Scheduling - Beginner-Intermediate Level: shift planning BEGINNER-INTERMEDIATE

Quick intensive drill ★ session: 20 beginner-intermediate-level scheduling questions. Worksheet 7 of 30 - Focus: shift planning. Practice shift planning, time slots, schedule constraints with instant feedback. Great for developing students needing building on fundamentals with moderate challenges practice.

📝 Worksheet 7 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner-intermediate level

What you'll learn in this worksheet:

Start with shift planning fundamentals and build up
Progress to advanced time slots problem-solving
Challenge yourself with intensive drill ★ scenarios
Deepen understanding of schedule constraints concepts
Complete the shift planning mastery track

Your progress through Scheduling

Worksheet 7 of 30 (23% complete)

Question 1

A delivery company has vehicles with capacity 15 units. Customer demands: - C1: 5 units - C2: 3 units - C3: 7 units What is the minimum number of vehicles needed to serve all customers?

Step-by-step solution:

1. Total demand: 15
2. Vehicle capacity: 15
3. Minimum vehicles: ⌈15 ÷ 15⌉ = 1

Answer: 1 vehicles

vehicle-routing, logistics, delivery, optimization, VRP

Question 2

A school needs to schedule 6 courses. The following courses have overlapping students and cannot be scheduled at the same time: - Physics conflicts with Chemistry - Chemistry conflicts with Biology - Chemistry conflicts with English - Chemistry conflicts with History - Chemistry conflicts with CS - English conflicts with Biology - English conflicts with CS What is the minimum number of time slots needed to schedule all courses without conflicts?

Step-by-step solution (Graph Coloring):

1. Model as graph coloring problem:
- Vertices = Courses
- Edges = Conflicts (courses that cannot be together)
2. Apply greedy coloring algorithm:
- Physics: Slot 1
- Chemistry: Slot 2
- English: Slot 1
- History: Slot 1
- Biology: Slot 3
- CS: Slot 4

3. Colors/slots used: 4

Answer: Minimum 4 time slots

Key Strategy: The chromatic number of the conflict graph gives the minimum slots needed.

timetable, conflict-resolution, graph-theory, chromatic-number, advanced

Question 3

A conference needs to schedule 6 sessions across 3 time slots and 3 rooms. Each room can hold one session per slot. The constraints are: - Prof. Garcia can only speak at 11:00-12:00 - Robotics and IoT cannot be in the same time slot - Dr. Chen and Prof. Wilson must speak in consecutive time slots - Data Science must be in Hall B Which speaker presents the Cloud Computing session?

Step-by-step solution:

Scheduling Grid Analysis:
1. Fix direct constraints:
- Prof. Garcia at 11:00-12:00
- Data Science in Hall B
2. Apply consecutive constraint: Dr. Chen and Prof. Wilson in consecutive slots
3. Apply conflict constraint: Robotics and IoT not together

4. Final Schedule:
9:00-10:00:
- Hall A: Blockchain by Dr. Taylor
- Hall B: Data Science by Dr. Lee
- Hall C: Robotics by Prof. Wilson
10:00-11:00:
- Hall A: Cloud Computing by Dr. Smith
- Hall B: AI Ethics by Dr. Chen
- Hall C: (empty)
11:00-12:00:
- Hall A: (empty)
- Hall B: IoT by Prof. Garcia
- Hall C: (empty)

Answer: Dr. Smith presents Cloud Computing

Key Strategy: Use a grid to solve the assignment problem and satisfy all constraints sequentially.

multi-constraint, professional, CSP, CAT-level

Question 4

An event runs for 8 hours. Staff needed per hour: - Hour 1: 4 - Hour 2: 4 - Hour 3: 4 - Hour 4: 5 - Hour 5: 8 (PEAK) - Hour 6: 4 - Hour 7: 5 - Hour 8: 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 5
2. Staff can work multiple hours → schedule around peak
3. Minimum staff needed: 8

Answer: 8 staff

event, staff, venue, hospitality, logistics

Question 5

Arrange the following activities in chronological order: Dinner, Evening Walk, Morning Yoga, Breakfast

Step-by-step solution:

Timeline Approach:
1. Convert all times to 24-hour format for easy comparison
- Dinner: 8:00 PM
- Evening Walk: 6:00 PM
- Morning Yoga: 6:00 AM
- Breakfast: 7:30 AM

2. Arrange in chronological order:
1. Morning Yoga at 6:00 AM
2. Evening Walk at 6:00 PM
3. Breakfast at 7:30 AM
4. Dinner at 8:00 PM

Final Schedule: Morning Yoga -> Evening Walk -> Breakfast -> Dinner

Key Strategy: Convert all times to 24-hour format and arrange from earliest to latest.

daily, time-based, chronological

Question 6

Project scheduling with two objectives: minimize time and minimize cost. - Schedule A: 100 days, $50K - Schedule B: 120 days, $40K - Schedule C: 90 days, $60K - Schedule D: 110 days, $45K - Schedule E: 95 days, $55K Which schedules are on the Pareto frontier (not dominated in both objectives)?

