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Learn through experiments

When faster work creates a bigger pile

Which stage should receive extra capacity?

Entering midway? Revisit Enough average capacity, yet a queue for the preceding worked example, or start here and use the explanation below.

1 · Try

Start with a concrete question

Original synthetic two-stage workshop: new items enter stage A each hour; stage B may process them in the same hour; unfinished items accumulate between stages.

Try the initial inputs, then write a prediction before changing one setting. All calculations run locally on your CPU.

Go directly to the experiment · Review basic mathematics

2 · Predict

What do you expect?

Predict whether increasing stage A from 8 to 12 improves output when demand is 6 and stage B can finish 4.

3 · Experiment

Change one thing. Inspect what happens.

  1. Record six-hour output and buffer at the defaults.
  2. Increase only A. Identify whether its extra capacity is used.
  3. Set demand to 10 and compare A capacities 8 and 12 while B remains 4.
  4. Improve B and then restrict A intake. Explain which change increases output and which reduces unfinished work.
Experiment inputs
Inputs
Your settingsMechanism
Calculation belowEvidence
Compare outcomes
Completed24 items
Unfinished buffer12 items
Stage B capacity used100 %

Compare the current results

Every bar starts at zero and uses the same numeric scale in this chart. The upper bound automatically adjusts to the largest current value (at least 1), so compare the numbers when changing inputs. Units and quantities come from each label; different kinds of quantity are not interchangeable. Displayed values are rounded to at most six significant digits.
012
  • Hour 1 buffer2
    Hour 1 buffer: 2Horizontal bar from zero to 2, on the shared zero to 12 numeric axis.
  • Hour 2 buffer4
    Hour 2 buffer: 4Horizontal bar from zero to 4, on the shared zero to 12 numeric axis.
  • Hour 3 buffer6
    Hour 3 buffer: 6Horizontal bar from zero to 6, on the shared zero to 12 numeric axis.
  • Hour 4 buffer8
    Hour 4 buffer: 8Horizontal bar from zero to 8, on the shared zero to 12 numeric axis.
  • Hour 5 buffer10
    Hour 5 buffer: 10Horizontal bar from zero to 10, on the shared zero to 12 numeric axis.
  • Hour 6 buffer12
    Hour 6 buffer: 12Horizontal bar from zero to 12, on the shared zero to 12 numeric axis.

Follow the calculation

  1. Hour 1: stage A makes min(6, 8) = 6; stage B finishes min(0 + 6, 4) = 4; buffer = 2.
  2. Hour 2: stage A makes min(6, 8) = 6; stage B finishes min(2 + 6, 4) = 4; buffer = 4.
  3. Hour 3: stage A makes min(6, 8) = 6; stage B finishes min(4 + 6, 4) = 4; buffer = 6.
  4. Hour 4: stage A makes min(6, 8) = 6; stage B finishes min(6 + 6, 4) = 4; buffer = 8.
  5. Hour 5: stage A makes min(6, 8) = 6; stage B finishes min(8 + 6, 4) = 4; buffer = 10.
  6. Hour 6: stage A makes min(6, 8) = 6; stage B finishes min(10 + 6, 4) = 4; buffer = 12.

Speeding a stage that is already ahead of the bottleneck can increase unfinished work without improving completed output.

Captures keep your inputs, prediction and observation. Results are recalculated from those inputs. Resetting inputs keeps your captures and challenge history.

4 · Understand

Explain the mechanism

What the experiment explains

Original synthetic two-stage workshop: new items enter stage A each hour; stage B may process them in the same hour; unfinished items accumulate between stages.

The bottleneck is the capacity that limits the flow of completed items. Improving another stage can leave total output unchanged.

At the defaults A produces six and B completes four per hour. After six hours output is 24 and the buffer is 12.

Capacity utilization describes how much available capacity was used; it is not itself the objective. Keeping every upstream resource busy may increase inventory without helping customers.

Read the relationship

A output = min(offered demand, A capacity). B output = min(previous buffer + A output, B capacity). Next buffer = previous buffer + A output − B output.

Use the trace as evidence

The trace recomputes from your current controls. Change one control at a time, record what changed, and compare the result with your prediction. The bars use the same quantities as the numerical trace; a larger bar is not automatically a better outcome.

Boundaries of the model

  • Deterministic identical items, unlimited buffer, and same-hour processing; no stage travel time.
  • Unaccepted demand at A is not queued or counted as lost sales; reported buffer is only work between stages.

Continue with Enough average capacity, yet a queue to investigate a different mechanism.

5 · Apply

Try a fresh case

A new line starts empty. A makes 7 items/hour, B finishes at most 5/hour, and demand is at least 7/hour. After 4 hours, how many unfinished items are between stages?

This is a public practice check. Retries support learning; matching a number does not certify independent proficiency.

Take the investigation further

Choose any extension. These are project prompts for you to carry out; they are not automatically assessed.

School investigation

Use paper tokens for two stages and compare completed work with work started.

College investigation

Add finite buffers and blocking, then measure throughput and total time in the system.

Workplace investigation

Propose one capacity investment and one intake policy, with evidence that identifies the actual limiting stage.

6 · Continue

Keep the evidence, choose your next step

Completion records your own decision that you have worked through this investigation. Practice checks and independent project evidence are separate.