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Scheduling - Advanced Level: monthly schedule ADVANCED

Quick competitive exam prep session: 20 advanced-level scheduling questions. Worksheet 27 of 30 - Focus: monthly schedule. Practice calendar scheduling, shift planning, time slots with instant feedback. Great for advanced students needing complex scenarios and multi-step problems practice.

📝 Worksheet 27 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Advanced level

What you'll learn in this worksheet:
Your progress through Scheduling
Worksheet 27 of 30 (90% complete)

Question 1

A factory has 5 machines. Each requires 2 day of preventive maintenance every 90 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: 5
2. Maintenance duration: 2 day
3. Staggered schedule: Never have all machines down simultaneously
4. Maximum operational: 5 - 1 = 4

Answer: 4 machines
maintenance, preventive, downtime, industrial, reliability

Question 2

A factory has 4 machines. Each requires 2 day of preventive maintenance every 30 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 3

6 tasks (A, B, C, D, E, F) are to be completed one after the other. The following conditions must be met: - Task C must be performed immediately after Task F. - Task B must be completed before Task E. - Task A is neither the first nor the last task to be completed. - Task A is performed exactly 3 positions after Task E. Which task is scheduled in the fifth position?
Step-by-step solution (Deductive Logic):

1. Apply Consecutive Constraint: 'C immediately after F' -> (F, C)
2. Apply Before Constraint: 'B before E'
3. Apply Exclusion Constraint: 'A not first or last'
4. Apply Gap Constraints: 'A is 3 after E'

Final Sequence: B → A → F → C → E → D

Answer: The task in the fifth position is E.

Key Strategy: Use fixed pairs and gap constraints to anchor positions.
linear-arrangement, relative-constraints, deduction, CAT-level

Question 4

A PhD thesis defense requires all 3 committee members to be present. Their availability (slots 1-8): - Prof. E: Slots 4, 7 - Prof. D: Slots 8, 6, 3 - Prof. B: Slots 8, 2, 3 What is the earliest slot when all can attend?
Step-by-step solution:

1. Find intersection of availability:
Prof. E: [4, 7]
∩ Prof. D: [3, 6, 8]
∩ Prof. B: [2, 3, 8]
= ∅ (No common slots)

Answer: No common slot available
thesis, defense, committee, academic, availability

Question 5

A machine needs to process 4 jobs. Processing times: - Job A: 84 minutes - Job B: 45 minutes - Job D: 71 minutes - Job C: 66 minutes The machine breaks down at 78 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 B → Job C → Job D → Job A
2. Simulate processing with breakdown:
- Job B: 0 → 45
- Job C: Starts at 45, breakdown at 78 (33 min completed), repair 34 min, resume 33 min → completes at 145
- Job D: 145 → 216
- Job A: 216 → 300

3. Total makespan: 300 minutes
4. Delay caused by breakdown: 34 minutes

Answer: 300 minutes

Key Strategy: Simulate the timeline, account for breakdown during active job processing.
manufacturing, breakdown, recovery, simulation, reliability

Question 6

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

Production Sequencing with Setup Times:
1. Calculate total production time (without setup):
- Product A: 1 x 3 = 3 hours
- Product C: 3 x 4 = 12 hours
- Product D: 2 x 1 = 2 hours
- Product B: 2 x 1 = 2 hours
- Base production time: 19 hours

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

Total: 22 hours

Key Strategy: Batch identical products together to minimize setup changes.
manufacturing, setup-time, sequencing, optimization

Question 7

Five subjects are scheduled on five different days of the week (Monday to Friday), one subject per day. The following information is given: - Mathematics is scheduled on Wednesday - History is scheduled immediately after Physics - There are exactly two classes between Chemistry and English - Physics is not on Monday On which day is History scheduled?
Step-by-step solution:

Table Method:
1. Create a timeline for Monday to Friday
2. Apply direct constraints:
- Mathematics is on Wednesday (fixed)
- Physics is not on Monday
3. Apply consecutive constraint:
- History immediately follows Physics
- Possible pairs: (Tue-Wed), (Wed-Thu), (Thu-Fri)
- Since Wednesday is occupied, options are (Tue-Wed) or (Thu-Fri)
4. Apply gap constraint:
- Two classes between Chemistry and English
5. Final schedule:
- Monday: Chemistry
- Tuesday: English
- Wednesday: Mathematics
- Thursday: Physics
- Friday: History

Answer: History is scheduled on Friday

Key Strategy: Fix direct constraints first, then work with consecutive and gap constraints.
weekly, academic, day-based, constraints

Question 8

A passenger travels from Atlanta to Dallas via Miami. The minimum layover at Miami is **90 minutes**. **Flights Atlanta -> Miami:** - F1-1: Dep 8:00 AM, Arr 10:35 AM - F1-2: Dep 11:00 AM, Arr 1:35 PM - F1-3: Dep 2:00 PM, Arr 4:35 PM **Flights Miami -> Dallas:** - F2-1: Dep 11:30 AM, Arr 3:24 PM - F2-2: Dep 1:30 PM, Arr 5:24 PM - F2-3: Dep 3:30 PM, Arr 7:24 PM What is the minimum total elapsed time for the journey from Atlanta to Dallas?
1. Timeline Approach & Constraint Application (Minimum Layover: 90 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 504 minutes is achieved by combining F1-2 (Arr: 1:35 PM) and F2-3 (Dep: 3:30 PM, Arr: 7:24 PM).
Total Elapsed Time = Final Arrival Time - Initial Departure Time.

3. Final Answer: The minimum elapsed time is 8 hours and 24 minutes.
transportation, time-interval, optimization, CAT-level

Question 9

Given these scheduling constraints: - Task A must be before Task D - Task C must be after Task D - Task B must be immediately after Task A Is a valid schedule possible?
Step-by-step solution:

1. Check for cycles: No circular dependencies
2. Check immediate constraints: Can be satisfied
3. Conclusion: Yes, a valid schedule exists

Answer: Yes, a valid schedule exists
feasibility, satisfiability, constraint-check, logic, verification

Question 10

A school has 5 exams in 3 time slots. Each time slot needs 2 invigilators. A teacher can invigilate at most one exam per time slot. What is the minimum number of teachers required?
Step-by-step solution:

1. Total invigilator slots per time: 2
2. Minimum teachers needed: At least 2 (one per invigilator slot)
3. Same teachers can invigilate multiple slots

Answer: 2 teachers
exam, invigilation, proctor, academic, constraints

Question 11

An event runs for 6 hours. Staff needed per hour: - Hour 1: 6 - Hour 2: 4 - Hour 3: 6 - Hour 4: 8 (PEAK) - Hour 5: 5 - Hour 6: 6 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 4
2. Staff can work multiple hours → schedule around peak
3. Minimum staff needed: 8

Answer: 8 staff
event, staff, venue, hospitality, logistics

Question 12

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

Production Sequencing with Setup Times:
1. Calculate total production time (without setup):
- Product C: 3 x 1 = 3 hours
- Product A: 1 x 1 = 1 hours
- Product B: 1 x 1 = 1 hours
- Product D: 3 x 2 = 6 hours
- Base production time: 11 hours

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

Total: 20 hours

Key Strategy: Batch identical products together to minimize setup changes.
manufacturing, setup-time, sequencing, optimization

Question 13

Real-time tasks with Rate Monotonic Scheduling (shorter period = higher priority): - Task A: Execution 7, Period 30 - Task B: Execution 6, Period 20 - Task C: Execution 6, Period 30 Is the task set schedulable under RM?
Step-by-step solution:

1. Calculate utilization:
- Task A: 7/30 = 0.233
- Task B: 6/20 = 0.300
- Task C: 6/30 = 0.200
Total U = 0.733
2. RM schedulability bound for 3 tasks: 0.780
3. Conclusion: Utilization 0.733 ≤ 0.780 (RM bound)

