Lesson 2 of 2 Math checked Facts checked against sources on 16 June 2026 20 min

Stretch case: operations to cost to organization

A South African insurer's claims backlog, its cost target, and the team structure behind both.

Key takeaways

The third stretch case moves from operations to cost to organization.
Fixing one bottleneck moves the limit to the next slowest step. At 700 a day the backlog clears slowly, which is why overtime was needed.
Parts of an integrated case connect. The cost answer must not break the operations answer, so savings came from spans and approval managers instead.

The third stretch case moves from operations to cost to organization. It is common for an operations fix to open a cost question, and for the cost answer to change who does what.

Kwelani claims department: people and cost (shared at the organization stage)

Kwelani claims department: people and cost (shared at the organization stage)
Role	People	Average cost per person (ZAR a year)
Frontline claims handlers	500	250,000
Team leaders	70	450,000
Managers	30	700,000

So-what

Staff cost about ZAR 177.5 million a year of the ZAR 200 million department budget, and each team leader looks after only about seven handlers.

Worked case

Stretch: Kwelani Insurance, from a claims backlog to cost to organization

The prompt

Kwelani Insurance, a South African car and home insurer, has a claims backlog. Customers wait about 21 working days for a decision, against about 7 working days at its main rivals. The exhibit shows the daily capacity of each step. The COO asks why, and how to fix it without raising cost.

Stretch case, interviewer-led. It starts as operations (steps 1 to 6), switches to cost at step 7 when the COO adds a 10 percent cost target, and switches to organization at step 9 when the interviewer shares the team structure.

Open this case to practice it with a partner

Clarifying questions, with the interviewer's answers

How many claims come in, and how many get decided each day?Answer: About 650 new claims a working day. The team decides about 500 a day. The backlog is about 10,500 claims.
What does a claim go through?Answer: Intake, document check, assessment, manager approval, and payment. The exhibit shows daily capacity for each step.
Are there limits on the fix?Answer: The COO does not want to raise the department's cost, which is about ZAR 200 million a year.

A hypothesis to say out loud: Waits this long usually come from one bottleneck step, so my hypothesis is that one step decides fewer claims than arrive, and that fixing it is a matter of rules or staffing at that step rather than more people everywhere.

The structure

Faster claims at lower costThis comes from claims decided = the lower of claims arriving and the slowest step, and total cost = claims x cost per claim.
- Key: Part 1, operations: find the bottleneck and clear the backlog
- Part 2, cost: size the target and the cost per claim
- Part 3, organization: spans, layers, and who approves what

The exhibit

Claims decided per working day at each step (capacity)(claims per day)

Working it through

1. Find the bottleneck
Candidate: "A process runs at the speed of its slowest step. From the chart, that is manager approval:"
System capacity (claims a day):min(1,200; 700; 900; 500; 1,500) = 500
2. Explain the wait
Candidate: "By Little's Law, the wait is the backlog divided by the rate we finish claims. 10,500 claims at 500 a day is exactly the 21 days customers see:"
Average wait (working days):10,500 ÷ 500 = 21
3. It is getting worse
Candidate: "And 650 arrive a day against 500 decided, so the backlog grows every working day by:"
Backlog growth (claims a day):650 - 500 = 150
4. Fix the rule, not the headcount
Candidate: "Why does every claim need a manager?" Interviewer: "It is an old rule. About 70 percent of claims are under ZAR 20,000." Candidate: "Then let assessors approve claims under ZAR 20,000 within set limits, with random audits. Managers would see only 30 percent of claims, so approval could handle about 1,667 claims a day, and the new bottleneck becomes document check:"
System capacity after the rule change (claims a day):min(1,200; 700; 900; 500 ÷ 0.3; 1,500) = 700
5. Clearing the backlog
Candidate: "At 700 a day against 650 arriving, we clear only 50 a day, which would take 210 working days. Too slow." Interviewer: "Overtime could add 200 document checks a day for a while." Candidate: "Then we clear 250 a day, and the backlog is gone in:"
Days to clear the backlog with overtime:10,500 ÷ (700 + 200 - 650) = 42
6. The cost of the overtime
Interviewer: "Overtime costs about ZAR 300 per extra claim checked." Candidate: "Over 42 working days at 200 extra checks a day, the one-off cost is about ZAR 2.5 million, a small price for cutting the wait from 21 days toward the market norm."
One-off overtime cost (ZAR):200 × 42 × 300 = 2,520,000
7. Switch to cost: the target
Interviewer: "The COO now adds a second goal: cut the department's cost by 10 percent within a year." Candidate: "So the question changes from speed to cost. I will size the target, look at cost per claim, and then find where the money is. Ten percent of ZAR 200 million is:"
Annual cost target (ZAR):200,000,000 × 0.1 = 20,000,000
8. Cost per claim today
Candidate: "With about 250 working days and 500 claims decided a day, each decided claim costs about:"
Cost per decided claim today (ZAR):200,000,000 ÷ (500 × 250) = 1,600
9. Switch to organization: spans
Interviewer: "Here is the team structure." (The interviewer shares the people table: 500 handlers, 70 team leaders, 30 managers.) Candidate: "The question is now who does what. First, spans: each team leader looks after about seven handlers. Many operations teams run spans of about 10 to 12 for work like this."
Handlers per team leader:500 ÷ 70 = 7.14
10. Savings from wider spans
Candidate: "At a span of 10, 500 handlers need 50 team leaders, 20 fewer. Most of those roles can close through people leaving, or by moving team leaders into handler vacancies as they open, so the number of handlers stays at 500. At ZAR 450,000 each, that saves:"
Saving from wider spans (ZAR a year):(70 - 500 ÷ 10) × 450,000 = 9,000,000
11. Fewer approval managers
Candidate: "After the rule change, managers approve only about 195 claims a day. Today 30 managers approve 500 a day, about 17 each, so 20 managers could approve about 333 a day, and 10 manager roles can go, saving ZAR 7 million a year." Interviewer: "Is there spare capacity for peaks?" Candidate: "Yes, about 138 approvals a day:"
Spare approval capacity with 20 managers (claims a day):20 × 500 ÷ 30 - 650 × 0.3 = 138
12. Cost per claim after the changes
Candidate: "Spans save ZAR 9 million and fewer managers ZAR 7 million, so we are ZAR 4 million short. About ZAR 22.5 million of the budget is not staff cost. Is any of that easy to cut?" Interviewer: "Moving document upload online would save about ZAR 4 million a year of courier and printing cost." Candidate: "Then we reach ZAR 20 million in total, the full target. With 650 claims decided a day, cost per claim falls from ZAR 1,600 to about ZAR 1,108:"
Cost per decided claim after the changes (ZAR):(200,000,000 - (9,000,000 + 10 × 700,000 + 4,000,000)) ÷ (650 × 250) = 1,108

