Operations Cases 2026: Find the Bottleneck, Then Size It

The rate of a line is the rate of one station

Here is the prompt. The station rates are ours, posed as assumptions, and a candidate should label their own the same way.

Halden Works assembles one product on a line of three stations in series. The plant runs two eight hour shifts, 250 days a year.

1. Station A. 120 units an hour.
2. Station B. 90 units an hour.
3. Station C. 110 units an hour.
4. Operating hours. Eight hours times two shifts times 250 days, so 4,000 hours a year.
5. Contribution. $18 a unit.
6. Fixed cost. $5.4 million a year.

Since the stations are in series, the line rate is the minimum of the three, which is 90 units an hour. Annual output is 4,000 times 90, so 360,000 units.

Contribution is 360,000 times $18, which is $6,480,000. Operating profit is $6,480,000 minus $5,400,000, so $1,080,000.

Note what Station A's capacity is doing in that calculation: nothing. At 120 units an hour it could produce 480,000 units a year, and 120,000 of those never happen. The same is true of Station C's spare 20 units an hour. Two thirds of the line has idle capacity and the plant's output is decided by the third that does not.

The first improvement, and then the second

Improve Station A by 20 percent, from 120 to 144 units an hour. The line rate is still the minimum of 144, 90 and 110, which is 90. Output is unchanged at 360,000 units, profit is unchanged at $1,080,000, and whatever the project cost was is a pure loss.

Now improve Station B by 20 percent instead, from 90 to 108. The line rate becomes the minimum of 120, 108 and 110, which is 108. Output rises to 4,000 times 108, so 432,000 units, an increase of 72,000 units or exactly 20 percent.

Contribution becomes 432,000 times $18, which is $7,776,000. Profit becomes $2,376,000. Against $1,080,000 before, that is a rise of 120 percent on a 20 percent output gain, so the leverage is 6.

Then push Station B a second 20 percent, from 108 to 130. The line rate becomes the minimum of 120, 130 and 110, which is 110, because Station C is now the slowest post. Output is 440,000 units, up 8,000 from 432,000, which is 1.85 percent.

Read the last two rows together. The first 20 percent at the bottleneck returned 20 percent of line output. The next 20 percent at the same station returned 1.85 percent, and the reason is not diminishing returns inside Station B. The constraint moved to Station C, and Station B stopped being the bottleneck partway through the second project.

The sentence that earns the credit in an operations case

An interviewer is listening for a specific claim, and it is easy to get slightly wrong.

The wrong version: improving the bottleneck has diminishing returns. That sounds right and describes the wrong mechanism.

The right version: an improvement at the constraint is worth the full output gain until the constraint relocates, and worth nothing after. The break point here is Station C at 110 units an hour. Any investment that takes Station B past 110 is buying capacity the line cannot use, so the project should be sized to 110 rather than to whatever the equipment vendor quotes.

That single reframing changes the recommendation from spend more at Station B to spend exactly enough at Station B and then look at Station C. It is also the sizing question that gets skipped, because the arithmetic of a 20 percent improvement is easier than the arithmetic of the right improvement.

Put a number on the difference. Taking Station B from 90 to 110 units an hour is a 22.2 percent gain and delivers the full 80,000 units of extra output, since 4,000 times 110 is 440,000 against 360,000. Taking it from 90 to 130 is a 44.4 percent gain and delivers the same 80,000 units. So half the second project's capacity is stranded on day one, before anything has gone wrong.

Then check the money against the bar. The extra 80,000 units carry $18 each, so $1,440,000 of additional contribution a year. A project that costs $2 million pays back in 1.39 years, and the same project sized to 130 units an hour would cost more and return exactly the same $1,440,000. The vendor quote is not the constraint. Station C is.

Utilization has two denominators, and they disagree

Break-even volume is $5,400,000 divided by $18, which is 300,000 units.

Now express that as a utilization rate, and watch what happens. Against current output of 360,000 units, 300,000 is 83.3 percent. Against Station A's own annual capacity of 4,000 times 120, which is 480,000 units, 300,000 is 62.5 percent.