Step-by-step solution:

1. Pareto dominance: Schedule X dominates Y if X is better in at least one objective and not worse in others
2. Pareto frontier schedules: Schedule A, Schedule B, Schedule C, Schedule D, Schedule E

Answer: Schedule A, Schedule B, Schedule C, Schedule D, Schedule E

pareto, multi-objective, trade-off, advanced, optimization

Question 7

Events need to be scheduled in rooms. Their time intervals are: - Event A: 13:00 to 14:00 - Event B: 2:00 to 10:00 - Event C: 1:00 to 9:00 - Event D: 14:00 to 22:00 - Event E: 13:00 to 18:00 - Event F: 2:00 to 3:00 - Event G: 10:00 to 12:00 - Event H: 2:00 to 9:00 What is the minimum number of rooms needed to schedule all events without overlap?

Step-by-step solution (Interval Graph):

1. Plot intervals on timeline:
Event A: █ from 13 to 14
Event B: ████████ from 2 to 10
Event C: ████████ from 1 to 9
Event D: ████████ from 14 to 22
Event E: █████ from 13 to 18
Event F: █ from 2 to 3
Event G: ██ from 10 to 12
Event H: ███████ from 2 to 9

2. Find maximum overlap:
Maximum 4 events overlap at once

Answer: 4 rooms needed

interval, overlap, room-allocation, graph-theory, optimization

Question 8

A JIT manufacturing system has 4 jobs with the following data: | Job | Processing (min) | Due Date (min) | Early Penalty/min | Late Penalty/min | |-----|-----------------|----------------|-------------------|------------------| | Component A | 55 | 116 | 4 | 18 | | Component D | 57 | 95 | 4 | 18 | | Component C | 60 | 129 | 4 | 11 | | Component B | 43 | 122 | 2 | 10 | Using the Earliest Due Date (EDD) sequencing rule, what is the total penalty incurred?

Step-by-step solution (JIT Penalty Calculation):

1. EDD Sequence: Component D → Component A → Component B → Component C
2. Calculate completion times and penalties:
- Component D: completes at 57, due 95, early by 38 min → penalty 152
- Component A: completes at 112, due 116, early by 4 min → penalty 16
- Component B: completes at 155, due 122, late by 33 min → penalty 330
- Component C: completes at 215, due 129, late by 86 min → penalty 946

3. Total penalty: 1444

Answer: 1444 penalty points

Key Strategy: JIT scheduling minimizes total earliness + tardiness penalties, balancing inventory costs and customer satisfaction.

JIT, earliness, tardiness, penalty, inventory, lean-manufacturing

Question 9

A factory has 3 production lines: Line 1, Line 2, Line 3. Three products require the following operations: **Product X:** - Cut: 30 min on Line 3 - Assemble: 45 min on Line 1 - Package: 15 min on Line 3 **Product Y:** - Cut: 20 min on Line 3 - Assemble: 60 min on Line 2 - Package: 20 min on Line 3 **Product Z:** - Cut: 40 min on Line 3 - Assemble: 30 min on Line 2 - Package: 25 min on Line 3 All products must be completed (all 3 operations each). Multiple operations can run in parallel on different lines. Which production line is the bottleneck, and what is its total load (in minutes)?

Step-by-step solution (Bottleneck Analysis):

1. Calculate total load per production line:
- Line 1: 45 minutes
- Line 2: 90 minutes
- Line 3: 150 minutes

2. Identify bottleneck: The line with maximum load = Line 3
3. Bottleneck load: 150 minutes

Answer: Line 3 (150 minutes)

Key Strategy: The bottleneck determines maximum throughput; optimize the bottleneck first for overall efficiency.

nested, bottleneck, resource-allocation, multi-line, factory

Question 10

Trains and their scheduled times (arrival, departure): - Train 5: 4:00 → 8:00 - Train 3: 11:00 → 15:00 - Train 1: 12:00 → 14:00 - Train 4: 12:00 → 13:00 - Train 2: 17:00 → 21:00 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: 3

Answer: 3 platforms

railway, platform, track, transportation, conflict

Question 11

In a single-elimination knockout tournament with 16 teams, how many total matches are played to determine the champion?

Step-by-step solution:

1. Single elimination principle: Each match eliminates exactly one team
2. Teams to eliminate: 16 - 1 = 15 teams must be eliminated
3. Matches needed: 15 matches

Answer: 15 matches

tournament, bracket, knockout, sports, competitive-exams

Question 12

A clinic operates for 4 hours with 20-minute appointment slots. If 9 patients need appointments, how many can be accommodated?

