Staffing Four Posts Around the Clock
Your protective detail must staff four fixed posts continuously, 24 hours a day, seven days a week. Each agent works one 8-hour shift per day, five days per week, for 40 hours. Agents receive 15 percent relief time for leave, training, and court appearances, applied to the total post-hour requirement. The detail currently has 18 agents assigned. A proposal would eliminate one of the four posts, leaving three. The detail commander wants to know whether 18 agents is adequate now and after the change, and whether post count or the relief factor is the more sensitive variable in planning.
1. Compute the agents required to staff four posts continuously, including relief, and determine whether the current 18 are adequate. Show each step and state the rounding rule you apply.
Read the worked answer
Step 1 - weekly post-hours. 4 posts x 24 hours x 7 days = 672 post-hours per week.
Step 2 - base full-time equivalents. 672 / 40 = 16.8 FTE.
Step 3 - apply relief. 16.8 x 1.15 = 19.32 FTE.
Step 4 - round. Round up at the final step. Rounding down produces a schedule that cannot be filled; the fraction represents a real partial shift someone must work. Requirement: 20 agents.
Conclusion: 18 agents are two short. The shortfall does not appear until relief is applied, which is why the unadjusted figure (16.8) is misleading - the detail could look adequately staffed on paper while every absence forces overtime or leaves a post uncovered.
2. Recompute for three posts and compare the result to the current 18 agents. Then compare the sensitivity of the requirement to (a) removing one post and (b) a five-point increase in the relief factor, and say which drives the answer.
Read the worked answer
Three posts: 3 x 24 x 7 = 504 post-hours; 504 / 40 = 12.6 FTE; 12.6 x 1.15 = 14.49 → 15 agents. Eighteen agents would then be adequate with a surplus of three.
Sensitivity comparison, in agent-equivalents:
- One post: 24 x 7 = 168 post-hours per week = 4.2 FTE before relief; x 1.15 = 4.83, so about 5 agents.
- Five points of relief (15% to 20%): the additional 0.05 applies to 16.8 FTE = 0.84, so about 1 agent.
Post count dominates by roughly five to one. A single post costs more staffing than a five-point swing in the relief factor.
Practical consequence: arguing about the relief percentage is a marginal exercise; the post decision is where the staffing risk sits. This also cuts the other way - if the relief factor is ever too low, the error compounds across every post, so the factor should still be audited even though it is not the lever.
3. The commander asks: if we keep four posts, can we close the gap by holding relief at 10 percent instead of 15? Answer the question, and explain why the arithmetic answer and the defensible answer may differ.
Read the worked answer
Arithmetic: 16.8 x 1.10 = 18.48, which rounds up to 19 agents. Even at 10 percent relief, 18 agents are short by one.
So the answer to the literal question is no - reducing relief does not make 18 sufficient. It only shrinks the gap from two agents to one.
Why the defensible answer differs: the relief factor is not a dial to turn until the roster fits. It represents leave, training, and court time that agents are contractually and legally entitled to take. Setting it at 10 percent does not reduce those obligations; it hides them, and the detail absorbs the difference through overtime, fatigue, or an uncovered post.
The sound framing for the commander is:
- Four posts require 20 agents at the current relief rate; 19 is the floor even at an unrealistically low rate.
- The options that actually close the gap are adding agents, reducing a post, or formally accepting documented overtime.
- Lowering the relief assumption is not a staffing solution; it is a deferral of the same shortfall into a shift where no one is available.