Find the bottleneck (classroom session): where to add capacity so it actually helps

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1. For the instructor

This is a ready-to-run 75-minute classroom session on finding the bottleneck — the single slowest step that sets how fast a whole process can go — and on deciding where to add capacity so it actually helps. It is built for a wide, mixed-ability university room: it is the operations bridge for engineering and CS students who are comfortable with numbers but have no business background. Every term is defined the first time it appears, and the arithmetic is deliberately small enough to do in your head, so nobody is stranded and no prep is required from you.

You can teach this cold. This pack contains everything: the case (section 3), a minute-by-minute run of show (section 4), the concepts you need and nothing more (section 5), a group exercise (section 6), a full facilitator answer key with the trade-offs (section 7), debrief prompts (section 8), a printable student handout (section 9), a stretch task for fast tables (section 10), and a slide deck you can present straight from (section 11). Read it once and you are ready.

How to run it in a mixed room. Put students in tables of 3–4 and mix confidence levels at each table. The core call is reachable by everyone; the stretch in section 10 keeps fast tables busy. Your job during the exercise is to circulate, ask the steering questions in section 7, and resist giving the answer — the learning is in the argument at the table.

A note on the clock. The run of show is a tight 75 minutes with little slack — in a 30-40 student room budget ~85 minutes in practice (set-up, table-forming, and report-backs always run long). If you fall behind, cap report-backs at two tables and cover two discussion prompts. Protect the group exercise and the answer-key debrief — those are the session.

One honest line to say out loud at the start: this is teaching material, not a certification and not a credit-bearing course. It is a session that leaves students able to locate a constraint and defend where to invest. That is the whole promise.

Deeper background and the self-serve version of this material live in the anchor Decide course, find-the-bottleneck (see section 2).

2. Session at a glance

Item	Value
Audience	Engineering/CS and applied students; no business background; the ops bridge
Class size	12–40
Total time	75 minutes
Difficulty	4 / 8
Format	Instructor-led; tables of 3–4; one group exercise with a single defensible call

By the end students can:

Locate the bottleneck in a simple flow process by reading station rates, and explain why the busiest-looking or first station is usually the wrong place to look.
Judge where an investment actually helps — decide whether spending money at a given station lifts the whole line’s output or is wasted, and name what would flip the call.
Defend the call in plain language, naming what each rejected option would have cost.

Further reading (the anchor Decide course): find-the-bottleneck — the self-serve version students can work through on their own afterward. This classroom session reuses its composite teaching case, adapted for a live room.

3. The case

Foldhaus is a composite (invented) company — a small manufacturer of flat-pack desks. Every figure below is illustrative, chosen to make the reasoning clean; no number here describes any real firm.

Foldhaus runs one assembly line. Every desk passes through five stations in sequence, in this order, and each station’s rate is how many finished desks’ worth of work it can do in an hour when it runs:

#	Station	What it does	Rate (desks/hr)
1	Cut panels	Saws the desktop and leg panels to size	45
2	Drill & edge	Drills fixing holes and applies edge banding	18
3	Sand & finish	Sands and applies the surface finish	30
4	Assemble hardware	Fits cam locks, feet and cable ports	22
5	Pack	Boxes the flat-pack and labels it	50

Orders are piling up faster than the line ships. Foldhaus has a fixed budget to speed up exactly one thing this quarter, and three suppliers are pitching:

Pitch A — a faster panel saw that raises Cut panels from 45 to 70 desks/hr.
Pitch B — a second Drill & edge cell that raises station 2 from 18 to 28 desks/hr.
Pitch C — a weekend overtime shift on Pack that raises station 5 from 50 to 65 desks/hr.

Each supplier has a slick number. Spend on the wrong station and the line ships not one extra desk, and the money is gone for the quarter. The question the room must answer: where should the money go, and why?

