Minimum Crewing Across Two Stations
Stations Alpha and Bravo each operate two pumps and must keep one pump available at all times. A pump requires a minimum crew of four firefighters. At 06:00 on a 24-hour shift, Alpha has ten personnel on duty and Bravo has seven. At Alpha, two firefighters are scheduled for a training course from 09:00 to 13:00 and cannot respond to calls. At Bravo, one firefighter is on light duties and cannot ride an appliance. At 10:20, a two-pump structure fire is reported. Alpha's pump can arrive in 8 minutes and Bravo's in 11 minutes. Station Charlie, the next nearest, can provide a pump in 45 minutes. Alpha's station officer can recall the two trainees, but they would need 15 minutes to return and change. Overtime crews at Bravo can be assembled in 20 minutes. A 13:00 community inspection also requires one pump at Alpha, but no extra staff.
1. At 10:20, calculate the riding strength at each station and determine whether each can send one pump while keeping one pump available.
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Alpha starts with 10 on duty. The two trainees are unavailable from 09:00 to 13:00, so Alpha has 10 - 2 = 8 riding firefighters. Sending a crew of 4 leaves 8 - 4 = 4 at the station, which exactly meets the minimum for one pump. Alpha can therefore send one pump and keep one pump available. Bravo starts with 7, but one firefighter is on light duties and cannot ride, leaving 7 - 1 = 6 riding. Sending a crew of 4 would leave 6 - 4 = 2, which is below the minimum of 4. Bravo cannot send a pump while maintaining station coverage. The limiting station is Bravo, which is short by 2 firefighters for a simultaneous send-and-cover task.
2. A second pump is needed on scene within 35 minutes. Compare recalling the Alpha trainees, assembling Bravo overtime, and waiting for Charlie. Recommend the least disruptive option that maintains minimum crewing.
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Recalling the Alpha trainees does not solve the problem. Alpha has already sent one crew, leaving 4 at the station. If the two trainees return, Alpha has 6, so it can spare only 2 firefighters, not a full crew of 4, without dropping below the minimum. Waiting for Charlie takes 45 minutes, which is outside the 35-minute requirement and would also remove Charlie's local coverage. Bravo overtime is the viable option: Bravo needs 2 extra riding firefighters to go from 6 to 8. With 8 riding, Bravo can send 4 and keep 4. Assembly takes 20 minutes, so the crew can depart at 10:40 and arrive at 10:51, which is 31 minutes after 10:20 and within the 35-minute window. The least disruptive compliant option is therefore 2 overtime firefighters at Bravo, with notification to the duty commander that station coverage is at minimum.
3. At 13:00, Alpha must provide one pump for a community inspection. With the Alpha crew still at the incident and the station holding minimum staff, can this be met? Explain.
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Yes, Alpha can meet the inspection if its station staffing remains at 4 riding firefighters and one of its two pumps is available. Alpha sent 4 to the incident and kept 4, which is exactly the minimum crew for one pump. Because Alpha operates two pumps, the station still has an appliance for the inspection. The limitation is that there is no spare crew: any additional call, leave, or absence would drop the station below minimum. The station officer should confirm that the four remaining firefighters are fit to ride at 13:00 and that the inspection pump is not the same appliance committed to the incident. If the incident crew returns before 13:00, staffing improves, but the inspection can be covered even without their return.