Scheduling - Intermediate Level: day scheduling INTERMEDIATE

Comprehensive weakness targeting worksheet covering 20 intermediate-level scheduling problems. Worksheet 18 of 30 emphasizes day scheduling. Master timetable puzzles, appointment logic, calendar scheduling through detailed explanations. Difficulty: moderate complexity with mixed patterns. Tailored for mid-level preparation.

📝 Worksheet 18 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate level

What you'll learn in this worksheet:

Achieve proficiency in timetable puzzles by completing this worksheet
Develop strong appointment logic skills with practical problems
Improve your scheduling solving speed through weakness targeting
Gain confidence in identifying calendar scheduling patterns
Master real-world applications of day scheduling

Your progress through Scheduling

Worksheet 18 of 30 (60% complete)

Question 1

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 2

A traveler needs to go from City A to City E. The transport schedule is: - T1: City A to City B, Departs 08:30, Arrives 12:25 PM - T2: City A to City C, Departs 09:00, Arrives 12:32 PM - T3: City B to City E, Departs 10:00, Arrives 12:10 PM - T4: City B to City C, Departs 11:00, Arrives 1:30 PM - T5: City C to City E, Departs 10:00, Arrives 12:35 PM - T6: City C to City B, Departs 13:30, Arrives 3:04 PM - T7: City D to City E, Departs 16:30, Arrives 6:25 PM - T8: City D to City B, Departs 14:30, Arrives 4:47 PM Minimum connection time is 45 minutes. What is the earliest arrival time at City E?

Step-by-step solution:

Network Path Analysis:
1. Identify all possible routes from City A to City E:
- City A→City B -> City B→City E
- City A→City C -> City C→City E
- City A→City B -> City B→City C -> City C→City E

No feasible route found with 45 min connection requirement.

Key Strategy: Enumerate all possible routes, verify connection times meet minimum requirements.

transportation, connections, optimization, railway-exams

Question 3

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 - Chemistry is scheduled immediately after English - There are exactly two classes between History and Physics - English is not on Monday On which day is Chemistry scheduled?

Step-by-step solution:

Table Method:
1. Create a timeline for Monday to Friday
2. Apply direct constraints:
- Mathematics is on Wednesday (fixed)
- English is not on Monday
3. Apply consecutive constraint:
- Chemistry 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 History and Physics
5. Final schedule:
- Monday: History
- Tuesday: English
- Wednesday: Mathematics
- Thursday: Chemistry
- Friday: Physics

Answer: Chemistry is scheduled on Thursday

Key Strategy: Fix direct constraints first, then work with consecutive and gap constraints.

weekly, academic, day-based, constraints

Question 4

A hospital needs one doctor on-call each day for 30 days. There are 4 doctors: Dr. Brown, Dr. Jones, Dr. Lee, Dr. Smith. If the schedule is as fair as possible, how many days will each doctor be on-call?

Step-by-step solution:

1. Total on-call days: 30
2. Base days per doctor: 30 ÷ 4 = 7 days
3. Remainder: 2 doctor(s) get one extra day

Answer: 7 days, with 2 doctor(s) getting 8 days

on-call, availability, emergency, medical, fairness

Question 5

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 6

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 7

A delivery company has vehicles with capacity 14 units. Customer demands: - C1: 7 units - C2: 5 units - C3: 7 units - C4: 6 units - C5: 4 units What is the minimum number of vehicles needed to serve all customers?

Step-by-step solution:

1. Total demand: 29
2. Vehicle capacity: 14
3. Minimum vehicles: ⌈29 ÷ 14⌉ = 3

Answer: 3 vehicles

vehicle-routing, logistics, delivery, optimization, VRP

Question 8

Computer Science courses with prerequisites: - CS201 requires CS101 - CS102 requires CS101 - CS401 requires CS101 - CS301 requires CS201 Which courses can be taken in the first semester?

Step-by-step solution:

1. Identify courses with prerequisites:
- CS201 needs CS101
- CS102 needs CS101
- CS401 needs CS101
- CS301 needs CS201

2. Courses without prerequisites (can take first): CS101

Answer: CS101

course, registration, prerequisite, academic, student

Question 9

A hospital needs to schedule 5 staff for 7 days (Wednesday, Friday, Saturday...). 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: 0 points
- Carol: 2 points
- David: 4 points
- Emma: 7 points
- Frank: 2 points

4. Fairness gap: 7 - 0 = 7

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 10

A factory has 4 machines. Each requires 2 day of preventive maintenance every 60 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 11

Eight people attend seminars in four different months (January, March, May, July) on two dates (5th and 15th). Two people attend per month. The constraints are: - S attends in March - Q attends on the 15th - Exactly two people attend between P and V - R attends in the same month as U In which month does P attend?

