Shift Patrol Allocation and Fuel Budget
Station X has three beat routes: A is 18 km, B is 24 km, and C is 30 km. The night shift runs from 20:00 to 06:00 (10 hours). Standing order: each beat must be visited at least twice during the shift by any available vehicle, not by every vehicle. The station has four scooters, but one is under repair, leaving three. Average patrol speed is 28 km/h including stop-and-go traffic. The officer-in-charge adds a 15% distance contingency for diversions and response calls. Fuel consumption is 12 km/L; diesel costs ₹96.50/L. Each vehicle needs a 20-minute break, but breaks can be staggered so that at least one vehicle remains on patrol. A market picket also requires one vehicle to stay stationary for 45 minutes. At 23:00, one of the three vehicles develops a brake fault and is withdrawn. The control room asks whether the remaining two vehicles can still complete the mandatory visits by 06:00.
1. Calculate the minimum total patrol distance, fuel volume, and fuel cost for the full shift, including the 15% contingency and a 15% fuel reserve.
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Base distance for two visits to each beat = 2 × (18 + 24 + 30) = 2 × 72 = 144 km. Contingency = 15% of 144 = 21.6 km, so planned distance = 165.6 km. Fuel at 12 km/L = 165.6 ÷ 12 = 13.8 L. Reserve = 15% of 13.8 = 2.07 L, so carry/budget 15.87 L. Cost = 15.87 × ₹96.50 = ₹1,531.46 (about ₹1,531.50). The 45-minute picket adds no distance. The answer changes if the order means every vehicle must visit every beat twice; that would be 3 × 144 = 432 km, which is not what the standing order says.
2. Show whether three vehicles can complete the visits within the 10-hour shift while preserving staggered breaks and the 45-minute picket. Use time calculations.
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Driving time for 165.6 km at 28 km/h = 165.6 ÷ 28 = 5.91 hours, about 5 h 55 min of total vehicle movement across the shift. Available vehicle-hours = 3 vehicles × 10 h = 30 h. Even after 3 × 20 min breaks (1 h total) and a 45 min stationary picket (0.75 h), 28.25 vehicle-hours remain. The task needs only 5.91 vehicle-hours of movement, so it is feasible with a wide margin. A simple schedule: two vehicles run the beats while the third takes the picket and break; rotate every 90–120 min. Keep one vehicle free for response calls. The binding constraint is not total time but maintaining at least one mobile unit and not leaving a beat unvisited for too long.
3. At 23:00 a vehicle is withdrawn. Can two vehicles finish the remaining mandatory visits? Recalculate and state any assumption.
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At 23:00, 3 hours of the 10-hour shift have passed. Even under a conservative assumption that only 40% of the planned distance is complete, remaining distance is 0.6 × 165.6 = 99.4 km. Two vehicles have 7 h each = 14 vehicle-hours; after two 20-min breaks and a 45-min picket, about 12.6 vehicle-hours remain. At 28 km/h that is about 352 km of capacity, far above 99.4 km. So yes, two vehicles can complete the mandatory visits, provided the control room prioritises the unvisited beats, drops non-essential diversions, and records the brake fault. The assumption to state is that the remaining visits are distributed across both vehicles and that no major response call absorbs more than the spare capacity.