4. Run of show

8 min — Hook: pose the Foldhaus situation and the three pitches (section 3). Ask the room to vote by show of hands for A, B or C before any teaching. Record the split on the board; don’t comment.
10 min — Teach the core idea: throughput and the bottleneck (section 5, first two points). Walk the station table once, out loud, and find the slowest step together.
7 min — Set up the group exercise: hand out the worksheet (section 9), form tables of 3–4, and read the task aloud so every table starts at the same line.
20 min — Group exercise: tables work the call and fill in the worksheet (section 6). Circulate and use the steering questions from section 7; do not give the answer.
12 min — Report back: two or three tables state their call and their reasoning. Put the competing answers side by side on the board.
10 min — Teach the rest: the five focusing steps and why local efficiency misleads (section 5), tied back to what the tables just found.
8 min — Debrief and close: run the section 8 prompts, land the one-sentence takeaway, and revisit the opening vote to see what changed.

Total: 75 minutes.

5. Teaching points

Teach only these, in this order — each is defined on first use, and together they are exactly what the call in section 7 needs.

Throughput. The rate at which the whole line produces finished desks. It is the number the customer actually sees.

Bottleneck (constraint). The single slowest station. Because every desk must pass through every station in order, the line can never finish faster than its slowest step. The model rule: a line’s throughput = the rate of its slowest station, so after any change, recompute the new minimum across all five stations. Read Foldhaus’s table — the rates are 45, 18, 30, 22, 50 — so the slowest is Drill & edge at 18 desks/hr, and the whole line ships 18 desks/hr. Not the average (which is 33), not the pace of the fast stations. Cut panels can prepare 45 an hour, but station 2 can only consume 18, so 27 panels an hour pile up in front of it as work-in-process (part-built units waiting for the next step). Key judgment: the bottleneck is often quiet and fully fed, while the visible pile of unfinished work sits upstream of it. Find it by the rates, not by which station looks frantic.

An hour spent where it counts. An improvement at a non-bottleneck station buys nothing; the same effort at the bottleneck lifts the entire line. Speed Cut panels to 70 and the line still ships 18 — you have only grown the pile faster. Raise Drill & edge from 18 toward higher, and throughput rises until the next-slowest station takes over as the new ceiling.

The five focusing steps (from the Theory of Constraints, Eliyahu Goldratt’s 1984 book The Goal — the standard framework for this): 1. Identify the constraint. 2. Exploit it — get the most out of it for free first: never let it sit idle for want of parts, never let it run work that will later be scrapped. 3. Subordinate everything else — pace the fast stations to the constraint instead of running them flat out and building piles. 4. Elevate it — only now spend money to raise its capacity. 5. Repeat — once you elevate it, a different station becomes the constraint; go again.

Why local efficiency misleads. Most plants score each station on utilization — the percentage of time it was busy. Rewarded on that, the Cut panels supervisor runs flat out at 45/hr to look “100% efficient,” producing 27 desks/hr of work-in-process the line can’t use. The scorecard looks great while the line still ships 18. The only efficiency that pays is throughput of finished units, not the busyness of any one station.

6. Group exercise

The task. At your table, decide where Foldhaus should spend its one budget — Pitch A, B, or C — and be ready to defend it in two minutes. Use the worksheet in section 9.

Steps (about 20 minutes):

Find today’s bottleneck. Read the station table. Which station is the slowest, and what is the line’s throughput right now? Write both down.
Test each pitch. For A, B and C in turn, ask: does this station’s speed limit the line today? If you made it faster, what would the line’s throughput become? Write the new throughput next to each pitch.
Make the call. Pick the pitch that actually raises finished output, and note where the constraint moves to after that pitch (the next-slowest station).
Name the cost of being wrong. For the two pitches you rejected, write in one line what that money would have bought — in extra desks shipped.
One free move. Before spending a cent, name one thing Foldhaus could do to get more out of the bottleneck for free (exploit / subordinate).

Every table should leave with a single call, a new throughput number, and a one-line reason.