Step-by-step solution:

1. Total slots available: (4 × 60) ÷ 20 = 12
2. Patients: 9
3. All patients can be scheduled

Answer: All 9 patients can be scheduled

clinic, appointment, doctor, healthcare, wait-time

Question 13

A student has 7 days to prepare for three exams: Physics, Computer Science, Mathematics. The required preparation days are: - Physics: 2 days - Computer Science: 1 days - Mathematics: 3 days If the student follows the optimal schedule starting today, on which day will the last exam be?

Step-by-step solution:

Timeline Planning Method:
1. Calculate total preparation time needed:
- Physics: 2 days
- Computer Science: 1 days
- Mathematics: 3 days
- Total: 6 days

2. Available days: 7 days
3. Extra buffer days: 1 days
4. Optimal schedule:
- Days 1-2: Prepare for Physics
- Day 3: Physics exam
- Days 4-4: Prepare for Computer Science
- Day 5: Computer Science exam
- Days 6-8: Prepare for Mathematics
- Day 9: Mathematics exam

Answer: The last exam will be on Day 7

Key Strategy: Schedule exams immediately after preparation period ends, accounting for all required prep days.

academic, deadline, preparation, timeline

Question 14

Real-time tasks with Rate Monotonic Scheduling (shorter period = higher priority): - Task A: Execution 5, Period 20 - Task B: Execution 7, Period 30 - Task C: Execution 4, Period 20 Is the task set schedulable under RM?

Step-by-step solution:

1. Calculate utilization:
- Task A: 5/20 = 0.250
- Task B: 7/30 = 0.233
- Task C: 4/20 = 0.200
Total U = 0.683
2. RM schedulability bound for 3 tasks: 0.780
3. Conclusion: Utilization 0.683 ≤ 0.780 (RM bound)

Answer: Schedulable

real-time, deadline, rate-monotonic, embedded, OS

Question 15

A conference needs to schedule 6 sessions across 3 time slots and 3 rooms. Each room can hold one session per slot. The constraints are: - Prof. Wilson can only speak at 9:00-10:00 - IoT and Cybersecurity cannot be in the same time slot - Prof. Garcia and Dr. Smith must speak in consecutive time slots - Machine Learning must be in Hall C Which speaker presents the Cloud Computing session?

Step-by-step solution:

Scheduling Grid Analysis:
1. Fix direct constraints:
- Prof. Wilson at 9:00-10:00
- Machine Learning in Hall C
2. Apply consecutive constraint: Prof. Garcia and Dr. Smith in consecutive slots
3. Apply conflict constraint: IoT and Cybersecurity not together

4. Final Schedule:
9:00-10:00:
- Hall A: Data Science by Dr. Lee
- Hall B: Cloud Computing by Dr. Taylor
- Hall C: IoT by Prof. Wilson
10:00-11:00:
- Hall A: Cybersecurity by Dr. Chen
- Hall B: AI Ethics by Dr. Smith
- Hall C: Machine Learning by Prof. Garcia
11:00-12:00:
- Hall A: (empty)
- Hall B: (empty)
- Hall C: (empty)

Answer: Dr. Taylor presents Cloud Computing

Key Strategy: Use a grid to solve the assignment problem and satisfy all constraints sequentially.

multi-constraint, professional, CSP, CAT-level

Question 16

Round Robin scheduling with time quantum = 4: - P1: Burst time 14 - P2: Burst time 15 - P3: Burst time 13 - P4: Burst time 11 - P5: Burst time 7 What is the average completion time?

Step-by-step solution:

1. Round Robin simulation:
2. Completion times:
- P5: 39
- P4: 54
- P1: 56
- P2: 59
- P3: 60

3. Average: 268 ÷ 5 = 53.6

Answer: 53.6

preemptive, interruptible, round-robin, OS, computer-science

Question 17

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 18

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

Answer: 2 machines

maintenance, preventive, downtime, industrial, reliability

Question 19

Trains and their scheduled times (arrival, departure): - Train 4: 2:00 → 5:00 - Train 5: 5:00 → 7:00 - Train 2: 7:00 → 10:00 - Train 1: 13:00 → 15:00 - Train 3: 14:00 → 18:00 - Train 6: 20:00 → 23:00 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 20

A clinic operates for 4 hours with 20-minute appointment slots. If 10 patients need appointments, how many can be accommodated?

Step-by-step solution:

1. Total slots available: (4 × 60) ÷ 20 = 12
2. Patients: 10
3. All patients can be scheduled

Answer: All 10 patients can be scheduled

clinic, appointment, doctor, healthcare, wait-time

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