Clinic siting in the Yoshino River plain
Three municipalities in the Yoshino River plain are considering one new wide-area clinic. Town A has 18,400 residents, of whom 2,100 are 75 or older; its aging rate is 34%, and it is 12 km by road from the prefectural hospital. Town B has 9,800 residents, 1,900 aged 75+, an aging rate of 41%, and is 25 km from the hospital. Town C has 27,600 residents, 2,600 aged 75+, an aging rate of 27%, and is 8 km from the hospital. Bus services per day are 4 to A, 2 to B, and 10 to C. The prefecture will fund only one clinic, with a capital budget of ¥1.2 billion and two full-time doctors; a telemedicine link can cover one additional site but cannot replace emergency care. The stated goal is for at least 60% of all residents aged 75+ to reach a clinic within 30 minutes by road. Existing road times from a central site are 20 minutes to A, 35 minutes to B, and 10 minutes to C.
1. Using the population figures and the 30-minute road times from the central site, calculate the share of residents aged 75+ who would be within the goal. Which town is left out, and why is that a problem beyond simple arithmetic?
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The total population aged 75+ is 2,100 + 1,900 + 2,600 = 6,600. From the central site, A is 20 minutes away and C is 10 minutes away, so both meet the 30-minute goal. B is 35 minutes away and does not. The covered population is therefore 2,100 + 2,600 = 4,700, or 4,700 ÷ 6,600 = 0.712, about 71.2%. That clears the 60% target.
The arithmetic hides an equity problem. B has the highest aging rate at 41% and the fewest buses, only two per day, yet it is the town excluded by the 30-minute rule. A high aggregate coverage rate can therefore coexist with the exclusion of the group with the greatest need. The goal is a threshold, not a fairness test: meeting 60% says nothing about whether the remaining 40% are randomly distributed or concentrated in the most vulnerable town.
2. The mayor proposes building at B because it has the highest aging rate. Evaluate this proposal against the coverage goal and the budget/staffing constraints, and recommend a defensible alternative.
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The mayor is right that B has the highest aging rate, but that fact alone does not show that a B site meets the 60% goal. The setup gives road times only from a central site, not from B to A and C. We therefore cannot calculate whether a B clinic would bring 60% of the 75+ population within 30 minutes. B has only 1,900 of the 6,600 residents aged 75+, about 28.8%, so serving B alone cannot satisfy a 60% target unless travel times from B to another town are favorable - and that data is missing.
A defensible alternative is the central site, which demonstrably covers 71.2%, combined with the telemedicine link at B and a scheduled shuttle or community transport for B residents. This uses the fixed budget and two doctors where they cover the most people, while directly addressing B's isolation. It does not fully solve B's emergency-access gap, so the plan should include ambulance response monitoring and a review trigger. Building at B should be treated as a hypothesis requiring travel-time data, not as a justified decision based on aging rate alone.
3. What two additional pieces of data would most change your recommendation, and how?
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First, actual road times between B and A/C, including winter conditions and bridge closures, would change the coverage calculation. If a B site could serve A or C within 30 minutes, B might meet the 60% goal while targeting the highest-need town; if not, the central-site recommendation becomes stronger. Second, the intra-town distribution of residents aged 75+ and their access to a car or bus would matter. A town-level average can conceal hamlets that are much farther from the proposed site. If many B residents live far from the B center, a clinic there may not improve their access at all. Emergency ambulance response times and doctor recruitment feasibility would also refine the choice, but the two travel/distribution datasets are the most decision-relevant.