Scheduling Worksheet 20 - Intermediate-Advanced Level (appointment logic) | 20 Questions

Question 1

A JIT manufacturing system has 4 jobs with the following data: | Job | Processing (min) | Due Date (min) | Early Penalty/min | Late Penalty/min | |-----|-----------------|----------------|-------------------|------------------| | Component B | 24 | 63 | 3 | 17 | | Component A | 24 | 38 | 4 | 10 | | Component C | 36 | 116 | 2 | 17 | | Component D | 24 | 70 | 3 | 20 | 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 A → Component B → Component D → Component C
2. Calculate completion times and penalties:
- Component A: completes at 24, due 38, early by 14 min → penalty 56
- Component B: completes at 48, due 63, early by 15 min → penalty 45
- Component D: completes at 72, due 70, late by 2 min → penalty 40
- Component C: completes at 108, due 116, early by 8 min → penalty 16

3. Total penalty: 157

Answer: 157 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 2

A job shop has 3 machines. Jobs and their routes: - Job A: M2 → M3 → M1 with times 33, 10, 39 - Job B: M1 → M3 → M2 with times 22, 25, 37 - Job C: M1 → M3 → M2 with times 31, 28, 24 What is a lower bound on the minimum makespan?

Step-by-step solution:

1. Machine load bound: 94
2. Job processing bound: 84
3. Lower bound: 94

Answer: 94

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

Question 3

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 4

Given these scheduling constraints: - Task C must be before Task D - Task A must be after Task D - Task B must be immediately after Task C 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 5

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: - Dr. Chen can only speak at 9:00-10:00 - Machine Learning and Robotics cannot be in the same time slot - Dr. Smith and Prof. Garcia must speak in consecutive time slots - Cloud Computing must be in Hall A Which speaker presents the Cloud Computing session?

Step-by-step solution:

Scheduling Grid Analysis:
1. Fix direct constraints:
- Dr. Chen at 9:00-10:00
- Cloud Computing in Hall A
2. Apply consecutive constraint: Dr. Smith and Prof. Garcia in consecutive slots
3. Apply conflict constraint: Machine Learning and Robotics not together

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

Answer: Dr. Chen 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 6

Four employees need to be scheduled for three shifts over three days. The constraints are: - Each employee works exactly one shift per day - No employee works the same shift two days in a row - Alice works Morning shift on Monday - Bob cannot work Night shift - Charlie works Evening shift on Tuesday Who works the Evening shift on Wednesday?

Step-by-step solution:

Table Method with Constraint Elimination:
1. Create a 3D table: Days x Shifts x Employees

2. Apply direct constraints:
- Monday Morning: Alice (fixed)
- Tuesday Evening: Charlie (fixed)
- Bob: Never Night shift (all days)

3. Apply rotation constraint:
- Alice (Morning Mon) cannot be Morning Tue
- Charlie (Evening Tue) cannot be Evening Wed

4. Fill Monday:
- Morning: Alice
- Evening: Charlie (can work evening)
- Night: Diana (Bob can't do night)

5. Fill Tuesday:
- Morning: Bob (Alice can't repeat, Charlie is evening)
- Evening: Charlie (fixed)
- Night: Diana (Bob can't)

6. Fill Wednesday:
- Charlie can't be Evening (was Evening Tue)
- Alice can be Evening (was Morning Mon, okay to shift)
- Answer: Alice works Evening on Wednesday

Key Strategy: Apply fixed constraints first, then use rotation rules to eliminate impossible assignments systematically.

shift-rotation, multi-person, constraints, professional

Question 7

A flow shop has 2 machines (M1 → M2). Jobs and processing times (M1, M2): - Job A: (26, 31) - Job B: (49, 48) - Job C: (49, 37) - Job D: (12, 41) - Job E: (47, 24) - Job F: (32, 10) 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 B → Job C → Job E → Job F → Job D → Job A
3. Calculate makespan: 261

Answer: 261

flow-shop, multi-stage, makespan, johnsons-rule, manufacturing

Question 8

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 - R attends on the 15th - Exactly two people attend between T and P - V attends in the same month as Q 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)
- R on 15th (any month, date 15)
- Two people between T and P
(If T at position 1, P at position 4)
- V and Q in same month

3. Systematic placement:
- Place W at Mar 5 (satisfies March constraint)
- Place R at Mar 15 (satisfies 15th constraint)
- For 'two between' constraint: If T at Jan 5, P at Mar 15
- V and Q 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 9

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 10

A hospital ward has 14 patients. Each nurse can handle at most 4 patients. What is the minimum number of nurses required?