Step-by-step solution:

Timeline Grid Method:
1. Create month-date grid:
Jan 5 | Jan 15 | Mar 5 | Mar 15 | May 5 | May 15 | Jul 5 | Jul 15

2. Apply constraints:
- S in March (Mar 5 or Mar 15)
- Q on 15th (any month, date 15)
- Two people between P and V
(If P at position 1, V at position 4)
- R and U in same month

3. Systematic placement:
- Place S at Mar 5 (satisfies March constraint)
- Place Q at Mar 15 (satisfies 15th constraint)
- For 'two between' constraint: If P at Jan 5, V at Mar 15
- R and U together: May 5 & May 15

4. Verification:
All constraints satisfied with P in March

Key Strategy: Use grid to visualize all slots, apply direct constraints first, then deduce positions using gap constraints.

month-based, date-based, gap-constraints, banking-exams

Question 12

Real-time tasks with Rate Monotonic Scheduling (shorter period = higher priority): - Task A: Execution 2, Period 10 - Task B: Execution 5, Period 20 - Task C: Execution 8, Period 30 Is the task set schedulable under RM?

Step-by-step solution:

1. Calculate utilization:
- Task A: 2/10 = 0.200
- Task B: 5/20 = 0.250
- Task C: 8/30 = 0.267
Total U = 0.717
2. RM schedulability bound for 3 tasks: 0.780
3. Conclusion: Utilization 0.717 ≤ 0.780 (RM bound)

Answer: Schedulable

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

Question 13

A bus route takes 43 minutes one-way. Peak frequency: 1 bus every 12 minutes. What is the minimum number of buses needed to maintain this frequency in both directions?

Step-by-step solution:

1. Round trip time: 43 × 2 = 86 minutes
2. Headway: 12 minutes
3. Buses needed: ⌈86 ÷ 12⌉ = 8

Answer: 8 buses

bus, timetable, frequency, public-transport, optimization

Question 14

Five patients need appointments. Their preferences are: - Patient A: Dr. Patel at 10:00 AM - Patient B: Dr. Kumar at 10:00 AM - Patient C: Dr. Patel at 10:30 AM - Patient D: Dr. Shah at 10:00 AM - Patient E: Dr. Patel at 11:00 AM Each doctor can see one patient per 30-minute slot. If all preferences are honored, how many patients need to be rescheduled?

Step-by-step solution:

Conflict Detection Method:
1. Create doctor-time matrix:
Doctor | 10:00 | 10:30 | 11:00 | 11:30
------------|-------|-------|-------|-------
Dr. Patel | A | C | E | ---
Dr. Kumar | B | --- | --- | ---
Dr. Shah | D | --- | --- | ---

2. Check for conflicts:
- Dr. Patel at 10:00: Only Patient A (No conflict)
- Dr. Patel at 10:30: Only Patient C (No conflict)
- Dr. Patel at 11:00: Only Patient E (No conflict)
- Dr. Kumar at 10:00: Only Patient B (No conflict)
- Dr. Shah at 10:00: Only Patient D (No conflict)

3. Verification:
- No doctor has multiple patients in same slot
- All preferences can be honored

Answer: 0 patients need rescheduling

Key Strategy: Map all appointments to a doctor-time grid and identify slots where multiple patients request the same doctor.

appointment, conflict-resolution, multi-person

Question 15

A student has 9 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: 9 days
3. Extra buffer days: 3 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 9

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

academic, deadline, preparation, timeline

Question 16

A bus route takes 52 minutes one-way. Peak frequency: 1 bus every 15 minutes. What is the minimum number of buses needed to maintain this frequency in both directions?

Step-by-step solution:

1. Round trip time: 52 × 2 = 104 minutes
2. Headway: 15 minutes
3. Buses needed: ⌈104 ÷ 15⌉ = 7

Answer: 7 buses

bus, timetable, frequency, public-transport, optimization

Question 17

Trains and their scheduled times (arrival, departure): - Train 1: 4:00 → 7:00 - Train 3: 8:00 → 10:00 - Train 5: 12:00 → 13:00 - Train 6: 12:00 → 16:00 - Train 4: 16:00 → 19:00 - Train 2: 19:00 → 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 18

A delivery company has vehicles with capacity 11 units. Customer demands: - C1: 6 units - C2: 4 units - C3: 8 units What is the minimum number of vehicles needed to serve all customers?

Step-by-step solution:

1. Total demand: 18
2. Vehicle capacity: 11
3. Minimum vehicles: ⌈18 ÷ 11⌉ = 2

Answer: 2 vehicles

vehicle-routing, logistics, delivery, optimization, VRP

Question 19

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 20

A machine needs to process 4 jobs. Processing times: - Job E: 53 minutes - Job B: 48 minutes - Job A: 31 minutes - Job C: 61 minutes The machine breaks down at 94 minutes and takes 21 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 A → Job B → Job E → Job C
2. Simulate processing with breakdown:
- Job A: 0 → 31
- Job B: 31 → 79
- Job E: Starts at 79, breakdown at 94 (15 min completed), repair 21 min, resume 38 min → completes at 153
- Job C: 153 → 214

3. Total makespan: 214 minutes
4. Delay caused by breakdown: 21 minutes

Answer: 214 minutes

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

manufacturing, breakdown, recovery, simulation, reliability

💪 Progress update: 58% complete. Worksheet 18 awaits!

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