means: Production rate while running
Illustration: Production rate while runningItems moving past a point on a conveyor; Production rate while running is how many pass in each unit of time.count pointpExample: 400 units/dayProduction rate while running
What it is
The number of units the process makes per working day while it is running this part, which must exceed the daily demand.
Units and format
Enter a number in units/day: units/day. The form accepts 0.000001 units/day or more. Required: the tool does not calculate until every input is valid.
Example
The form opens with 400 units/day as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
A faster rate builds stock faster, lowering the economic batch towards the plain EOQ.
Get it right
Use the real output rate after scrap and minor stops, not the nameplate rate.
What this means: Working days per year
Illustration: Working days per yearA timeline from a start mark to an end mark; Working days per year is the time between them.startendtExample: 240 daysWorking days per year
What it is
The number of days a year the plant works, used to turn annual demand into a daily demand rate.
Units and format
Enter a number in days: days. The form accepts 1 days to 366 days. Use a whole number. Required: the tool does not calculate until every input is valid.
Example
The form opens with 240 days as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
More working days lower the daily demand, slightly lowering the economic batch.
Get it right
Use working days, matching the production rate, which is per working day.
What this means: Set-up cost per run
Illustration: Set-up cost per runA stack of coins and a note representing the money amount Set-up cost per run.SExample: 450 AUDSet-up cost per run
What it is
The cost of one changeover to this part: set-up labour, trial parts, scrap, first-off inspection and lost output if the machine is a bottleneck.
Units and format
Enter a number in AUD: Australian dollars. The form accepts 0 AUD or more. Required: the tool does not calculate until every input is valid.
Example
The form opens with 450 AUD as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
The economic batch rises with the square root of the set-up cost.
Get it right
Include lost output only where the machine is the constraint; elsewhere set-up time costs only labour.
What this means: Holding cost per unit per year
Illustration: Holding cost per unit per yearA stack of coins and a note representing the money amount Holding cost per unit per year.HExample: 2.5 AUDHolding cost per unit per year
What it is
The cost of keeping one unit in stock for a year: the capital tied up, storage, handling, insurance and the risk of obsolescence.
Units and format
Enter a number in AUD: Australian dollars. The form accepts 0.000001 AUD or more. Required: the tool does not calculate until every input is valid.
Example
The form opens with 2.5 AUD as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
A higher holding cost lowers the economic batch with its square root.
Get it right
Often taken as a share of the unit cost per year; use the rate your finance team uses.

Current practice

What this means: Current batch size
Illustration: Current batch sizeA row of identical items being counted; Current batch size is how many there are.QExample: 5000 unitsCurrent batch size
What it is
The batch size currently made, whose yearly set-up and holding cost is compared with the optimum.
Units and format
Enter a number in units: a count of units. The form accepts 0.000001 units or more. Required: the tool does not calculate until every input is valid.
Example
The form opens with 5000 units as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
Only changes the current cost and the extra cost over the optimum.
Get it right
Use the batch actually run, not the order quantity on the system if they differ.
What this means: Extra cost accepted over the optimum
Illustration: Extra cost accepted over the optimumA bar of 100 parts with the share marked; Extra cost accepted over the optimum is that share out of 100. The bar follows the value you type.0 %100 %Example: 10%Extra cost accepted over the optimum
What it is
How far above the lowest possible yearly cost you are prepared to run before changing the batch size.
Units and format
Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0% to 1000%. Required: the tool does not calculate until every input is valid.
Example
The form opens with 10% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
Only moves the pass or fail line.
Get it right
The cost curve is flat near the optimum, so a modest allowance lets you choose a convenient batch.

Method and formulas

  1. Daily demand d = D ÷ working days; production must exceed demand (p > d).
  2. Yearly cost C(Q) = D S ÷ Q + H Q (1 − d ÷ p) ÷ 2; minimum at Q* = √[2 D S ÷ (H (1 − d ÷ p))] (finite replenishment rate, Silver, Pyke and Thomas).
  3. Run length Q ÷ p; cycle Q ÷ d; peak stock Q (1 − d ÷ p); runs per year D ÷ Q; production days D ÷ p.
  4. Example: the best batch is 3,394.1 units; batches of 5000 cost 7.5981 % more a year.

Limitations

  • Steady demand, a fixed production rate and set-up cost; shared capacity, minimum batch sizes and shelf life can override the optimum.
  • The cost curve is flat near the optimum, so a convenient batch close to Q* costs little more.
  • Example values are illustrations. Replace them with values for your actual task.

Typical uses

  • Set the batch size for a part made on a shared machine
  • Show the cost of over-large batches
  • Check how much machine time a part takes each year

Who it is for

  • Production planners
  • Operations managers
  • Business owners of small manufacturers

What you get

  • Economic production quantity
  • Run length, cycle length, peak stock and runs per year
  • Production days used per year
  • Yearly cost of the current batch against the optimum

Interpreting the result

  • Halving the set-up cost cuts the economic batch by about 30 %: set-up reduction is the lever, not batch size alone.

References

  • Silver E. A., Pyke D. F. and Thomas D. J., Inventory and Production Management in Supply Chains (CRC Press): finite replenishment rate (economic production quantity).

Learn the Concepts Behind This Tool

These KEVOS® Library readings explain the method this tool uses, with worked examples.

KEVOS® tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.

Open the Economic Production Quantity Check (Batch Size, Run Length, Peak Stock, Cost against Current Batch) calculator

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