7. Facilitator answer key

The call: Pitch B — the second Drill & edge cell. Drill & edge at 18 desks/hr is the current bottleneck, so it is the only station where money reaches the customer.

Derive the new throughput — don’t guess it. The model rule is: a line’s throughput = the rate of its slowest station, so after any change, recompute the new minimum. Apply it to Pitch B. Before: the stations are 45 / 18 / 30 / 22 / 50, minimum 18. Pitch B raises Drill & edge from 18 to 28, so the stations become 45 / 28 / 30 / 22 / 50 — and the new minimum is 22 (Assemble hardware is now the slowest). So Pitch B lifts the line from 18 to 22 desks/hr — a real gain of 4/hr — not to 28. That “stops at 22” detail is the point, not a flaw: the payoff of elevating a bottleneck is only as large as the gap to the second-slowest step, and the constraint has simply moved to Assemble hardware.

Correcting a table that computes 28. Say exactly this: “You raised Drill & edge to 28, but the line still caps at the slowest station, now Assemble at 22.” Then walk the recomputed row (45 / 28 / 30 / 22 / 50) with them and ask which number is smallest.

What each option costs. Pitch A (faster saw, 45→70) buys zero extra desks: Cut panels was never the limit, so the line still ships 18 and the extra panels pile up as work-in-process — cash trapped in a taller pile. Pitch C (pack overtime, 50→65) also buys zero: Pack is the fastest station already; paying overtime there speeds up the step that was never waited on. Both A and C feel productive and show up as higher utilization, which is exactly the trap. Only Pitch B, at the constraint, moves the number the customer sees.

The free move first. Before approving B, exploit and subordinate: keep Drill & edge fed and scrap-free (an hour it spends on a unit that later fails is throughput thrown away), and pace Cut panels to ~18/hr instead of 45 so it stops building a pile. These cost nothing and may lift output before any purchase.

Common wrong turns. Tables pick A because 45→70 is the biggest number, or C because “shipping” sounds like the goal. Steer with: “If that station runs faster, what does the slowest step do?” If a table freezes, ask them to name the slowest station first — everything follows from that.

8. Discussion & debrief

Run these after the report-back:

Our opening vote split across A, B and C. What made the wrong pitches tempting — was it the size of the number, the word “shipping,” or something else?
The bottleneck station can look calm and fully fed while panels pile up in front of it. Why does the visible pile sit upstream of the real constraint?
After Pitch B the constraint jumps to Assemble hardware at 22. What would you do next quarter — and how do you know when to stop?
A supervisor is rewarded for keeping Cut panels “100% utilized.” How does that reward quietly hurt the whole line?
Suppose Foldhaus could only sell 15 desks a day no matter how fast the line runs. Does the bottleneck move? Where to?

One-sentence takeaway: A line runs at the speed of its slowest step, so the only capacity worth buying is capacity at the constraint.

9. Student handout

Foldhaus — where should the budget go? (All figures are illustrative; Foldhaus is an invented company.)

Every desk passes through all five stations in order. The rate is desks per hour that station can do.

#	Station	Rate (desks/hr)
1	Cut panels	45
2	Drill & edge	18
3	Sand & finish	30
4	Assemble hardware	22
5	Pack	50

The three pitches (pick one):

A — faster saw: Cut panels 45 → 70
B — second cell: Drill & edge 18 → 28
C — pack overtime: Pack 50 → 65

Work it out:

Today’s bottleneck is station ____ (____ desks/hr). The line ships ____ desks/hr today.
New line throughput if we buy A: ____ B: ____ C: ____
Our call is Pitch . After it, the new constraint is station ____ ( desks/hr).
The two pitches we rejected would each have bought ____ extra desks/hr, because ______________.
One free move to get more out of the bottleneck before spending: ______________.

