Question 1
A hospital needs to schedule 5 staff for 7 days (Saturday, Sunday, Monday...). Each day has 3 shifts: Morning, Evening, Night.
Undesirable shifts (higher weight = more undesirable):
- Weekend Night: weight 3
- Weekend Evening: weight 2
- Any Night: weight 1
After creating a fair schedule, what is the fairness gap (difference between max and min undesirable weights assigned to any staff)?
Step-by-step solution (Fairness Scheduling):
1. Total shifts to assign:
- 7 days × 3 shifts = 21 shifts
2. Shifts per person: 21 ÷ 5 = 4 with 1 extra shifts
3. Undesirable weight distribution:
- Alice: 3 points
- Bob: 3 points
- Carol: 6 points
- David: 1 points
- Frank: 2 points
4. Fairness gap: 6 - 1 = 5
Key Strategy: Fair scheduling aims to minimize the maximum difference in undesirable shift assignments across all staff.
1. Total shifts to assign:
- 7 days × 3 shifts = 21 shifts
2. Shifts per person: 21 ÷ 5 = 4 with 1 extra shifts
3. Undesirable weight distribution:
- Alice: 3 points
- Bob: 3 points
- Carol: 6 points
- David: 1 points
- Frank: 2 points
4. Fairness gap: 6 - 1 = 5
Key Strategy: Fair scheduling aims to minimize the maximum difference in undesirable shift assignments across all staff.