In a typical first-round slate of eight, five candidates turn an operations case into a profitability tree with extra formulas. Two of those five still pass on polish. None of them sound like people I would put in front of a plant manager. The sheet is narrower than the prep industry admits: find the stage that caps system output, then decide whether to exploit it, elevate it, or leave it alone—and prove the cash math on that one choice.
That is the whole interview. Throughput is set by the constraint. Everything upstream of it is inventory waiting. Everything downstream of it is idle capacity you already paid for. After this page you should be able to map a line in under a minute, convert OEE losses into lost units, and recommend a capacity move with a payback the interviewer can recompute.
This piece is the system view. For the P&L driver chase, see the operations cost framework. For network flow and inventory days, see the supply chain case.
What the room is actually scoring
Firms that sell manufacturing and supply-chain work—McKinsey's Operations practice is the public face of that market—use ops cases because client work looks like plant math, not market-entry slides. The interviewer is not testing whether you memorized seven "ops frameworks." They are testing whether you treat the business as a process with a rate.
| Candidate move | What the sheet hears |
|---|---|
| Open with revenue minus cost | Wrong object; this is a flow |
| "Improve every station by 10%" | Did not find the constraint |
| "Buy another machine" before OEE | Capex before exploitation |
| Bottleneck rate, lost units, exploit vs elevate | Passable structure |
Pin three definitions before you touch the exhibit. Throughput here means finished good units per unit time that leave the system and can be sold—not machine busy time. Capacity is the maximum sustainable rate of a stage under stated assumptions (shifts, mix, scrap). Utilization is actual output divided by that capacity. Mixing "busy" with "productive" is how people invent fake bottlenecks.
Bottlenecks first: Goldratt's focusing steps
Eliyahu Goldratt's Theory of Constraints, introduced in The Goal (1984) and summarized in Scholarpedia's TOC entry, says a goal-seeking system is limited by at least one constraint, and that you manage three operational measures: throughput, inventory (investment), and operating expense. Net profit is throughput minus operating expense. That is why polishing a non-constraint station feels productive and does nothing to shipped units.
MIT Sloan's open materials on capacity and flow (Lecture 06, D-Lab Supply Chains) walk the same five focusing steps interviewers expect you to voice:
- Identify the constraint.
- Exploit it (no idle time, no lunch that starves it, no scrap fed into it).
- Subordinate everything else to that decision.
- Elevate it (add capacity, outsource the step, change the process).
- Repeat—do not let inertia create a new fake constraint.
In the room, step 2 before step 4 is the tell. Candidates who jump to a second autoclave before asking whether the current one sits empty for changeovers or waits on bad upstream parts are spending the client's capital for the interviewer.
Little's law: the inventory the bottleneck creates
John Little's 1961 result in Operations Research—L = λW—is the bridge between rate and piles of stuff. In plant language: average WIP = throughput × average cycle time, when the system is stable and flow is conserved. Hold throughput fixed and cut WIP, and cycle time falls. Flood the line with WIP hoping to "keep stations busy," and you mostly buy queue time in front of the constraint.
I use Little's law in cases for one sentence: if the bottleneck runs 40 units per hour and average WIP ahead of it is 200 units, expected wait is about five hours. That is enough to kill a same-day promise without touching demand. Supply-chain cases lean harder on days of inventory; here you only need enough of the law to explain why non-bottleneck overtime creates WIP, not shipments.
OEE: why nameplate capacity is a lie
Nameplate says 100 units per hour. The floor ships 55. The gap is not a mystery if you break it the way equipment standards do. Overall equipment effectiveness (the TPM metric popularized by Seiichi Nakajima, and the basis for semiconductor standards such as SEMI E10/E79) multiplies three loss factors: availability, performance (speed and operational losses), and quality. In interview shorthand:
OEE = Availability × Performance × Quality
Availability is productive time over planned time (after scheduled and unscheduled downtime). Performance is actual rate over ideal rate while running. Quality is good units over total units processed. Multiply them. Do not average them.
Disclosed plant numbers are scarce, but public write-ups give order of magnitude. In McKinsey's piece on mature fabs, tool-level analysis found wafer output 43 percent below true capacity—exactly the exhibit shape you get in a case: theoretical max versus actual, then a Pareto of losses. When a candidate treats the brochure rate as the bottleneck rate, I stop listening.
| Factor | Example | Lost units on a 100/hr nameplate, 8-hr shift |
|---|---|---|
| Availability 0.85 | Downtime, changeover | 120 |
| Performance 0.90 | Slow cycles, micro-stops | ~68 more |
| Quality 0.95 | Scrap and rework | ~34 more |
| OEE 0.73 | Productive good-unit rate ~73/hr | ~216 of 800 theoretical |
The bottleneck for the system is the stage with the lowest effective good-unit rate after OEE, not the slowest brochure.
Capacity decisions and quality cost
A capacity case is usually one of three asks: match demand next year, choose make-versus-buy at a step, or pick between fixing losses and buying a machine. Sequence them the same way every time.
- Demand in good units per period.
- Effective capacity of the current constraint (rate × time × OEE).
- Gap in units.
- Cost to close the gap by exploitation (maintenance, setup reduction, scrap upstream of the constraint) versus elevation (overtime, second shift, capital).
- Payback and risk (mix change, yield, learning curve).
