Scheduling Worksheet 11 - Beginner-Intermediate Level (weekly schedule) | 20 Questions

Question 1

A passenger travels from Chicago to Atlanta via Dallas. The minimum layover at Dallas is **45 minutes**. **Flights Chicago -> Dallas:** - F1-1: Dep 5:30 AM, Arr 8:25 AM - F1-2: Dep 8:30 AM, Arr 11:25 AM - F1-3: Dep 11:30 AM, Arr 2:25 PM **Flights Dallas -> Atlanta:** - F2-1: Dep 1:00 PM, Arr 3:42 PM - F2-2: Dep 3:00 PM, Arr 5:42 PM - F2-3: Dep 5:00 PM, Arr 7:42 PM What is the minimum total elapsed time for the journey from Chicago to Atlanta?

1. Timeline Approach & Constraint Application (Minimum Layover: 45 min):
The fastest total time is found by checking all 9 combinations and ensuring the layover time (F2 Dep Time - F1 Arr Time) is at least the minimum required.

2. Optimal Path Calculation:
The minimum elapsed time of 432 minutes is achieved by combining F1-2 (Arr: 11:25 AM) and F2-1 (Dep: 1:00 PM, Arr: 3:42 PM).
Total Elapsed Time = Final Arrival Time - Initial Departure Time.

3. Final Answer: The minimum elapsed time is 7 hours and 12 minutes.

transportation, time-interval, optimization, CAT-level

Question 2

A hospital ward has 8 patients. Each nurse can handle at most 5 patients. What is the minimum number of nurses required?

Step-by-step solution:

1. Patients: 8
2. Capacity per nurse: 5
3. Minimum nurses: ⌈8 ÷ 5⌉ = 2

Answer: 2 nurses

nurse, patient, assignment, healthcare, ratio

Question 3

A production line needs to manufacture: - Product A: 2 units (each takes 4 hours) - Product B: 2 units (each takes 3 hours) - Product C: 3 units (each takes 1 hours) Setup time required when switching products: - P->P: 3 hour What is the minimum total time if production starts with Product C?

Step-by-step solution:

Production Sequencing with Setup Times:
1. Calculate total production time (without setup):
- Product A: 2 x 4 = 8 hours
- Product B: 2 x 3 = 6 hours
- Product C: 3 x 1 = 3 hours
- Base production time: 17 hours

2. Minimize setup time by batching:
- Optimal sequence: Product C -> Product C -> Product C -> Product A -> Product A -> Product B -> Product B
3. Total with setups:
- Product C: 1 hours
- Product C: 1 hours (no setup)
- Product C: 1 hours (no setup)
- Setup Product C→Product A: 3 hour + Product A: 4 hours
- Product A: 4 hours (no setup)
- Setup Product A→Product B: 3 hour + Product B: 3 hours
- Product B: 3 hours (no setup)

Total: 23 hours

Key Strategy: Batch identical products together to minimize setup changes.

manufacturing, setup-time, sequencing, optimization

Question 4

A manager has 4 tasks to complete over 8 working hours. The task details are: - Report: Priority High, Duration 3 hours, Deadline 5 hours - Email: Priority Low, Duration 1 hours, Deadline 6 hours - Presentation: Priority High, Duration 2 hours, Deadline 4 hours - Analysis: Priority Medium, Duration 2 hours, Deadline 7 hours If tasks are scheduled based on priority first and deadline second, which task should be completed first?

Step-by-step solution:

Priority-Deadline Scheduling Algorithm:
1. Assign priority weights:
- High = 3, Medium = 2, Low = 1

2. Create priority-deadline table:
Task | Priority | Deadline | Duration
--------------|----------|----------|----------
Report | High | 5 | 3
Email | Low | 6 | 1
Presentation | High | 4 | 2
Analysis | Medium | 7 | 2

3. Sorting criteria:
- Primary: Highest priority first
- Secondary: Earliest deadline (if priority is same)

4. Sorted order:
1. Presentation (Priority: High, Deadline: 4)
2. Report (Priority: High, Deadline: 5)
3. Analysis (Priority: Medium, Deadline: 7)
4. Email (Priority: Low, Deadline: 6)

Answer: Presentation should be completed first

Key Strategy: Sort by priority first (descending), then by deadline (ascending) for tasks with equal priority.

priority-based, deadline-driven, task-ordering

Question 5

A clinic operates for 4 hours with 30-minute appointment slots. If 9 patients need appointments, how many can be accommodated?

