Interviewer view · keep this screen to yourself
Crowding on a Tokyo rail platform
You run the case. Read the prompt, answer questions from the notes below, and share data only when the candidate asks for it or gets stuck. Score at the end.
Case timer
00:00
1. Read the prompt aloud
Read it slowly, then pause. Let the candidate ask questions before they structure.
A Tokyo rail operator has dangerous crowding on one station platform during the morning peak. How would you think about fixing it?
Format note: Candidate-led: there is no framework for this. You build your own flow model and ask for the numbers; the interviewer answers and challenges.
2. Answers to clarifying questions
Give these answers only if the candidate asks. If they ask something not listed, give a sensible answer or say it does not matter here.
If asked: What exactly is the problem: safety, delays, or passenger comfort?
Answer: Safety first. When the platform is too full, staff must close the ticket gates, which causes delays across the line.
If asked: How many people can the platform hold safely?
Answer: About 1,500.
If asked: Is this every weekday, and for how long?
Answer: Every weekday, for about one hour of the morning peak.
3. The hypothesis a strong candidate states
Listen for an early, testable guess like this one. It does not need to match word for word.
A platform fills up when people arrive faster than trains take them away. My hypothesis is that trains cannot carry the peak flow, so people build up on the platform, and that moving some trips out of the peak is cheaper than adding train capacity.
4. A model structure
Compare the candidate's structure with this one. A different split can be just as good if it is clean and fits the problem.
- People on the platform = arrivals minus people the trains take away
- Arrivals per hour at the peak
- Key: Train capacity: trains per hour x free space per train
- Levers: more trains, longer trains, or fewer peak arrivals
- Cost and speed of each lever
5. The working, step by step
Each step shows how a strong candidate works it out. Share a new fact from it only when the candidate asks or is stuck, and let them do the math: the result in the dark box is what they should reach.
Step 1: Train capacity
What a strong candidate does: Candidate: "How often do trains come, and how many people can each take from this station?" Interviewer: "One every 3 minutes, with room for about 800 more passengers each."
Passengers the trains can take (per hour): 60 ÷ 3 × 800 = 16,000
Step 2: The gap
What a strong candidate does: Interviewer: "About 18,000 people arrive in the peak hour." Candidate: "Then about 2,000 more people arrive each hour than the trains can take."
Excess arrivals (per hour): 18,000 - 60 ÷ 3 × 800 = 2,000
Step 3: People on the platform
What a strong candidate does: Between trains, about 900 people arrive; over the hour, the extra 2,000 build up on top. That is almost twice the safe limit of 1,500.
People waiting at the end of the peak: 18,000 ÷ 20 + (18,000 - 60 ÷ 3 × 800) = 2,900
Step 4: How many trips must move
What a strong candidate does: Candidate: "To stay within train capacity, this share of peak trips would have to move outside the peak."
Share of peak trips to move (%): (18,000 - 16,000) ÷ 18,000 × 100 = 11.11
Step 5: Cost of an off-peak discount
What a strong candidate does: Candidate: "What if people who enter this station before 7:30 get JPY 40 off that morning trip?" Interviewer: "About 5,000 people already travel then and would get it too, and we run about 245 working days a year."
Yearly cost of the discount (JPY): (2,000 + 5,000) × 40 × 245 = 68,600,000
Step 6: Compare with more trains
What a strong candidate does: Interviewer: "A new signaling system would allow a train every 2.5 minutes, for about JPY 3 billion." Candidate: "That is the cost of more than 40 years of the discount."
Years of discount equal to the signaling cost: 3,000,000,000 ÷ ((2,000 + 5,000) × 40 × 245) = 43.73
The recommendation to listen for
At the end, say: "The CEO walks in. What is your recommendation?"
I recommend an off-peak fare incentive and better crowd control now, with the signaling upgrade kept in the long-term plan. First, trains can take about 16,000 people an hour but 18,000 arrive, so about 2,900 are waiting by the end of the peak. Second, moving about 11 percent of peak trips closes the gap, and a JPY 40 early-travel discount costs about JPY 69 million a year. Third, the upgrade costs as much as more than 40 years of the discount, so it makes sense only if demand keeps growing. Test the discount for three months.
Risks a strong answer names: Fewer people may change their travel time than needed, because work start times are fixed; Crowding may move to the next station on the line; Peak demand may keep growing, bringing the upgrade forward.
Next steps: Ask the three largest employers near the station about flexible start times; Run the discount trial and track arrivals every five minutes; Include the signaling upgrade in the five-year investment plan.
Strong versus weak
A strong answer
Built a flow model with no framework, found the exact gap, turned it into the number of trips to move, and compared a cheap lever with an expensive one on cost.
A weak answer
Suggested more staff to push passengers onto trains and nicer signs, with no model of why the platform fills up.
Score the candidate
Score each criterion from 1 to 5. A 2 or a 4 sits between the descriptions.
This case has no exhibit. Score Exhibit reading on how the candidate used the data you gave them: did they pick out the number that matters and say what it means?
Total
0 out of 25
Score all five criteria to see the band and the feedback template.