Operations and process improvement
Something runs slow or costly; walk the process, compare it with demand, find the real bottleneck, and put a value on fixing it.
Key takeaways
- Map the steps and their capacities, compare with demand, find the step that limits output, and put a money value on fixing it before proposing any spend.
- Operations cases tend to be quantitative and exhibit-heavy. Expect a capacity table and a clear right answer for the bottleneck, which rewards careful reading.
- The strong answer targets the constraint that caps output and shows the fix pays.
What this case type is and when it shows up
An operations case has a process that is too slow, too costly, or makes too many errors. The skill is to walk the process end to end, find the one step that limits the whole thing (the bottleneck), check that demand is higher than what the process makes today, and fix that step rather than one that only looks broken.
The underlying theory, in plain language
A process can produce no more per hour than its slowest step, the bottleneck. Adding capacity anywhere else does nothing for total output. But first check demand: if customers want fewer units than the bottleneck can make, the limit is demand, not the process.
Once found, you speed up the bottleneck, reduce the work reaching it, or rebalance the steps around it. Then a new bottleneck appears, and you repeat.
Utilization is the work a step does divided by its capacity. Steps close to 100 percent utilization build long queues. Little's Law links queues and time: the average number of items waiting equals the rate at which items leave the queue (in a stable system, the arrival rate) multiplied by the average wait. Turned around, the average wait equals the number of items in the queue divided by the rate at which items leave it.
What the prompts sound like, from simple to hard
- Simple: a coffee shop in Singapore has long lunchtime queues; why.
- Medium: a factory line in Poland runs below target; find the constraint.
- Hard: a hospital discharge process in the UK is slow across several handoffs.
Finding and narrowing the real problem
Key idea
Map the steps and their capacities, compare with demand, find the step that limits output, and put a money value on fixing it before proposing any spend.
Frameworks for this type, each as a thinking tool with its limit
- Process walk: List each step and its capacity to find the bottleneck. Limit: Needs the step capacities; without them you are guessing.
- Throughput thinking: Output equals the lower of demand and the slowest step's capacity. Limit: Real processes have variation and queues that this simple view ignores.
- Little's Law: Wait time = items in the queue / rate at which items leave it (in a stable system, the arrival rate). Limit: It gives averages; peaks can be much worse.
Methods for solving this type
- Map the steps and their rates
- Compare with demand
- Identify the slowest step
- Value the lost output and compare with the cost of the fix
- Recheck for the next constraint
The math patterns it relies on
- Units per hour at each step
- Output = lower of demand and the slowest step
- Lost units x contribution x hours x days
- Wait = number waiting / service rate
Bar chart: Steps and capacity on a sandwich line. Values in sandwiches per hour. Prep: 120; Assemble: 60; Wrap: 100; Checkout: 90.
So-what
The whole line can make only 60 an hour because Assemble is the bottleneck. Speeding up Prep or Wrap changes nothing until Assemble improves.
Worked cases
Worked case
Lifting a London sandwich line's output
The prompt
A sandwich kitchen in London has the step capacities in the chart above. Lunch demand is 85 sandwiches an hour over a three-hour peak, and each sandwich earns GBP 3 of contribution. A second assembly worker would raise Assemble to 100 an hour and cost GBP 30,000 a year. Is it worth it?
Interviewer-led: the interviewer shows the capacity chart and asks for the bottleneck, the value of fixing it, and what limits the line next.
Clarifying questions, with the interviewer's answers
- Is demand higher than what we make today?Answer: Yes, about 85 sandwiches an hour at lunch; customers leave when the queue is long.
- How long is the peak, and how many days a year?Answer: About three hours a day, on about 250 working days.
A hypothesis to say out loud: Assemble is the slowest step, so my hypothesis is that it caps output below demand, and that adding capacity there, and only there, pays for itself.
The structure
- Output equals the lower of demand and the slowest step
- Find the bottleneck and compare with demand
- Key: Value of the lost sales
- Cost of the fix and the next constraint
Working it through
1. Find the bottleneck
The slowest step is Assemble at 60 an hour, so the line makes 60 an hour, below lunch demand of 85.
Slowest step (sandwiches per hour):min(120; 60; 100; 90) = 602. Lost sales per hour
Demand the line cannot serve at peak.
Lost sandwiches per peak hour:85 - 60 = 253. After the fix
With Assemble at 100, the slowest step becomes Checkout at 90, which is above demand of 85. The line can now serve all lunch demand.
Slowest step after the fix (sandwiches per hour):min(120; 100; 100; 90) = 904. Value of the fix
25 extra sandwiches an hour at GBP 3 each, for 3 peak hours on 250 days.
Extra contribution (GBP a year):25 × 3 × 3 × 250 = 56,2505. Net gain
Minus the GBP 30,000 cost of the second worker.
Net gain (GBP a year):56,250 - 30,000 = 26,250
The recommendation
Add the second assembly worker. First, Assemble caps output at 60 an hour, so about 25 sandwiches an hour of lunch demand are lost. Second, the fix serves all 85 an hour and adds about GBP 56,250 of contribution a year for GBP 30,000 of cost, a net gain of about GBP 26,250. Third, spending on Prep or Wrap would change nothing, because they already have spare capacity. Checkout, at 90 an hour, becomes the next limit if lunch demand grows above 90.
Risks: Lunch demand may be lower on some days, reducing the gain; Two assemblers may get in each other's way in a small kitchen.
Next steps: Trial the second assembler for four weeks and measure output at peak.
A strong candidate
Checked demand, found the bottleneck, valued the lost sales, compared with the cost of the fix, and named the next constraint.
A weak candidate
Suggested faster prep equipment, which was never the limit, and never put a money value on anything.