Step-by-step solution:

1. Patients: 14
2. Capacity per nurse: 4
3. Minimum nurses: ⌈14 ÷ 4⌉ = 4

Answer: 4 nurses

nurse, patient, assignment, healthcare, ratio

Question 11

A hospital needs one doctor on-call each day for 30 days. There are 4 doctors: Dr. Lee, Dr. Brown, Dr. Jones, Dr. Patel. 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 12

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 9:00-10:00 - IoT and AI Ethics cannot be in the same time slot - Dr. Lee and Prof. Brown must speak in consecutive time slots - Robotics must be in Hall C Which speaker presents the AI Ethics session?

Step-by-step solution:

Scheduling Grid Analysis:
1. Fix direct constraints:
- Prof. Garcia at 9:00-10:00
- Robotics in Hall C
2. Apply consecutive constraint: Dr. Lee and Prof. Brown in consecutive slots
3. Apply conflict constraint: IoT and AI Ethics not together

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

Answer: Dr. Chen presents AI Ethics

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

multi-constraint, professional, CSP, CAT-level

Question 13

A football league has 7 teams. Each team plays every other team twice (home and away). What is the minimum number of rounds needed if each round has the maximum possible matches?

Step-by-step solution:

1. Total matches in double round-robin: 7 × (7-1) = 42
2. Maximum matches per round: 3
3. Minimum rounds: 42 ÷ 3 = 7 rounds

Answer: 7 rounds

league, fixture, home-away, sports, optimization

Question 14

An event runs for 4 hours. Staff needed per hour: - Hour 1: 6 - Hour 2: 4 - Hour 3: 12 (PEAK) - Hour 4: 5 What is the minimum number of staff needed if staff can work multiple consecutive hours?

Step-by-step solution:

1. Identify peak demand: 12 staff at hour 3
2. Staff can work multiple hours → schedule around peak
3. Minimum staff needed: 12

Answer: 12 staff

event, staff, venue, hospitality, logistics

Question 15

Hospital OR scheduling with 3 operating rooms (8 hours each): - Emergency: 49 min, Priority 1 - Urgent: 70 min, Priority 2 - Elective A: 92 min, Priority 3 - Elective B: 89 min, Priority 3 - Routine: 141 min, Priority 4 Can all surgeries be completed in one day?

Step-by-step solution:

1. Total surgery time: 441 min = 7.3 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

Project tasks with uncertain durations (optimistic, likely, pessimistic) in days: - Design: (3, 5, 7) - Development: (4, 5, 7) - Testing: (3, 5, 6) - Deployment: (4, 5, 7) 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: (3 + 4×5 + 7)/6 = 5.0
- Development: (4 + 4×5 + 7)/6 = 5.2
- Testing: (3 + 4×5 + 6)/6 = 4.8
- Deployment: (4 + 4×5 + 7)/6 = 5.2

2. Total expected duration: 20.2 days

Answer: 20.2 days

fuzzy, uncertainty, duration, advanced, real-world

Question 17

A clinic operates for 4 hours with 20-minute appointment slots. If 12 patients need appointments, how many can be accommodated?

Step-by-step solution:

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

Answer: All 12 patients can be scheduled

clinic, appointment, doctor, healthcare, wait-time

Question 18

Four employees need to be scheduled for three shifts over three days. The constraints are: - Each employee works exactly one shift per day - No employee works the same shift two days in a row - Alice works Morning shift on Monday - Bob cannot work Night shift - Charlie works Evening shift on Tuesday Who works the Evening shift on Wednesday?

Step-by-step solution:

Table Method with Constraint Elimination:
1. Create a 3D table: Days x Shifts x Employees

2. Apply direct constraints:
- Monday Morning: Alice (fixed)
- Tuesday Evening: Charlie (fixed)
- Bob: Never Night shift (all days)

3. Apply rotation constraint:
- Alice (Morning Mon) cannot be Morning Tue
- Charlie (Evening Tue) cannot be Evening Wed

4. Fill Monday:
- Morning: Alice
- Evening: Charlie (can work evening)
- Night: Diana (Bob can't do night)

5. Fill Tuesday:
- Morning: Bob (Alice can't repeat, Charlie is evening)
- Evening: Charlie (fixed)
- Night: Diana (Bob can't)

6. Fill Wednesday:
- Charlie can't be Evening (was Evening Tue)
- Alice can be Evening (was Morning Mon, okay to shift)
- Answer: Alice works Evening on Wednesday

Key Strategy: Apply fixed constraints first, then use rotation rules to eliminate impossible assignments systematically.

shift-rotation, multi-person, constraints, professional

Question 19

A bus route takes 58 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: 58 × 2 = 116 minutes
2. Headway: 12 minutes
3. Buses needed: ⌈116 ÷ 12⌉ = 10

Answer: 10 buses

bus, timetable, frequency, public-transport, optimization

Question 20

Given these scheduling constraints: - Task C must be before Task A - Task B must be after Task A - Task D must be immediately after Task C 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

Scheduling - Intermediate-Advanced Level: appointment logic INTERMEDIATE-ADVANCED

What you'll learn in this worksheet:

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20