Short answer
An operations case asks how a process can produce more, faster or cheaper. Map the process step by step, calculate each step's capacity and find the bottleneck, because the slowest step sets the output of the whole system. Then use utilization and Little's law (L = λW) to link queues to waiting time, size the fix, and check where the bottleneck moves next.
Key takeaways
- The step with the lowest capacity sets the output of the whole process, so find it before proposing any fix.
- Utilization is demand divided by capacity; any step above 100% builds a queue that grows every hour.
- Little's law, L = λW, links the number of items in a system, the arrival rate and the time spent, so any two give you the third.
- After you fix a bottleneck, recalculate every step: the constraint usually moves to the next slowest step.
- Takt time (available time divided by demand) tells you the pace each step must hold.
What is an operations case?
An operations case asks how a factory, warehouse, hospital, airport or service team can produce more, deliver faster or spend less. The method is the same in every setting: map the process as a chain of steps, put a capacity number on each step, compare it with demand and find the bottleneck. The case then turns on sizing the fix and checking what breaks next.
Operations cases reward clean arithmetic more than business intuition. Most numbers are rates (units per hour, customers per minute), so the math is division and multiplication with round numbers. Our case interview math guide covers the speed drills, and the chart guide shows how to read the capacity and utilization exhibits these cases often include.
Four types of operations case
| Type | Typical prompt | First number to find | Common trap |
|---|---|---|---|
| Capacity and bottleneck | A plant cannot meet demand | Capacity of each step per hour | Adding capacity at a step that is not the constraint |
| Queues and service levels | Customers wait too long | Arrival rate against service rate | Planning for the daily average when the peak hour drives the queue |
| Productivity and cost | Cost per unit has risen | Labor hours and cost per unit by step | Cutting staff at the bottleneck |
| Inventory and supply chain | Stock is high and service is poor | Days of stock per product group | Treating every product the same |
Cost questions often sit inside a profitability case, where the operations work explains one branch of the cost tree.
Five formulas to know cold
| Formula | What it answers | 10-second example |
|---|---|---|
| Capacity = stations x units per station per hour | How much can a step produce | 4 machines x 50 per hour = 200 per hour |
| Bottleneck = step with the lowest capacity | What limits total output | Steps at 200, 150 and 180 per hour: output is 150 |
| Utilization = demand / capacity | How busy is a step | 120 demanded / 150 capacity = 80% |
| Little's law: L = λW | How many items are inside, or how long each one stays | 30 arrivals per hour x 0.5 hours = 15 inside |
| Takt time = available time / demand | How often one unit must be finished | 480 minutes / 240 units = 2 minutes per unit |
Little's law says the average number of items in a system (L) equals the arrival rate (λ) times the average time each item spends inside (W). John D. C. Little published the first proof in Operations Research in 1961, and the journal reviewed it on its 50th anniversary in 2011 (official). It holds for any stable system, whatever the arrival pattern, which makes it the most useful formula in an operations case.
Worked example: a Dutch parcel hub at night
Prompt (fictional): A parcel carrier's hub near Utrecht must process 120,000 parcels between 20:00 and 04:00 so vans can leave for next-day delivery. For weeks, about a fifth of parcels have missed their trucks. The operations director asks why and what to do.
Step 1: required rate. The shift lasts 8 hours, so the hub must process 120,000 / 8 = 15,000 parcels per hour.
Step 2: capacity and utilization by step.
| Step | Setup | Capacity per hour | Utilization at 15,000 per hour |
|---|---|---|---|
| Unloading | 8 docks x 2,000 | 16,000 | 15 / 16 = 94% |
| Sorting | 1 automated sorter | 12,000 | 15 / 12 = 125% |
| Loading | 10 doors x 1,800 | 18,000 | 15 / 18 = 83% |
Step 3: find the bottleneck. The sorter caps output at 12,000 x 8 = 96,000 parcels a night, so 24,000 are left over. That is 24 / 120 = 20%, exactly the fifth in the prompt, a useful sanity check to say out loud.
The floor tells the same story. Parcels arrive at 15,000 per hour and leave the sorter at 12,000, so the pile in front of it grows by 3,000 per hour and reaches 8 x 3,000 = 24,000 by 04:00. Little's law turns the floor count into a performance measure: once the hub runs smoothly, if supervisors count an average of 7,500 parcels inside, each parcel spends W = L / λ = 7,500 / 15,000 = 0.5 hours from truck to truck.
Step 4: fix it and recalculate. A second induction line raises the sorter to 20,000 per hour. The bottleneck moves to unloading at 16,000 per hour, or 128,000 a night: enough for 120,000 with 8,000 to spare.