Answer: Schedulable
real-time, deadline, rate-monotonic, embedded, OS

Question 14

Project tasks with uncertain durations (optimistic, likely, pessimistic) in days: - Design: (4, 6, 9) - Development: (2, 4, 7) - Testing: (2, 5, 7) - Deployment: (4, 7, 9) 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: (4 + 4×6 + 9)/6 = 6.2
- Development: (2 + 4×4 + 7)/6 = 4.2
- Testing: (2 + 4×5 + 7)/6 = 4.8
- Deployment: (4 + 4×7 + 9)/6 = 6.8

2. Total expected duration: 22.0 days

Answer: 22.0 days
fuzzy, uncertainty, duration, advanced, real-world

Question 15

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 16

Four team members (Alice, Bob, Eva, Charlie) must be assigned to four unique tasks (Design, Testing, Documentation, Deployment). The assignments must follow these rules: 1. Alice must handle Design. 2. Bob cannot handle Deployment. 3. Eva and Charlie must be adjacent in (Design → Testing → Documentation → Deployment). Based on the constraints, which statement MUST be true?
No valid schedule found given the constraints. The only guaranteed assignment is: Alice must handle Design.
If the constraints cannot all be satisfied, fallback is to force rule 1's assignment.
multi-person, shift-scheduling, constraint-satisfaction, puzzle

Question 17

A company has 8 employees working in 3 shifts. Shifts rotate every 14 days. After how many days does an employee return to the same shift pattern?
Step-by-step solution:

1. Rotation cycle: 8 employees × 14 days = 112 days
2. Verification: Each employee cycles through all shifts

Answer: 112 days
rotation, cyclic, shift-pattern, workforce, healthcare

Question 18

Trains and their scheduled times (arrival, departure): - Train 4: 2:00 → 4:00 - Train 1: 7:00 → 9:00 - Train 5: 8:00 → 12:00 - Train 2: 11:00 → 12:00 - Train 3: 15:00 → 18:00 - Train 6: 18:00 → 20:00 What is the minimum number of platforms needed to avoid conflicts?
Step-by-step solution:

1. Sort trains by arrival time
2. Greedy platform allocation
3. Maximum overlapping trains: 2

Answer: 2 platforms
railway, platform, track, transportation, conflict

Question 19

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (22, 16) - Job B: (22, 14) - Job C: (32, 41) - Job D: (41, 34) - Job E: (10, 46) Using Johnson's Rule, what is the minimum makespan?
Step-by-step solution (Johnson's Rule):

1. Apply Johnson's Rule:
- If M1 time < M2 time, schedule early
- If M2 time < M1 time, schedule late
2. Optimal sequence: Job D → Job A → Job B → Job E → Job C
3. Calculate makespan: 192

Answer: 192
flow-shop, multi-stage, makespan, johnsons-rule, manufacturing

Question 20

Five subjects are scheduled on five different days of the week (Monday to Friday), one subject per day. The following information is given: - Chemistry is scheduled on Wednesday - Physics is scheduled immediately after English - There are exactly two classes between Biology and Mathematics - English is not on Monday On which day is Physics scheduled?
Step-by-step solution:

Table Method:
1. Create a timeline for Monday to Friday
2. Apply direct constraints:
- Chemistry is on Wednesday (fixed)
- English is not on Monday
3. Apply consecutive constraint:
- Physics immediately follows English
- Possible pairs: (Tue-Wed), (Wed-Thu), (Thu-Fri)
- Since Wednesday is occupied, options are (Tue-Wed) or (Thu-Fri)
4. Apply gap constraint:
- Two classes between Biology and Mathematics
5. Final schedule:
- Monday: Biology
- Tuesday: English
- Wednesday: Chemistry
- Thursday: Physics
- Friday: Mathematics

Answer: Physics is scheduled on Thursday

Key Strategy: Fix direct constraints first, then work with consecutive and gap constraints.
weekly, academic, day-based, constraints
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