Bottleneck Calculator
Find the station that limits the line and what the line can produce.
What this calculator does
The minimum of the entered station capacities, with the position of that station reported. Optional stations left at zero are excluded rather than treated as stopped.
Inputs and what they mean
- Station 1 capacity
- — number value.
- Station 2 capacity
- — number value.
- Station 3 capacity (optional)
- — Optional. Leave at 0 to exclude it from the result..
- Station 4 capacity (optional)
- — Optional. Leave at 0 to exclude it from the result..
- Station 5 capacity (optional)
- — Optional. Leave at 0 to exclude it from the result..
- Station 6 capacity (optional)
- — Optional. Leave at 0 to exclude it from the result..
How to use it
- Enter your own figures — the calculator never fills in a rate, price or benchmark for you.
- Press Calculate to see the result.
- Read the formula, variables, assumptions and source below the result before you rely on it.
Formula
Line capacity = the smallest station capacity entered; Held-back capacity = Fastest station − Line capacity
Worked example
Six stations, one constraint
The line can only go as fast as its slowest station, whatever the others can do.
Reading the result
The headline figure is the main answer. Any breakdown underneath shows the parts that make it up, so you can check the working and see what changes when you adjust an input.
Limitations and assumptions
Results depend entirely on the figures you enter and are rounded for display. They are for general information and education, not professional advice.
Reference: Massachusetts Institute of Technology — 2.854 Introduction to Manufacturing Systems
Last reviewed:
Common questions
Formula, source and verification
The slowest station sets the capacity of the whole line, whatever the other stations can do.
The question it answers: Which station is holding the line back, and how evenly is the work spread across the stations?
The formula
Line capacity = the smallest station capacity entered; Held-back capacity = Fastest station − Line capacity
- ci — Station capacity
- (count). Units per hour each station can produce; stations left at zero are not counted.
- Cmin — Line capacity
- (count). The smallest entered station capacity.
- Cmax — Fastest station
- (count). The largest entered station capacity.
Units: Units per hour in and out.
What kind of calculation this is
Deterministic formula. The same inputs always give the same answer. The maths is fixed and does not depend on judgement.
Method
The minimum of the entered station capacities, with the position of that station reported. Optional stations left at zero are excluded rather than treated as stopped.
Assumptions built into the result
- Mathematical: Every quantity, time and rate is the figure the user entered, measured over the period they describe.
- Mathematical: Times and counts refer to the same period and the same resource.
- Mathematical: Stations run in sequence with no parallel routing and no buffer large enough to break the constraint.
Figures this calculator will never guess for you
- No industry benchmark, target utilisation or target availability is supplied or applied.
- No shift length, break allowance, downtime allowance or standard rate is assumed.
- Optional components are excluded from the result when left at zero.
Limitations
- Arithmetic over the figures entered — it cannot tell whether the measurements behind them are right.
- A measured result, an industry benchmark and an organisation's target are three different things; only the entered figures are used.
- A single sequential line is assumed. Parallel paths, shared resources and large buffers change where the constraint sits.
Source and version
- Standard or reference
- Manufacturing systems — throughput, cycle time, work in process and line balancing — MIT OpenCourseWare (MIT OpenCourseWare 2.854 Introduction to Manufacturing Systems — throughput is output per unit of time, cycle time is run time divided by the units produced, line capacity is set by the slowest station, and balance efficiency compares total work content with the number of stations multiplied by the longest station time.)
- Published source
- Massachusetts Institute of Technology — Fall 2016
- Formula version
- Version 1
- Verification
- Reviewed against the cited source on
- How much weight the source carries
- Academic
- Applies to
- Currency
- The result is a ratio or index, so it does not depend on currency.
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