Sources checked 24 October 2026. The factory, processing times, and numerical results below are original worked examples, not observations of a real business.
A furniture factory has a quote for a cutting machine that can work twice as fast. The cutting supervisor wants it. Sales has orders waiting. The floor already holds stacks of parts awaiting inspection. At the investment meeting, the manager needs to explain how many more finished orders the purchase would allow the factory to deliver.
Consider a hypothetical line making one standard product. Cutting can handle 12 units an hour, inspection 8, and packing 10. Customers want 12. Each unit passes through all three stages. Once the line is running steadily, inspection limits finished output to 8 an hour. Doubling cutting capacity leaves that limit at 8.
The proposed machine may still improve safety, reliability, or cost. Those benefits deserve their own evidence. A claim about additional deliveries needs a different calculation.
Illustrative steady-flow line making one standard product. All units pass through every stage; no defects, downtime, or transfer delays. The four squares represent one hour’s increase in unfinished inventory under unrestricted release.
Count the work that reaches the customer
Capacity describes what a stage can process in a given period. Throughput describes what the system completes. In a simple serial line with a common flow unit, output cannot exceed demand or the capacity of any required stage. MIT’s capacity lecture separates this calculation from congestion analysis, which also considers how arrivals and processing times vary. [1]
That distinction matters here. If cutting releases 12 units an hour while the line completes 8, unfinished inventory grows by 4 an hour in our simplified steady-flow example. After four hours, 16 additional units are in progress. Faster cutting has given the factory more work to store and track, without changing the number it can finish.
A persistent queue is a reason to investigate a stage. It does not prove that the stage has too little equipment. Inspection might be waiting for drawings, handling large batches, or spending time on defects that could have been found earlier. Follow several orders and record both productive time and the interruptions.
Protect the time you already have
Goldratt’s theory of constraints offers a practical sequence: find the constraint, make better use of it, align other work with it, add capacity where necessary, and check the system again. The TOC Institute describes these as the five focusing steps. They are a management method, not a guaranteed percentage improvement. [2]
For this factory, the manager could first check whether inspectors receive complete work instructions and whether suitable material is ready when they are. MIT’s production-flow teaching notes include reducing setup time and checking quality before the bottleneck among possible interventions. [3] Inspection standards still apply; making a safety check shorter without establishing its adequacy is a different decision.
The cutting team also needs a release rule. If its performance measure rewards every additional part, it has a reason to keep adding to the pile. In the example, limiting new releases to 8 an hour stops further inventory growth. It does not remove the existing queue or guarantee an on-time order. Real operations need enough protection against interruptions to keep the constrained stage supplied.
The Pareto exercise from Monday can help investigate repeated causes of lost inspection time. Record minutes as well as incident counts, and keep serious quality problems visible even when they occur rarely. Choosing an investigation priority and choosing which stage needs more capacity are related decisions, with different evidence.
The constraint can move when the orders change
Suppose the factory also makes a more complex version of the product. A standard unit needs 5 minutes of cutting, 7.5 of inspection, and 6 of packing. A complex unit needs 8, 10, and 12 minutes respectively. Each stage has 60 working minutes available per hour. These are assumed processing times for the example.
With equal numbers of standard and complex units, average packing time becomes 9 minutes per unit. Its capacity is about 6.67 units an hour. Inspection can handle about 6.86, and cutting about 9.23. Packing now limits the line. An investment justified using only last month’s standard-product orders could target the wrong stage for next month.
These averages assume a stable mix and no setup losses, rework, shortages, or downtime. A real change in sequence can add work that the averages omit. Different products may also earn different contributions and use scarce time differently. The playground compares physical capacity; it cannot choose a profitable product mix or establish an investment return.
Take one constraint to the next review
Start with the playground’s base case, then double cutting capacity. Finished output stays at 8 units an hour. Restore the base case and add 50% inspection capacity: packing becomes the constraint at 10. Set demand to 6 and the orders themselves limit output. Each change asks the manager to identify what would have to be true for more capacity to help.
Use the same discipline on a live process. Bring one flow map, comparable capacity estimates for the expected mix, and a short record of why work waited. Name the evidence you still need. A queue measured on one difficult afternoon may justify investigation; it is a weak basis for a permanent equipment purchase.
Before approving the next change, write its expected effect on completed orders, the conditions that could prevent that effect, and the date you will check it. Give someone responsibility for measuring the finished result. If the constraint moves, update the decision before repeating the investment.
Sources
[1] Jérémie Gallien, MIT OpenCourseWare, Class 3: Capacity Lecture (2004 course). Slides 5–8 distinguish service capacity, flow, inventory build-up, and stochastic congestion. Used for the model, not a business performance claim.
[2] Theory of Constraints Institute, Five Focusing Steps. Practitioner explanation of the improvement sequence. Its promotional improvement percentages are not adopted.
[3] MIT OpenCourseWare, Capacity Planning and Production Flow Control (2014). Teaching material on dependent operations and bottleneck interventions, including setup time and quality checks.
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