Holiday Duty Roster: Counting Clerk-Minutes Before Posting the Order
Nine Junior Administrative Assistants are available for public holiday duty at the district court on 15 August. Five filing counters must remain open from 10:00 to 17:00 with one clerk at each counter at all times, and the enquiry window must likewise stay staffed for the whole day. The e-filing help desk needs two clerks from 11:00 to 13:00 only. Each clerk is entitled to a 45-minute lunch break, which cannot be taken while a counter would be left unattended. Clerk C is on sanctioned leave. Clerk F must attend a training programme from 14:00 to 16:00. A proposed roster keeps five clerks on the counters and one on the enquiry window throughout, assigns two clerks to e-filing from 11:00 to 13:00, and schedules all eight lunch breaks between 13:00 and 14:00.
1. Which constraint does the proposed roster break first, and by how much?
Read the worked answer
The lunch schedule, not the counter staffing.
During 11:00 to 13:00 the roster needs eight bodies at once: five counters, one enquiry window, two e-filing. Eight are available (nine less C), so that block is exactly tight but workable.
During 13:00 to 14:00 the e-filing desk has closed, so six posts must be staffed. Eight clerks are available, which means at most two may be on lunch at any moment. A 60-minute window with a maximum of two absent at a time yields 2 x 60 = 120 clerk-minutes of lunch capacity. The entitlement is 8 x 45 = 360 clerk-minutes. The roster therefore fails by 240 clerk-minutes: four clerks would return late or six counters would be uncovered.
A secondary fault appears at 14:00, when F leaves for training: exactly six clerks remain for six posts, so any late return from lunch leaves a counter unattended.
2. Compute total available clerk-minutes and spare capacity for the day, stating your assumptions.
Read the worked answer
Assume a clerk on duty is available for the whole span including the lunch entitlement, so productive minutes are availability minus lunch.
- Seven clerks available 10:00-17:00: 7 x 420 = 2,940 clerk-minutes.
- Clerk F available 10:00-14:00 and 16:00-17:00: 5 hours = 300 clerk-minutes.
- Clerk C: nil.
- Total availability: 3,240 clerk-minutes.
- Less lunch: 8 x 45 = 360. Productive capacity: 2,880 clerk-minutes.
Requirement:
- Six continuous posts for 7 hours: 6 x 420 = 2,520.
- E-filing: 2 x 120 = 240.
- Total requirement: 2,760 clerk-minutes.
Spare capacity is only 120 clerk-minutes - under thirty minutes of one clerk's time, or roughly two and a half minutes per clerk across the day. That is why the roster has no room for a lunch block crammed into one hour: the arithmetic is tight everywhere, and a single late arrival consumes the whole margin.
3. Revise the roster minimally and state the two rules a revised version must obey.
Read the worked answer
Spread lunch breaks against the post requirement instead of clustering them.
- 10:00-11:00: two clerks on lunch. Six remain, which exactly meets five counters plus the enquiry window.
- 11:00-13:00: no lunch. All eight are needed for six posts plus two at e-filing.
- 13:00-14:00: two clerks on lunch (eight present, six posts).
- 14:00-15:00: one clerk on lunch (F is at training, seven present, six posts).
- 15:00-16:00: one clerk on lunch.
- 16:00-17:00: two clerks on lunch (F returns, eight present).
- F's own break must fall before 14:00, so it goes in the 10:00-11:00 or 13:00-14:00 slot.
Two rules govern any revision: (1) at every moment, present clerks minus those on lunch must be at least the number of required posts; (2) during 11:00-13:00 and 14:00-16:00 the margin is zero to one, so no leave, errand or late return can be absorbed. Record the roster with the post requirement and the break slots in the same table, so the checking is visible.