Step 5: test the December peak. At 150,000 parcels, the hub needs 150,000 / 8 = 18,750 per hour.
| Step | Capacity after fix | Utilization, normal night | Utilization, peak night | Action for peak |
|---|---|---|---|---|
| Unloading | 16,000 | 94% | 117% | Add 2 temporary docks (20,000) |
| Sorting | 20,000 | 75% | 94% | None |
| Loading | 18,000 | 83% | 104% | Add 1 door (19,800) |
Recommendation: "The sorter is the bottleneck and explains the full 24,000-parcel shortfall. Adding a second induction line restores capacity with 7% headroom. Plan now for December, when unloading and then loading become the constraint, by adding two temporary docks and one loading door."
Worked example: an airport security queue
This exercise anchors one real number to fictional assumptions. CBS reports that Schiphol handled about 68.8 million passengers in 2025 (official), or about 68.8M / 365 = 190,000 a day.
Assumptions (fictional): half of them depart (95,000), one security filter handles a quarter of departures (about 24,000 a day), the busiest hour carries 10% of the day (2,400 passengers, or 40 per minute), and one lane screens 150 passengers per hour.
Lanes needed. To keep up: 2,400 / 150 = 16 lanes at 100% utilization. Arrivals bunch, so plan for about 80%: 2,400 / 0.8 = 3,000 per hour, or 3,000 / 150 = 20 lanes.
Queue trigger. The target is a wait under 10 minutes. With λ = 40 per minute, Little's law gives L = 40 x 10 = 400. Supervisors get a simple rule: when the line passes 400 people, the wait exceeds 10 minutes and more lanes must open.
The cost of opening late. With 12 lanes (1,800 per hour, or 30 per minute) the line grows by 40 - 30 = 10 people a minute and reaches 600 after an hour. A passenger who joins then waits about 600 / 30 = 20 minutes. Clearing that line within 10 minutes while 40 more arrive each minute would need 60 + 40 = 100 passengers a minute, or 40 lanes. Staffing must lead the peak, because catching up afterwards costs far more.
Lean ideas interviewers expect you to recognize
Toyota describes its production system as resting on two pillars (official). Jidoka means stopping work at any abnormality so defects never travel downstream. Just-in-time means making only what is needed, when it is needed, at the pace of sales, with each step pulling from the one before. Takt time is that pace in numbers.
In a case, these ideas show up as three observations. A pile of stock between two steps marks a bottleneck, as in the parcel hub. Time lost at the bottleneck is lost output for the whole system, while time saved elsewhere adds nothing until the constraint moves. Rework that loops back through the bottleneck is the most expensive defect in the plant.
Which firms ask operations cases
Any generalist firm can give one. Road to Offer, citing another prep provider, describes Kearney as strongest in operations, procurement and supply chain cases (reported). PwC's official case prep asks candidates to consider people, process and technology together, a natural cut for operations cost questions (official). BCG lists structuring, analyzing data and quick calculations as core case work (official).
Six operations prompts to practice
- A Dutch outpatient clinic is fully staffed, yet patients wait 50 minutes. Hint: map check-in, triage, consultation and checkout, then apply L = λW.
- Crane productivity at a Rotterdam container terminal has fallen 15%. Hint: split crane time into moving, waiting and repairs.
- A central bakery cannot meet Saturday demand. Hint: compare takt time with the oven cycle.
- Pick errors at a Belgian e-commerce warehouse have doubled. Hint: find where a stop-at-defect rule would catch them.
- Hold times at an energy company's call center spike on Mondays. Hint: staff by hourly arrival rate.
- A German car-parts plant holds 40 days of stock and still misses deliveries. Hint: split stock by product.
Present each answer top-down, as the MECE and pyramid guide explains, and find more prompts in our case interview questions. For timed, calculator-free practice with dense exhibits, The Second Key to the PST offers a full 26-question test with worked answers.
Frequently asked questions
What is the best framework for an operations case?
Draw the process as a chain of steps, then put a capacity and a demand number on each. For cost questions, add a people, process and technology cut. Tailor it to the prompt instead of reciting a generic list.
What is Little's law in simple terms?
The average number of items in a system equals the rate at which they arrive times the average time each one spends inside. If 30 customers arrive per hour and each stays half an hour, about 15 are inside at any moment.
What is the difference between capacity and utilization?
Capacity is the maximum a step can process per period. Utilization is the share of that capacity that demand actually uses, so a step with capacity 150 per hour facing demand of 120 runs at 80%.
Why do queues grow so fast near full utilization?
Arrivals come in bursts. When a step runs close to 100% it has no spare capacity to absorb a burst, so each one adds to the line and the line takes long to clear.
Do I need to know lean manufacturing for a consulting interview?
Recognizing the core ideas helps: just-in-time, pull, stopping the line at defects and takt time. Applying them to the case matters more than reciting definitions.