The Water Station Delivery Route
A water refilling station delivers to four customers each afternoon using one driver and one vehicle. The driver leaves the station at 1:00 PM. Travel times between locations (in minutes) are fixed: Station→A = 10, Station→B = 20, Station→C = 15, Station→D = 25. Between customers: A→B = 12, A→C = 8, A→D = 18, B→C = 14, B→D = 10, C→D = 9. Each delivery takes 6 minutes on site. The driver must return to the station after the last delivery; return times are A→Station = 10, B→Station = 20, C→Station = 15, D→Station = 25. The driver must be back by 2:30 PM. A new customer, E, calls and asks to be added, but E is 40 minutes from the station and 35 minutes from every other stop.
1. Test the route Station→A→C→D→B→Station and report total time and whether the 2:30 PM deadline is met.
Read the worked answer
Sum the legs and on-site time:
- Station→A: 10
- A→C: 8
- C→D: 9
- D→B: 10 (same as B→D)
- B→Station: 20
- Travel subtotal: 10 + 8 + 9 + 10 + 20 = 57 min
- On-site: 4 deliveries × 6 = 24 min
- Total: 57 + 24 = 81 min
Leaving at 1:00 PM, the driver returns at 2:21 PM, which meets the 2:30 PM deadline with 9 minutes to spare.
2. Determine whether customer E can be added to the 1:00 PM run without missing the 2:30 PM deadline, and explain your reasoning.
Read the worked answer
The current route already uses 81 of the 90 available minutes, leaving only 9 minutes of slack. Adding E requires at minimum a Station→E leg (40 min) plus E→Station (40 min) if E is done first or last, or 35 min to reach E from another stop plus 35 min back - far more than 9 minutes. Adding E also adds 6 minutes of on-site time.
Even the cheapest insertion (replacing one existing leg with two E-legs) adds at least 35 + 35 − (the leg it replaces) ≥ 60 minutes. The run would end well past 2:30 PM. E cannot be added to this run. E should be offered a separate trip or a slot on a different day. The correct answer is to decline the addition, not to squeeze it in and hope.
3. The owner wants to know the earliest time the driver could leave the station to still complete the A-C-D-B route by 2:30 PM, assuming no other changes.
Read the worked answer
The route takes 81 minutes regardless of start time (travel and on-site times are fixed). To finish by 2:30 PM (14:30), the driver must leave no later than 14:30 − 81 min = 13:09 (1:09 PM).
So the earliest permissible departure is any time up to 1:09 PM; leaving at 1:00 PM as planned is fine and gives 9 minutes of buffer. This buffer is the key number: it is too small to absorb customer E, which is why the earlier answer is to decline E rather than reshuffle.