Quality sits inside that math, not beside it. The prevention–appraisal–failure (PAF) model used across quality costing—surveyed in this CoQ literature review—splits prevention, appraisal, internal failure, and external failure. In an ops case, internal failure at a non-constraint is mostly operating expense and WIP. Internal failure at the constraint is lost throughput—the scarcest resource. Scrap after the bottleneck already burned constraint minutes; scrap before it may be cheaper to detect early so bad parts never consume those minutes. That is why "inspect everything" and "cut QC to save cost" are both wrong until you place the defect relative to the constraint.
Worked example: Helix Coatings and the cure oven
Helix Coatings (fictional) coats industrial fasteners. Demand is firm at 1,200 good parts per shift. Three stages in series: wash (2,000/hr nameplate), coat (1,800/hr), cure oven (200/hr nameplate). One 8-hour shift. Management wants to know whether to buy a second oven for $480,000 or "improve the line."
Observed oven losses this month: availability 0.80 (changeovers and unplanned stops), performance 0.95, quality 0.98. Effective oven rate:
200 × 0.80 × 0.95 × 0.98 ≈ 149 parts per hour
Per shift: 149 × 8 ≈ 1,192 good parts. Gap to demand: about 8 parts per shift—tight, but not an obvious crisis until you check variability. With a 5% demand spike week, they miss ~60 parts. Contribution margin is $18 per good part after variable material and energy. Fixed plant overhead does not move with this decision.
Option A — exploit for 90 days, then reassess:
- Cut oven changeovers: availability to 0.88 (engineering and scheduling, $25,000 one-time).
- Incoming coat inspection so scrap does not enter the oven: quality to 0.995 ($8,000/year appraisal).
- New effective rate: 200 × 0.88 × 0.95 × 0.995 ≈ 166/hr → 1,328 per shift.
- Surplus vs 1,200: ~128 parts/shift. Annual value of the previously missed spike capacity, if sold: Ned's estimate ~$40,000–$60,000 contribution if they take the overflow work; otherwise they mainly buy schedule reliability.
- Payback on the $25,000 is weeks if they sell the freed capacity; months if they only avoid overtime elsewhere.
Option B — elevate: second oven at $480,000, same OEE, adds ~1,192 parts/shift of capacity. Annual depreciation and capital charge aside, they do not have demand for a second full oven. Utilization on oven capacity would fall below 50%. Wrong object.
| Lever | Capex / one-time | Effective capacity | Fit to 1,200 demand |
|---|---|---|---|
| Status quo | $0 | ~1,192/shift | Misses spikes |
| Exploit (A) | ~$25k + light appraisal | ~1,328/shift | Clears demand with headroom |
| Second oven (B) | $480k | ~2,384/shift | Overbuilt |
Recommendation: exploit first. Elevate only if demand crosses ~1,300 sustained good parts per shift after OEE is fixed. State the kill criteria out loud; that is what the sheet rewards.
Ned's rule. Never buy capacity for a bottleneck you have not timed with a watch. Brochure rates lie; changeover calendars and scrap tags usually do not.
Drill the decision today
Open a production case and force yourself to write four lines before any framework: goal unit, stage rates, bottleneck effective rate, exploit-versus-elevate choice with dollars. Then run one scored rep on CoachNed—start is three typed turns with instant scores and no account, or take the live voice case on /interview. Everything is open for seven days, no card; then $120 for a recruiting season or $49 a month.
Frequently asked questions
What is an operations case interview?
It is a case about how a system produces output under physical constraints—plants, kitchens, call centers, warehouses—rather than whether to enter a market or buy a company. The core ask is where throughput is capped and what it costs to relieve that cap.
How do you find the bottleneck in a case?
Map sequential stages, convert each to good units per hour after downtime and scrap, and pick the lowest effective rate. Confirm demand exceeds that rate; otherwise the constraint may be commercial, not operational.
What formulas do you need for operations cases?
Throughput = rate × time × yield (or OEE factors), utilization = output / capacity, and Little's law (WIP ≈ throughput × cycle time). Cost per unit and fixed-versus-variable splits matter when the case turns into a cost problem; keep them secondary until the constraint is named.
Do McKinsey and BCG still give operations cases?
Yes, especially where the practice sells manufacturing, supply chain, or service operations work. Formats vary by office and round; treat firm blogs as marketing, not a confidential process map. CoachNed is not affiliated with McKinsey, BCG, Bain, Deloitte, or any firm named here.
Should I recommend buying equipment in an ops case?
Only after you have shown that exploitation cannot close the gap and that demand will fill the new capacity. Capex that leaves utilization soft is a common fail.
Sources
- Theory of Constraints (Scholarpedia) — TOC measures (throughput, inventory, operating expense) and constraint logic. Checked 2026-09-24.
- MIT OCW 15.772J Lecture 06 PDF — five focusing steps and bottleneck control. Checked 2026-09-24.
- Little (1961), L = λW (RePEc/INFORMS record) — Little's law primary citation. Checked 2026-09-24.
- Overall equipment effectiveness (Wikipedia) — Availability × Performance × Quality definition and TPM lineage. Checked 2026-09-24.
- McKinsey: Rapid throughput improvement at mature semiconductor fabs — plant gap (output 43% below true capacity). Checked 2026-09-24.
- A literature survey of cost of quality models — PAF (prevention, appraisal, failure) model. Checked 2026-09-24.
- McKinsey Operations practice — firm positioning of operations work. Checked 2026-09-24.
- Goldratt, Eliyahu M. The Goal (1984) — origin of TOC narrative for commercial systems.