Worked case
Why a Johannesburg car-service workshop runs out of time
The prompt
A chain of car-service workshops in Johannesburg is losing customers because cars are not ready on time and the workshops turn bookings away. The owner thinks each workshop needs more bays. What would you do?
Candidate-led: you map the process and ask for the numbers; the interviewer answers only what you ask.
Clarifying questions, with the interviewer's answers
- What is the complaint exactly: long waits, or cars not finished the same day?Answer: Both. Customers book a same-day service, and many cars are not ready by closing time.
- Do we turn customers away?Answer: Yes. When the day is full, callers are told to come another day, and many go to a rival.
- Is this one workshop or all of them?Answer: Start with one typical workshop; the others are similar.
A hypothesis to say out loud: A workshop is limited by its service bays, so my hypothesis is that bays are the bottleneck, and that something other than the repair work itself, such as waiting for parts, is using up bay time.
The structure
- Bay capacity versus demand, and what uses up bay time
- Demand: cars arriving per day
- Key: Capacity: bays x hours / hours each car holds a bay
- Repair work
- Key: Waiting for parts in the bay
- Value of recovered capacity and cost of the fix
Working it through
1. Capacity in theory
Candidate: "How many bays, how long is the day, and how long does a service take?" Interviewer: "Six bays, open nine hours, and a service is about two hours of work."
Cars per day in theory:6 × 9 ÷ 2 = 272. Compare with demand
Interviewer: "About 24 cars a day want a service." Candidate: "In theory the bays should cope, at about 89 percent use. So something else is using bay time."
Required utilization in theory (%):24 ÷ 27 × 100 = 88.893. Find the hidden bay time
Candidate: "Do cars ever sit in a bay without being worked on?" Interviewer: "Yes. About 30 percent of cars wait for parts, on average for four hours, and they stay in the bay while they wait."
Average bay hours per car:2 + 0.3 × 4 = 3.24. Real capacity
With each car holding a bay for 3.2 hours on average, the workshop can finish far fewer cars than demand.
Cars per day in practice:6 × 9 ÷ (2 + 0.3 × 4) = 16.885. Cars lost each day
Demand the workshop cannot serve.
Cars turned away per day:24 - 6 × 9 ÷ (2 + 0.3 × 4) = 7.136. Value of the lost work
Interviewer: "Each service earns about ZAR 1,200 of contribution, and we open about 300 days a year."
Lost contribution (ZAR a year):(24 - 16.875) × 1,200 × 300 = 2,565,0007. Cost of the fix
Candidate: "Instead of building bays, move cars that wait for parts to a parking area and keep the 40 most-used parts in stock." Interviewer: "A driver to move cars costs ZAR 180,000 a year, and the parts stock needs ZAR 250,000 one time."
Net gain in year one (ZAR):2,565,000 - 180,000 - 250,000 = 2,135,000
The recommendation
Do not build more bays; free the bays that already exist. First, in theory six bays can service 27 cars a day against demand of 24, so the bays are not too few. Second, cars waiting for parts hold a bay for four hours, which raises average bay time from 2 to 3.2 hours and cuts real capacity to about 17 cars a day, so about 7 cars a day are turned away. Third, moving waiting cars out of the bays and stocking common parts recovers that capacity for about ZAR 430,000 in year one, against about ZAR 2.6 million a year of lost contribution. Pilot the change in one workshop for a month, then roll it out.
Risks: Moving cars in and out of bays adds some handling time; Parts that are not stocked will still cause delays; At about 89 percent use, the bays will still build queues on busy days.
Next steps: Record for two weeks how long each car holds a bay and why; Agree faster delivery times with the two main parts suppliers; Pilot the parking area and parts stock in one workshop.
A strong candidate
Compared capacity in theory with demand, noticed they did not explain the problem, found the hidden bay time, and valued a cheap fix against an expensive one.
A weak candidate
Agreed with the owner to add two bays at each workshop, which costs far more and leaves cars still waiting for parts in the new bays.
Prompt: "The line is below target; what do we do?"
Weaker answer
Proposes hiring more prep staff and buying faster wrapping machines, neither of which is the limiting step.
Stronger answer
Maps step capacities, compares with demand, names Assemble as the bottleneck, values the lost sales at about GBP 56,000 a year, and points to Checkout as the next constraint.
Why the stronger answer wins: The strong answer targets the constraint that caps output and shows the fix pays. The weak one spends money on steps that do not change total output.
Common mistakes, traps, and curveballs
- Improving a step that is not the bottleneck
- Adding capacity when demand, not the process, is the limit
- Adding capacity everywhere instead of at the constraint
- Ignoring variation and queues
- Cutting a step that catches errors
Operations cases tend to be quantitative and exhibit-heavy. Expect a capacity table and a clear right answer for the bottleneck, which rewards careful reading. Formats differ by office and change over time, so check the current process for your target office.
Practice
An airport security line in Dubai has 600 people waiting and screens 1,200 people an hour. About how long is the wait, in minutes?
A clinic in Riyadh sees 90 patients a day. It has 4 doctors, and each can see 25 patients a day. What is the utilization of the doctors, in percent?
A Singapore bank completes 200 loan files a day and has 1,400 files in progress. On average, how many days does a file spend in the process?
Three steps have capacities of 50, 40, and 70 units an hour. Demand is 35 units an hour. What limits output?
Demand is above capacity. You double the speed of a step that is not the bottleneck. What happens to output?
A step runs at 98 percent utilization. What should you expect?
Output is the lower of demand and the slowest step. Fix only the step that limits output, and only if the value of the extra output beats the cost.
Sources for this lesson (1)
- Recognized public explanations of case-interview concepts and frameworks
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