Border Outpost Duty Roster Under Leave Pressure
A border outpost has 18 personnel available for the coming 21-day cycle. Standing orders require that at least 6 personnel be on active duty at any time, and each person can work at most 6 consecutive days before receiving a rest day. Three personnel have approved leave starting on day 10 for 5 days, and one of them is the only trained radio operator on the roster. On day 8 a patrol reports unusual movement near a river crossing 2 km from the outpost, and the commander must decide whether to send a 4-person patrol, which would leave the outpost below the standing minimum unless the duty plan is adjusted. The commander also has a written warning from sector headquarters that patrols near the crossing have been observed three times in the past week.
1. Calculate the minimum number of duty days the outpost can cover over the 21-day cycle given the 6-person minimum, and assess whether the current roster can meet it before day 10. Show your arithmetic.
Read the worked answer
The duty requirement is 6 persons × 21 days = 126 person-days. Before day 10 the full roster of 18 is available, so the outpost can cover 6 persons per day easily: 18 personnel × 6 consecutive duty days = 108 person-days of capacity before rest days, which exceeds the 126 total only if rest days are managed carefully. A simple check: over 21 days, 18 personnel each working at most 6 consecutive days and then resting 1 day yields roughly 6/7 of days as duty days, or about 18 × 21 × 6/7 = 324 person-days of capacity, far above 126. So the raw arithmetic is not the constraint. The real constraint is the leave block: from day 10 to day 14 only 15 personnel are present, giving 15 × 6/7 ≈ 12.8 duty-capable persons per day, still above 6. The commander can therefore maintain the 6-person minimum throughout, but only if the roster is rebuilt before day 10 and rest days are not clustered.
2. The commander wants to send a 4-person patrol on day 8. Using the numbers in the setup, explain what the duty plan must do to keep the outpost at or above the standing minimum, and identify the single biggest risk in that adjustment.
Read the worked answer
On day 8 all 18 personnel are present. Sending 4 on patrol leaves 14 for the outpost, which is above the 6-person minimum, so the patrol itself is feasible on day 8. The problem is the interaction with the leave block: if the 4 patrol members are also scheduled for duty on days 10–14, their absence plus the 3 on leave reduces the available pool. The plan must either (a) schedule the patrol members for rest days immediately after the patrol so they are fresh, or (b) move the patrol to day 9 and rotate the patrol members out of the day 10–14 duty roster. The biggest risk is the radio operator: if that person is on the patrol or on leave, the outpost loses its only trained operator during a period of repeated sightings near the crossing. The commander should either keep the radio operator at the outpost or arrange a qualified substitute before authorizing the patrol.
3. Given the sector warning about three sightings in the past week, recommend a course of action and justify it in terms of risk, not just rules.
Read the worked answer
The sightings are a pattern, not an isolated event, so the commander should treat the river crossing as a likely infiltration route. A reasonable recommendation is to send the 4-person patrol but keep the radio operator at the outpost, notify sector headquarters before departure, and set a fixed check-in time (for example every 30 minutes). The patrol should avoid the crossing itself and observe from cover. The justification is proportionality: the standing minimum of 6 protects the outpost, but the pattern of sightings raises the probability of an incident, so the marginal risk of a 4-person patrol is lower than the risk of ignoring the warning. If the radio operator cannot be replaced, the patrol should be reduced or postponed until a substitute arrives.