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Scheduling - Expert Level: daily schedule EXPERT

Comprehensive self assessment worksheet covering 20 expert-level scheduling problems. Worksheet 28 of 30 emphasizes daily schedule. Master shift planning, time slots, schedule constraints through detailed explanations. Difficulty: challenging problems and time-bound practice. Tailored for expert-level preparation.

📝 Worksheet 28 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Expert level

What you'll learn in this worksheet:
Your progress through Scheduling
Worksheet 28 of 30 (93% complete)

Question 1

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

Question 2

Computer Science courses with prerequisites: - CS201 requires CS102 - CS101 requires CS102 - CS202 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 CS102
- CS101 needs CS102
- CS202 needs CS101
- CS301 needs CS201

2. Courses without prerequisites (can take first): CS102

Answer: CS102
course, registration, prerequisite, academic, student

Question 3

A hospital needs to schedule 5 staff for 7 days (Tuesday, Monday, Thursday...). 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: 4 points
- Bob: 4 points
- Carol: 1 points
- David: 3 points
- Emma: 3 points

4. Fairness gap: 4 - 1 = 3

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 4

A hospital needs one doctor on-call each day for 30 days. There are 4 doctors: Dr. Brown, Dr. Jones, Dr. Smith, Dr. Lee. 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

A machine can process up to 6 jobs simultaneously as a batch. Each batch takes 46 minutes. If 13 jobs need to be processed, what is the minimum total time required?
Step-by-step solution:

1. Jobs per batch: 6
2. Number of batches: ⌈13 ÷ 6⌉ = 3
3. Total time: 3 × 46 = 138 minutes

Answer: 138 minutes
batch, parallel-machines, capacity, manufacturing, optimization

Question 7

A PhD thesis defense requires all 3 committee members to be present. Their availability (slots 1-8): - Prof. E: Slots 8, 6, 3 - Prof. B: Slots 1, 3, 4, 7 - Prof. D: Slots 6, 5 What is the earliest slot when all can attend?
Step-by-step solution:

1. Find intersection of availability:
Prof. E: [3, 6, 8]
∩ Prof. B: [1, 3, 4, 7]
∩ Prof. D: [5, 6]
= ∅ (No common slots)

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

Question 8

Hospital OR scheduling with 2 operating rooms (8 hours each): - Emergency: 50 min, Priority 1 - Urgent: 53 min, Priority 2 - Elective A: 102 min, Priority 3 - Elective B: 96 min, Priority 3 - Routine: 127 min, Priority 4 Can all surgeries be completed in one day?
Step-by-step solution:

1. Total surgery time: 428 min = 7.1 hours
2. Available OR hours: 2 × 8 = 16 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 9

A hospital needs to schedule 5 staff for 7 days (Wednesday, Tuesday, 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: 5 points
- Bob: 3 points
- Carol: 0 points
- David: 2 points
- Emma: 5 points

4. Fairness gap: 5 - 0 = 5

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

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 - English is scheduled immediately after Physics - There are exactly two classes between Chemistry and Biology - Physics is not on Monday On which day is English 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:
- English 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 Biology
5. Final schedule:
- Monday: Chemistry
- Tuesday: Biology
- Wednesday: Mathematics
- Thursday: Physics
- Friday: English

Answer: English is scheduled on Friday

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

Question 11

A machine can process up to 3 jobs simultaneously as a batch. Each batch takes 30 minutes. If 14 jobs need to be processed, what is the minimum total time required?
Step-by-step solution:

1. Jobs per batch: 3
2. Number of batches: ⌈14 ÷ 3⌉ = 5
3. Total time: 5 × 30 = 150 minutes

Answer: 150 minutes
batch, parallel-machines, capacity, manufacturing, optimization

Question 12

A clinic operates for 4 hours with 15-minute appointment slots. If 9 patients need appointments, how many can be accommodated?
Step-by-step solution:

1. Total slots available: (4 × 60) ÷ 15 = 16
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 flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (47, 46) - Job B: (35, 11) - Job C: (31, 28) - Job D: (45, 41) - Job E: (22, 44) - Job F: (34, 33) 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 A → Job D → Job F → Job C → Job B → Job E
3. Calculate makespan: 258

Answer: 258
flow-shop, multi-stage, makespan, johnsons-rule, manufacturing

Question 14

Computer Science courses with prerequisites: - CS301 requires CS202 - CS401 requires CS202 - CS201 requires CS401 - CS101 requires CS401 Which courses can be taken in the first semester?
Step-by-step solution:

1. Identify courses with prerequisites:
- CS301 needs CS202
- CS401 needs CS202
- CS201 needs CS401
- CS101 needs CS401

2. Courses without prerequisites (can take first): CS202

Answer: CS202
course, registration, prerequisite, academic, student

Question 15

Trains and their scheduled times (arrival, departure): - Train 1: 1:00 → 3:00 - Train 5: 7:00 → 10:00 - Train 4: 11:00 → 14:00 - Train 2: 16:00 → 17:00 - Train 3: 17:00 → 18:00 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 16

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: - W attends in March - P attends on the 15th - Exactly two people attend between T and V - R attends in the same month as U In which month does T 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:
- W in March (Mar 5 or Mar 15)
- P on 15th (any month, date 15)
- Two people between T and V
(If T at position 1, V at position 4)
- R and U in same month

3. Systematic placement:
- Place W at Mar 5 (satisfies March constraint)
- Place P at Mar 15 (satisfies 15th constraint)
- For 'two between' constraint: If T at Jan 5, V at Mar 15
- R and U together: May 5 & May 15

4. Verification:
All constraints satisfied with T 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 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

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 19

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 20

Events need to be scheduled in rooms. Their time intervals are: - Event A: 17:00 to 20:00 - Event B: 6:00 to 7:00 - Event C: 16:00 to 17:00 - Event D: 0:00 to 8:00 - Event E: 0:00 to 1:00 - Event F: 7:00 to 10:00 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 17 to 20
Event B: █ from 6 to 7
Event C: █ from 16 to 17
Event D: ████████ from 0 to 8
Event E: █ from 0 to 1
Event F: ███ from 7 to 10

2. Find maximum overlap:
Maximum 3 events overlap at once

Answer: 3 rooms needed
interval, overlap, room-allocation, graph-theory, optimization
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