Weekly beat-patrol roster with a staff shortage
A police station has a sanctioned strength of 42 constables. At present, 6 are on leave or training, and 4 are permanently assigned to office and record-room work. The station must cover 7 beat patrols. On the day shift and evening shift, one constable is needed per beat. On the night shift, two constables are needed per beat because of recent chain-snatching incidents. Each field constable can be rostered for a maximum of 6 duty days in a week, with one weekly off. The inspector wants to know whether the present strength can sustain this pattern for a full week without overtime. If two more constables go on medical leave next week, the inspector must either reduce night patrols or cancel leave. The station also has 3 woman constables, who are currently included in the field strength; night duty for woman constables requires a minimum of two together on a beat. The inspector must prepare a roster that is both legal and practical.
1. Calculate the field strength and the weekly person-day requirement. Is the roster feasible without overtime? Show the arithmetic.
Read the worked answer
Field strength = 42 - 6 - 4 = 32 constables. Daily requirement = day shift 7 + evening shift 7 + night shift 14 = 28 constables per day. Weekly requirement = 28 x 7 = 196 person-days. Weekly capacity at the legal maximum = 32 x 6 = 192 person-days. Since 192 is less than 196, the roster is short by 4 person-days and cannot be run for a full week without overtime or a reduction in deployment. The shortfall is small but real, so the inspector must adjust the plan rather than assume the roster will work.
2. If two more constables go on medical leave, calculate the new shortfall and propose two legal adjustments that avoid overtime.
Read the worked answer
With two more on leave, field strength = 30. Weekly capacity = 30 x 6 = 180 person-days. Requirement remains 196, so the shortfall becomes 196 - 180 = 16 person-days. Two legal adjustments: first, reduce one night beat on four nights; each night beat uses 2 constables, so 4 nights x 2 = 8 person-days saved. Second, merge two low-risk night beats into one on four more nights, saving another 8 person-days. Together that saves 16 person-days. Alternatively, deploy four trained office constables for one night shift each, adding 4 person-days, and reduce night beats on six nights to save the remaining 12. The inspector should record the reduced coverage and the reason.
3. How does the rule on woman constables at night affect the roster, and what is the practical consequence?
Read the worked answer
The station has 3 woman constables. Because night duty requires a minimum of two woman constables together on a beat, only two of them can cover one night beat as a pair. The third cannot be sent alone on night duty; she must be placed on day or evening shift, or paired with another woman if one becomes available. This means the station cannot spread the three women across three different night beats. If one of the pair is on leave, the station loses woman night coverage unless another woman constable is deputed. The inspector must plan the pair in advance and keep the third woman on a shift where the rule is satisfied.