Weight-Limited Medical Delivery
You are moving a 9-tonne truck with 200 kg of medical supplies from Base to Clinic. The direct road is impassable. The usable roads are: Base–Junction, 8 km, 15 minutes, no weight limit; Base–Village, 12 km, 25 minutes, 6-tonne limit; Junction–Bridge, 5 km, 10 minutes, 12-tonne limit; Bridge–Clinic, 7 km, 12 minutes, 5-tonne limit; Junction–Village, 6 km, 14 minutes, no limit; Village–Clinic, 9 km, 18 minutes, 10-tonne limit; Bridge–Village, 4 km, 9 minutes, no limit. The truck must arrive within 55 minutes of leaving Base. A police checkpoint on Junction–Village adds 5 minutes unless the truck carries a movement pass; the truck does not have one. The Village–Clinic road has a 10-tonne limit. The Bridge–Clinic road is the only direct approach to Clinic from the north.
1. Find the fastest route that the 9-tonne truck can legally use. If two routes tie on time, state the tie-break you apply and justify it.
Read the worked answer
Test only routes whose every link can carry 9 t.
- Base–Junction–Village–Clinic: limits are none, none and 10 t - compliant. Time = 15 + 14 + 5 (checkpoint) + 18 = 52 min. Distance = 8 + 6 + 9 = 23 km.
- Base–Junction–Bridge–Village–Clinic: limits are none, 12 t, none and 10 t - compliant. Time = 15 + 10 + 9 + 18 = 52 min. Distance = 8 + 5 + 4 + 9 = 26 km.
- Base–Junction–Bridge–Clinic: Bridge–Clinic is limited to 5 t, so the 9-t truck cannot use it.
- Base–Village–Clinic: Base–Village is limited to 6 t, so it fails immediately.
Both compliant routes take 52 min, which is within 55 min. On a time tie, choose the shorter distance: Base–Junction–Village–Clinic (23 km). Operationally, however, the checkpoint introduces a variable delay, so the longer bridge route may be more reliable if the 5-minute figure is not guaranteed.
2. If the Village–Clinic road closes 30 minutes after the truck leaves Base, can the truck still deliver the supplies on a compliant route? Show your reasoning.
Read the worked answer
On the chosen route, the truck reaches Village after 15 + 14 = 29 min, plus the 5-minute checkpoint = 34 min, or 29 min if the checkpoint delay is treated separately. Either way it is at or near Village when the closure takes effect.
The only diversion is Village–Bridge–Clinic: 9 + 12 = 21 min, giving about 50–55 min total. But Bridge–Clinic has a 5-tonne limit, and the truck is 9 tonnes. The diversion is therefore not compliant. There is no other compliant link to Clinic for a 9-tonne vehicle. Conclusion: the truck cannot complete the delivery on a compliant route after that closure; the load would need transshipment to a smaller vehicle or a different approach.
3. What is the heaviest loaded vehicle that can use Bridge–Clinic, and how should that affect contingency planning for this task?
Read the worked answer
Bridge–Clinic is posted at 5 tonnes, so no vehicle heavier than 5 tonnes can use it. The 9-tonne truck is therefore excluded, even though the medical load is only 200 kg; the limit depends on vehicle weight, not cargo weight.
Contingency planning should not treat the bridge route as a fallback for the 9-tonne truck. Either pre-position a vehicle of 5 tonnes or less at the bridge to transfer the 200 kg, or keep the southern Village–Clinic approach open. The plan should identify the transfer point, the smaller vehicle, and a radio check at the bridge. Without that, a closure of Village–Clinic leaves the supplies stranded on the wrong side of a weight-limited link.