Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
Operations analysis help?
The sheriff’s department schedules police officers for 8 hour shifts. The beginning times for the shifts are 8:00 a.m., noon, 4:00 p.m., 8:00 p.m., midnight, and 4:00 a.m. An officer beginning a shift at one of these times works for the next 8 hours. During normal weekday operations, the number of officers needed varies depending on the time of day. The department staffing guidelines require the following minimum number of officers on duty:
Time of day Minimum Officers on Duty
8:00 a.m. – noon 5
Noon – 4:00 p.m. 7
4:00 p.m. – 8:00 p.m. 10
8:00 p.m. – midnight 8
Midnight – 4:00 a.m. 4
4:00 a.m. – 8:00 a.m. 6
Determine the number of police officers that should be scheduled to begin the 8 hour shifts at each of the six times to minimize the total number of officers required. Are there any surpluses? If so, during which shifts?
I just need help finding the constraints on this. I can't seem to work through this one in my head. Thanks.
1 Answer
- Here2HelpLv 61 decade agoFavorite Answer
I suggest that you draw a vertical bar chart for this problem, so that you may visualize it properly.
Plot the 4-hr time periods on the horizontal axis and the minimum number of officers on duty on the vertical axis,
The trick here is to determine the pairs of successive 4-hr periods whose minimum number of officers on duty are as close to each other as possible.
These pairs of successive 4-hr periods that would minimize the total number of officers required would be:
8am-4pm: assign 7 officers
4pm-midnight: assign 10 officers
midnight-8am: assign 6 officers
Total number of officers on duty for the day: 7 + 10 + 6 = 23 officers
There will be surpluses on the following shifts:
8am-12nn: surplus of 2 officers (7 minus 5)
8pm-midnight: surplus of 2 officers (10 minus 8)
midnight-4am: surplus of 2 officers (6 minus 4)
An alternative pairing of successive 4-hr periods, but would result in greater number of officers required would be:
12nn-8pm: assign 10 officers
8pm-4am: assign 8 officers
4am-12nn: assign 6 officers
Total number of officers on duty for the day: 10 + 8 + 6 = 24 officers
There will be greater surpluses on the following shifts:
12nn-4pm: surplus of 3 officers (10 minus 7)
midnight-4am: surplus of 4 officers (8 minus 4)
8am-12nn: surplus of 1 officer (6 minus 5)