Our one-line reason: ________________________________________________

10. Stretch

For fast tables who finish early:

The demand twist. Sales says Foldhaus can only sell 20 desks/hr right now, whatever the line produces. After Pitch B lifts the line to 22, where is the binding constraint — inside the plant, or in the market? What should the money do instead? (The constraint can be external: past a point, more line speed just builds unsold desks.)
The scrap twist. Suppose Drill & edge scraps 1 desk in 6 at the next station’s check. What is its effective good-output rate, and what would “exploiting the constraint” (cutting that scrap) be worth before you buy any capacity at all?

Facilitator answer: the constraint runs at 18/hr but 1 in 6 of those units is later scrapped, so only 5 of every 6 are good — effective good output is 18 × 5/6 = 15 desks/hr, and the line ships 15, not 18. Cutting the scrap to zero (better fixtures, in-station checks) lifts the line straight back to 18/hr — a +3/hr gain for no capital at all. That is exploiting the constraint: an hour the bottleneck spends on a desk that later fails is throughput you already owned and threw away. It should come before the Pitch B purchase, and it changes the value of B (from a 15 baseline, elevating the drilled-good rate is worth even more).
The hardest one — a floating bottleneck. Foldhaus adds a premium desk that needs double the drilling time but half the assembly time. Sketch how the bottleneck might move as the product mix shifts, and how you would decide where to invest when the constraint no longer sits still.

11. Slides

Slide 1 — Find the bottleneck

Where do you add capacity so it actually helps?
Foldhaus: a flat-pack desk line, orders piling up, one budget to spend
Presenter note: Say the honest line — teaching material, not a certification.

Slide 2 — The case & the three pitches

Five stations in sequence: Cut 45 · Drill&edge 18 · Sand 30 · Assemble 22 · Pack 50
Pitch A: saw 45→70 · Pitch B: drill 18→28 · Pitch C: pack 50→65
Presenter note: Take the vote now, before any teaching. Record the split; don’t comment.

Slide 3 — The bottleneck sets the throughput

Every desk passes through every station in order
The line can’t finish faster than its slowest step → 18 desks/hr
Not the average (33), not the fast stations
Presenter note: The bottleneck is often quiet; the pile sits upstream of it.

Slide 4 — An hour spent where it counts

Speed a non-bottleneck (A or C) → line still ships 18, pile just grows
Speed the bottleneck (B) → line rises to 22, then Assemble (22) takes over
Only improvement at the constraint reaches the customer

Slide 5 — Your table’s call

Find the bottleneck → test each pitch → make the call → name the cost of being wrong
One free move before spending any money
Presenter note: Circulate; ask “if that station runs faster, what does the slowest step do?”

Slide 6 — The five focusing steps

Identify → Exploit → Subordinate → Elevate → Repeat
Elevate (spend money) is step four, after the free gains
Once you elevate, the constraint moves — go again

Slide 7 — Why local efficiency lies

Rewarding “100% busy” pushes fast stations to build work-in-process
The only efficiency that pays is throughput of finished desks
Presenter note: Tie back to the opening vote — the big number (A) was the trap.

Slide 8 — Takeaway

A line runs at the speed of its slowest step
The only capacity worth buying is capacity at the constraint
Further reading: the find-the-bottleneck Decide course

12. Sources & license

Sources. See SOURCES.md in this folder for full provenance.

Data honesty. Foldhaus and every figure attached to it are composite — an invented company with illustrative numbers, built from ordinary, realistic manufacturing dynamics for clean teaching. No number or claim here describes, or is drawn from, any real company or real data.

License & disclaimer. This classroom material is free for instructors to use and reproduce under the project’s classroom-use license — the canonical wording is maintained in company/legal/classroom-license.md; refer to it, and do not substitute other terms. In plain English: this material is provided as-is, it is not a certification and carries no guaranteed outcomes, and it is teaching material for a live classroom session — nothing more is promised.

Instructor teaching material, provided as-is. Not accredited, not a certification, and not affiliated with or endorsed by any university. Uses composite (invented) companies and illustrative figures.