Step-by-step solution:

1. Total slots available: (4 × 60) ÷ 30 = 8
2. Patients: 9
3. Overflow: 9 - 8 = 1 patients

Answer: 1 patients will need to wait or be rescheduled

clinic, appointment, doctor, healthcare, wait-time

Question 6

A machine can process up to 5 jobs simultaneously as a batch. Each batch takes 37 minutes. If 14 jobs need to be processed, what is the minimum total time required?

Step-by-step solution:

1. Jobs per batch: 5
2. Number of batches: ⌈14 ÷ 5⌉ = 3
3. Total time: 3 × 37 = 111 minutes

Answer: 111 minutes

batch, parallel-machines, capacity, manufacturing, optimization

Question 7

Project tasks with uncertain durations (optimistic, likely, pessimistic) in days: - Design: (2, 5, 6) - Development: (4, 6, 8) - Testing: (2, 5, 8) - Deployment: (3, 4, 6) Using the PERT formula (O + 4M + P)/6, what is the expected total project duration?

Step-by-step solution (PERT):

1. Calculate expected duration for each task:
- Design: (2 + 4×5 + 6)/6 = 4.7
- Development: (4 + 4×6 + 8)/6 = 6.0
- Testing: (2 + 4×5 + 8)/6 = 5.0
- Deployment: (3 + 4×4 + 6)/6 = 4.2

2. Total expected duration: 19.8 days

Answer: 19.8 days

fuzzy, uncertainty, duration, advanced, real-world

Question 8

A machine needs to process 4 jobs. Processing times: - Job A: 69 minutes - Job D: 30 minutes - Job E: 89 minutes - Job B: 59 minutes The machine breaks down at 120 minutes and takes 34 minutes to repair. Jobs are scheduled using Shortest Processing Time (SPT) first rule. What is the total completion time (makespan) after handling the breakdown?

Step-by-step solution (Breakdown Recovery):

1. Original SPT order: Job D → Job B → Job A → Job E
2. Simulate processing with breakdown:
- Job D: 0 → 30
- Job B: 30 → 89
- Job A: Starts at 89, breakdown at 120 (31 min completed), repair 34 min, resume 38 min → completes at 192
- Job E: 192 → 281

3. Total makespan: 281 minutes
4. Delay caused by breakdown: 34 minutes

Answer: 281 minutes

Key Strategy: Simulate the timeline, account for breakdown during active job processing.

manufacturing, breakdown, recovery, simulation, reliability

Question 9

An event runs for 8 hours. Staff needed per hour: - Hour 1: 4 - Hour 2: 3 - Hour 3: 5 - Hour 4: 6 - Hour 5: 8 (PEAK) - Hour 6: 4 - Hour 7: 4 - Hour 8: 3 What is the minimum number of staff needed if staff can work multiple consecutive hours?

Step-by-step solution:

1. Identify peak demand: 8 staff at hour 5
2. Staff can work multiple hours → schedule around peak
3. Minimum staff needed: 8

Answer: 8 staff

event, staff, venue, hospitality, logistics

Question 10

A hospital ward has 13 patients. Each nurse can handle at most 4 patients. What is the minimum number of nurses required?