So the same plant at the same output is either at 83.3 percent or at 62.5 percent of capacity, and both figures are correct. The difference is entirely the denominator: one is what the line currently produces, the other is what the fastest station could produce.

This is why a utilization number handed over in a case is a question rather than an answer. Ask which station it refers to, or whether it refers to the line. A plant described as running at 60 percent utilization may have a bottleneck running flat out, in which case there is no spare capacity at all and the number is describing idle assets behind a full one.

The Federal Reserve's own series makes the same point at a different scale. Table 7 of the G.17 release reports August 2026 readings of 76.3 percent for total industry and 75.7 percent for manufacturing, each with a 1972 to 2025 average beside it at 79.4 and 78.2 percent, checked 30 September 2026 at federalreserve.gov. Those are weighted indexes across whole branches of industry. No plant's slowest station appears in them, and the release makes no claim that one does.

Two firms, two definitions of an operations case

Deloitte publishes an operations case with no arithmetic in it. A general contractor is behind schedule, and the case explains why: "A project concrete subcontractor has not been able to pour concrete due to poor weather conditions" and "a project plastics supplier has not been able to deliver piping due to supply chain impacts", checked 30 September 2026 at usrecruiting.deloitte.com.

Its three questions ask which stakeholders to involve, which documents to request, and what remedies exist. The remedy list is itself a useful artifact, because it is a published catalogue of ways to compress a schedule: "Increasing manpower Increasing # of subs Increasing labor hours / second shifts / night shifts Resequencing schedule activities Stacking work disciplines Explore alternative schedule logic".

Notice that every item on that list is a way of adding capacity at a constrained step. The case never computes one, but the vocabulary maps directly onto the arithmetic above.

Oliver Wyman publishes the opposite convention on a comparable problem. Its fleet case supplies four cost lines with their drivers and a note that "They do not expect costs to rise in a 1:1 proportion, because different types of costs are expected to change in different ways", published at oliverwyman.com. There the answer is a dollar figure.

So the opening question in an operations prompt is what kind of answer the client needs. A rate and a dollar figure, or a sequence and a set of contractual remedies. Both are published conventions from large firms and neither is the default. Which convention you meet also depends on where the firm files the work, and manufacturing sits inside Operations at McKinsey among seven different labels the same territory carries.

What an input price does to an operations gain

One sanity check belongs in every operations recommendation, and it is a comparison rather than a calculation.

The improvement at Station B added $1,296,000 of annual profit. Set that against the annual volatility of a single purchased input. The Energy Information Administration puts US retail No 2 diesel at $3.748 a gallon in September 2025 and $6.291 in September 2026, a rise of 67.8 percent, checked 30 September 2026 at eia.gov.

A plant with a $2 million annual freight and fuel bill would have seen that line rise by roughly $1,356,000 over those twelve months, which is more than the bottleneck project earns. We are posing the $2 million, so treat the comparison as an order of magnitude rather than a result.

The habit is what carries over. Before recommending an operations project, ask what the project earns against the annual noise in the plant's largest purchased input. If the noise is larger, the recommendation has to address both, and a structure with only internal branches cannot.

Where the points go on a throughput case

The scheme set out below is ours alone. Its dimensions and weights come from the grading code in src/lib/grading, and no consulting firm publishes a rubric, so these carry our name rather than anyone else's.

What is not in the public record

We looked for a first-hand candidate account of an operations case and found nothing citable. Reddit refuses connections from this network, and the session had no video transcript tooling. Deloitte publishes a tips video on its case page and no account of any specific case. Oliver Wyman publishes two consultant profiles that do not mention its practice cases. Competitor preparation blogs discuss operations cases at length and are not citable sources.

Four gaps are worth naming. Nobody publishes station level throughput for a real plant, so all three station rates above are ours. The Federal Reserve publishes a weighted branch index and not the operating rate of any single asset, which the release itself states. The Deloitte delay case contains no figures at all, which is the nature of the case rather than a limit of our reading. And no firm publishes how often an operations case is quantitative, so this page describes the two published conventions and leaves the frequency alone.