Radar Maintenance Roster
The radar site at Punggol requires two maintenance technicians on duty at all times, 24 hours a day, seven days a week. The roster uses three 8-hour shifts. Each technician is contracted for five shifts per week, but historical data show that 15% of contracted shifts are lost to leave, medical appointments, and mandatory training. The site currently has nine technicians. When staffing falls short, the site can either pay overtime at $45 per technician-hour or hire a contractor at $85 per technician-hour. Overtime is capped at 12 hours per technician per week. The site commander wants to know the minimum number of additional technicians needed to eliminate routine overtime, the weekly shortfall in technician-hours if no action is taken, and the cheaper short-term cover for the shortfall. Assume all shifts are 8 hours and that a technician cannot work two shifts in a row.
1. Calculate the weekly technician-shifts required, the current effective capacity, and the minimum number of additional technicians needed.
Read the worked answer
Required cover is 2 technicians × 3 shifts per day × 7 days = 42 technician-shifts per week. Each technician supplies 5 contracted shifts × 0.85 availability = 4.25 effective shifts per week. Nine technicians therefore supply 9 × 4.25 = 38.25 shifts. The shortfall is 42 − 38.25 = 3.75 shifts, or 3.75 × 8 = 30 technician-hours per week. One additional technician raises capacity to 10 × 4.25 = 42.5 shifts, which exceeds the requirement. Because a fraction of a technician cannot be hired, the minimum is one additional technician. The 0.5-shift surplus is about 4 hours per week of buffer, not enough to cover a full additional absence, so the site should monitor absence closely.
2. Compare the cost of covering the 30-hour shortfall with overtime versus a contractor, and check whether the overtime cap permits the overtime option.
Read the worked answer
Overtime cost is 30 hours × $45 = $1,350. Contractor cost is 30 hours × $85 = $2,550. Overtime is cheaper by $1,200. The overtime cap is 12 hours per technician per week, so 30 hours cannot be placed on one person. It can be distributed across at least three technicians: for example, 10 hours each, which is within the 12-hour cap. The cap therefore does not block the overtime option. The cheaper short-term cover is overtime, provided the three technicians are available and fatigue limits are respected. If the shortfall were larger than 36 hours, the cap would bind because three technicians could supply at most 36 overtime hours.
3. If absence rises to 25%, how many technicians are needed in total, and what does this imply for the commander's decision?
Read the worked answer
At 25% absence, each technician supplies 5 × 0.75 = 3.75 effective shifts per week. Required headcount is 42 ÷ 3.75 = 11.2, which rounds up to 12 technicians. The site currently has nine, so three additional technicians would be needed, not one. This implies the decision is sensitive to the absence assumption. Hiring only one technician solves the 15% case but leaves a shortfall if absence worsens: 10 technicians at 25% absence supply 37.5 shifts, a 4.5-shift or 36-hour weekly gap. The commander should either validate the absence rate, build in planned relief staff, or accept a defined overtime/contractor contingency rather than assuming the 15% figure is stable.