Step-by-step solution:

1. Patients: 13
2. Capacity per nurse: 4
3. Minimum nurses: ⌈13 ÷ 4⌉ = 4

Answer: 4 nurses

nurse, patient, assignment, healthcare, ratio

Question 11

An airline crew has the following flights: - Flight 101: 08:00 → 10:00 - Flight 102: 10:30 → 12:30 - Flight 103: 13:00 → 15:00 - Flight 104: 15:30 → 17:30 - Flight 105: 18:00 → 20:00 Crew duty time limit is 8 hours. Minimum connection time between flights is 30 minutes. What is the maximum number of flights a crew can operate in a single duty period?

Step-by-step solution:

1. Convert all times to minutes for easier calculation:
- Flight 101: Departs at 8:00, Arrives at 10:00
- Flight 102: Departs at 10:30, Arrives at 12:30
- Flight 103: Departs at 13:00, Arrives at 15:00
- Flight 104: Departs at 15:30, Arrives at 17:30
- Flight 105: Departs at 18:00, Arrives at 20:00

2. Duty time limit: 480 minutes (8 hours)
3. Minimum connection time: 30 minutes

4. Find optimal sequence of flights:
Best sequence found: Flight 103 → Flight 104 → Flight 105
- Take Flight 103: Departs at 13:00
- Connection time: 30 minutes
- Take Flight 104: Departs at 15:30
- Connection time: 30 minutes
- Take Flight 105: Departs at 18:00

Total duty time: 420 minutes (7 hours, 0 minutes)

5. Maximum flights possible: 3

Answer: 3 flights

✓ Duty time check: 7h 0m ≤ 8h (PASSED)

airline, crew, flight, aviation, rostering

Question 12

A hospital needs to schedule 5 staff for 7 days (Friday, Wednesday, Tuesday...). 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: 4 points
- David: 3 points
- Emma: 2 points

4. Fairness gap: 4 - 2 = 2

Key Strategy: Fair scheduling aims to minimize the maximum difference in undesirable shift assignments across all staff.

fairness, shift-scheduling, workforce, equity, human-resources

Question 13

Four colleagues need to schedule a meeting. Their available time slots are: - Alex: 9:00 AM, 10:00 AM, 2:00 PM, 3:00 PM - Ben: 10:00 AM, 11:00 AM, 2:00 PM - Cara: 9:00 AM, 11:00 AM, 12:00 PM, 3:00 PM - Diana: 10:00 AM, 12:00 PM, 2:00 PM, 3:00 PM What is the earliest time slot when all four can meet?

Step-by-step solution:

Set Intersection Method:
1. List all availability:
- Alex: {9:00 AM, 10:00 AM, 2:00 PM, 3:00 PM}
- Ben: {10:00 AM, 11:00 AM, 2:00 PM}
- Cara: {9:00 AM, 11:00 AM, 12:00 PM, 3:00 PM}
- Diana: {10:00 AM, 12:00 PM, 2:00 PM, 3:00 PM}

2. Find common slots (intersection):
- Common to all = Alex AND Ben AND Cara AND Diana
- Result: Empty set (No common time)

3. Conclusion: No common time slot available

Key Strategy: Use set intersection to find common availability, then choose the earliest time.

multi-person, time-slots, availability

Question 14

A job shop has 3 machines. Jobs and their routes: - Job A: M1 → M3 → M2 with times 37, 36, 27 - Job B: M1 → M3 → M2 with times 25, 12, 15 - Job C: M2 → M3 → M1 with times 23, 24, 30 What is a lower bound on the minimum makespan?

Step-by-step solution:

1. Machine load bound: 92
2. Job processing bound: 100
3. Lower bound: 100

Answer: 100

job-shop, routing, complex, np-hard, advanced

Question 15

Hospital OR scheduling with 3 operating rooms (8 hours each): - Emergency: 36 min, Priority 1 - Urgent: 85 min, Priority 2 - Elective A: 78 min, Priority 3 - Elective B: 93 min, Priority 3 - Routine: 137 min, Priority 4 Can all surgeries be completed in one day?

