Patrol Allocation with a Desk Officer Removed
A city police station has 24 patrol officers for the night shift, but one must remain at the station desk, leaving 23 for field patrol. The station covers five barangays. Average nightly incident counts and populations are: A, 10 incidents and 18,000 residents; B, 8 and 12,000; C, 12 and 30,000; D, 4 and 9,000; E, 6 and 21,000. Station policy requires at least 2 officers in every barangay. The remaining officers are distributed in proportion to average nightly incidents, using whole officers and the largest-remainder method. No barangay may receive more than 7 officers. The commander also wants to know which barangay has the highest incidents per assigned officer after the allocation, and whether one additional officer from the traffic unit can reduce that highest ratio below 2.0. The desk officer cannot be reassigned. The station must submit the deployment plan before the 8 p.m. briefing.
1. Compute the 23-officer allocation using the stated policy. Show the quotas, floors, remainders, and final assignment.
Read the worked answer
Total incidents = 10 + 8 + 12 + 4 + 6 = 40.
Base allocation: 2 officers each = 10 officers. Remaining officers = 23 - 10 = 13.
Remaining quotas are 13 × incident share:
- A: 13 × 10/40 = 3.25
- B: 13 × 8/40 = 2.60
- C: 13 × 12/40 = 3.90
- D: 13 × 4/40 = 1.30
- E: 13 × 6/40 = 1.95
Floors: A 3, B 2, C 3, D 1, E 1. Sum = 10. Need 3 more officers.
Remainders: A .25, B .60, C .90, D .30, E .95. Largest three are E, C, and B.
Extra allocation: A 3, B 3, C 4, D 1, E 2.
Final with base 2 each:
- A: 5
- B: 5
- C: 6
- D: 3
- E: 4
Check: 5 + 5 + 6 + 3 + 4 = 23. No barangay exceeds 7.
2. Compute incidents per assigned officer and identify the highest ratio. Explain what the ratio does and does not measure.
Read the worked answer
Using final assignments:
- A: 10/5 = 2.00
- B: 8/5 = 1.60
- C: 12/6 = 2.00
- D: 4/3 = 1.33
- E: 6/4 = 1.50
The highest ratio is 2.00, shared by A and C.
The ratio measures workload per officer using reported incidents. It does not measure travel time, backlogs, violence level, population density, or the time each incident consumes. Barangay C has more incidents and more residents than A, so equal incidents per officer may still mean C's officers handle more people and more complex cases. The commander should use the ratio as a screening tool, not as the only deployment rule.
3. Can one additional officer from the traffic unit reduce the highest ratio below 2.0? Recommend an assignment and justify it.
Read the worked answer
No. With one additional officer, total patrol strength becomes 24. If the officer is added to A, A becomes 10/6 = 1.67, but C remains 12/6 = 2.00, so the maximum is still 2.00. If the officer is added to C, C becomes 12/7 = 1.71, but A remains 10/5 = 2.00, so the maximum is still 2.00. Adding to B, D, or E does not touch either highest ratio.
To pull the maximum below 2.00, both A and C must gain an officer. With only one officer available, the commander cannot meet that goal.
Recommendation: if the sole objective is the maximum ratio, either A or C is defensible. If a tie-break is needed, place the officer in C because it has the larger absolute incident count and population, so the extra officer absorbs more demand. State in the deployment plan that the maximum remains 2.00 and that a second additional officer is needed to lower it.