What the exhibit shows

Manager approval handles only 500 claims a day, fewer than the 650 that arrive, so the backlog grows every day.

The recommendation

Change the approval rule, clear the backlog with about eight weeks of overtime, and fund the target through wider spans and fewer approval managers. First, manager approval decides only 500 claims a day against 650 arriving, which is why customers wait 21 days; letting assessors approve the 70 percent of claims under ZAR 20,000 lifts capacity to 700 a day. Second, 200 extra document checks a day clear the 10,500-claim backlog in about 42 working days, roughly eight weeks, for about ZAR 2.5 million one-off. Third, the department can meet its ZAR 20 million cost target: ZAR 9 million from team leader spans of 10, ZAR 7 million from 10 fewer approval managers, and ZAR 4 million from online documents, cutting cost per claim from ZAR 1,600 to about ZAR 1,108. The main risks are fraud on claims approved without a manager and morale during the change. Next steps: set approval limits and an audit sample, start overtime in document check this month, and plan role changes with the people affected.

Risks: Fraud or errors may rise on claims approved without a manager, so audits must be set before the rule changes; Staff morale may fall when team leader and manager roles are removed; Document check may still slow down in storm seasons, when claims rise sharply.

Next steps: Set approval limits for assessors and a random audit sample of about 5 percent of those claims; Start overtime in document check this month and track the backlog weekly; Plan the new team structure and offer moves into open handler roles before any redundancy.

A strong candidate

Found the bottleneck from the chart, used Little's Law to explain the 21 days exactly, fixed a rule instead of adding people, checked where the next bottleneck would be, and carried the rule change into both the cost and the organization answers.

A weak candidate

Proposed hiring more staff at every step, which breaks the cost limit, then treated the cost target as a separate question and suggested cutting handlers, which would make the backlog worse.

Practice

Timed math drill

A visa office has 3,600 applications waiting and decides 240 a day. By Little's Law, how many days does an applicant wait on average?

Timed math drill

A call center has 360 agents and 45 supervisors, each costing GBP 40,000 a year. If spans widen to 12 agents per supervisor, how much is saved a year, in GBP?

Timed math drill

A factory line has three steps with capacities of 320, 280, and 350 units an hour. What is the line's capacity, in units an hour?

Check your understanding

After removing the approval bottleneck, why did the candidate check the next slowest step?

Check your understanding

Why was cutting frontline handlers the wrong way to meet the cost target?

Check your understanding

What makes a strong final recommendation in an integrated case?

Terms in this lesson

Bottleneck Little's law Capacity utilization

Sources for this lesson (1)

Recognized public explanations of case-interview concepts and terms

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