Step-by-step solution:

1. Total surgery time: 429 min = 7.2 hours
2. Available OR hours: 3 × 8 = 24 hours
3. Total ≤ Available → Can complete in one day

Answer: All surgeries can be scheduled within one day

surgery, operating-room, hospital, healthcare, critical

Question 16

Four colleagues need to schedule a meeting. Their available time slots are: - Alex: 9:00 AM, 10:00 AM, 2:00 PM, 3:00 PM - Ben: 10:00 AM, 11:00 AM, 2:00 PM - Cara: 9:00 AM, 11:00 AM, 12:00 PM, 3:00 PM - Diana: 10:00 AM, 12:00 PM, 2:00 PM, 3:00 PM What is the earliest time slot when all four can meet?

Step-by-step solution:

Set Intersection Method:
1. List all availability:
- Alex: {9:00 AM, 10:00 AM, 2:00 PM, 3:00 PM}
- Ben: {10:00 AM, 11:00 AM, 2:00 PM}
- Cara: {9:00 AM, 11:00 AM, 12:00 PM, 3:00 PM}
- Diana: {10:00 AM, 12:00 PM, 2:00 PM, 3:00 PM}

2. Find common slots (intersection):
- Common to all = Alex AND Ben AND Cara AND Diana
- Result: Empty set (No common time)

3. Conclusion: No common time slot available

Key Strategy: Use set intersection to find common availability, then choose the earliest time.

multi-person, time-slots, availability

Question 17

A project involves two events, Event A (Meeting) and Event B (Training). The constraints are: - **Event A:** Duration 90 minutes. Must start between 9:00 AM and 11:00 AM. - **Event B:** Duration 60 minutes. Must finish by 3:00 PM. - **Gap:** A minimum of 2 hours is required between the end of Event A and the start of Event B. Assuming all constraints must be met, what is the earliest possible start time for Event B?

Step-by-step solution (Time Arithmetic):

1. Goal: To find the earliest start time for Event B, we must use the earliest possible schedule for Event A.
2. Calculate Earliest Finish Time for Event A:
- Earliest Start for A: 9:00 AM
- Duration of A: 90 minutes (1 hour 30 minutes)
- Earliest Finish for A: 9:00 AM + 1 hour 30 minutes = 10:30 AM.
3. Apply Minimum Gap:
- Earliest Start for B = (Earliest Finish A) + (Minimum Gap)
- Minimum Gap: 2 hours (120 minutes)
- Earliest Start for B: 10:30 AM + 2 hours = 12:30 PM.
4. Check Deadline for Event B:
- If B starts at 12:30 PM, its finish time is 12:30 PM + 60 minutes = 1:30 PM.
- The latest finish time for B is 3:00 PM. Since 1:30 PM is before 3:00 PM, the schedule is valid.
Answer: The earliest possible start time for Event B is 12:30 PM.
Key Strategy: To find the minimum time for the second event, use the minimum time for the first event, plus the mandatory gap.

time-arithmetic, gap-constraint, optimization, banking-exams

Question 18

A factory has 4 machines. Each requires 2 day of preventive maintenance every 45 days. If maintenance is staggered, what is the maximum number of machines that can be operational at any time?

Step-by-step solution:

1. Total machines: 4
2. Maintenance duration: 2 day
3. Staggered schedule: Never have all machines down simultaneously
4. Maximum operational: 4 - 1 = 3

Answer: 3 machines

maintenance, preventive, downtime, industrial, reliability

Question 19

Project tasks with uncertain durations (optimistic, likely, pessimistic) in days: - Design: (2, 4, 7) - Development: (3, 5, 6) - Testing: (4, 7, 10) - Deployment: (3, 4, 6) Using the PERT formula (O + 4M + P)/6, what is the expected total project duration?

Step-by-step solution (PERT):

1. Calculate expected duration for each task:
- Design: (2 + 4×4 + 7)/6 = 4.2
- Development: (3 + 4×5 + 6)/6 = 4.8
- Testing: (4 + 4×7 + 10)/6 = 7.0
- Deployment: (3 + 4×4 + 6)/6 = 4.2

2. Total expected duration: 20.2 days

Answer: 20.2 days