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Resource-Constrained Scheduling Beginner-Intermediate Worksheet: Focus on common variations practice Resource-Constrained Scheduling BEGINNER INTERMEDIATE

Level up your Resource-Constrained Scheduling skills! You're at Worksheet 4 of 10 (33% through this series). This step-up challenge worksheet features 20 beginner-intermediate-level problems with a focus on common variations practice. Topics covered: resource-constrained scheduling for competitive exams, how to solve resource-constrained scheduling, resource-constrained scheduling tricks.

📝 Worksheet 4 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner Intermediate level

What you'll learn in this worksheet:
Your progress through Resource-Constrained Scheduling
Worksheet 4 of 10 (33% complete)

Question 1

A project has 5 tasks with the following requirements: - T1: Duration 3 days, Requires 2 resources - T2: Duration 4 days, Requires 3 resources - T3: Duration 3 days, Requires 3 resources - T4: Duration 5 days, Requires 2 resources - T5: Duration 5 days, Requires 2 resources Maximum 4 resources are available at any time. What is the minimum project completion time?
Step-by-step solution:

Resource-Constrained Scheduling:
1. List all tasks with resource requirements:
- T1: 3 days, 2 resources
- T2: 4 days, 3 resources
- T3: 3 days, 3 resources
- T4: 5 days, 2 resources
- T5: 5 days, 2 resources

2. Available resources: 4 per day

4. Optimal schedule:
Days 0-4: T2 (3 resources)
Days 4-7: T3 (3 resources)
Days 7-10: T1 (2 resources)
Days 7-12: T4 (2 resources)
Days 10-15: T5 (2 resources)

5. Total time: 15 days

Key Strategy: Identify task combinations that fit within resource limits.

Question 2

A project has 7 tasks with the following requirements: - T1: Duration 3 days, Requires 1 resources - T2: Duration 2 days, Requires 3 resources - T3: Duration 3 days, Requires 2 resources - T4: Duration 2 days, Requires 1 resources - T5: Duration 2 days, Requires 1 resources - T6: Duration 4 days, Requires 2 resources - T7: Duration 2 days, Requires 1 resources Maximum 5 resources are available at any time. What is the minimum project completion time?
Step-by-step solution:

Resource-Constrained Scheduling:
1. List all tasks with resource requirements:
- T1: 3 days, 1 resources
- T2: 2 days, 3 resources
- T3: 3 days, 2 resources
- T4: 2 days, 1 resources
- T5: 2 days, 1 resources
- T6: 4 days, 2 resources
- T7: 2 days, 1 resources

2. Available resources: 5 per day

4. Optimal schedule:
Days 0-2: T2 (3 resources)
Days 0-3: T3 (2 resources)
Days 2-6: T6 (2 resources)
Days 2-5: T1 (1 resources)
Days 2-4: T4 (1 resources)
Days 2-4: T5 (1 resources)
Days 4-6: T7 (1 resources)

5. Total time: 6 days

Key Strategy: Identify task combinations that fit within resource limits.

Question 3

A project has 6 tasks with the following requirements: - T1: Duration 5 days, Requires 3 resources - T2: Duration 3 days, Requires 2 resources - T3: Duration 2 days, Requires 3 resources - T4: Duration 2 days, Requires 3 resources - T5: Duration 4 days, Requires 3 resources - T6: Duration 5 days, Requires 3 resources Maximum 4 resources are available at any time. What is the minimum project completion time?
Step-by-step solution:

Resource-Constrained Scheduling:
1. List all tasks with resource requirements:
- T1: 5 days, 3 resources
- T2: 3 days, 2 resources
- T3: 2 days, 3 resources
- T4: 2 days, 3 resources
- T5: 4 days, 3 resources
- T6: 5 days, 3 resources

2. Available resources: 4 per day

4. Optimal schedule:
Days 0-5: T1 (3 resources)
Days 5-7: T3 (3 resources)
Days 7-9: T4 (3 resources)
Days 9-13: T5 (3 resources)
Days 13-18: T6 (3 resources)
Days 18-21: T2 (2 resources)

5. Total time: 21 days

Key Strategy: Identify task combinations that fit within resource limits.

Question 4

A project has 5 tasks with the following requirements: - T1: Duration 4 days, Requires 2 resources - T2: Duration 3 days, Requires 1 resources - T3: Duration 5 days, Requires 2 resources - T4: Duration 5 days, Requires 3 resources - T5: Duration 5 days, Requires 3 resources Dependencies: - T1 must be completed before T2 - T3 must be completed before T4 Maximum 4 resources are available at any time. What is the minimum project completion time?
Step-by-step solution:

Resource-Constrained Scheduling:
1. List all tasks with resource requirements:
- T1: 4 days, 2 resources
- T2: 3 days, 1 resources
- T3: 5 days, 2 resources
- T4: 5 days, 3 resources
- T5: 5 days, 3 resources

2. Available resources: 4 per day

3. Dependencies considered

4. Optimal schedule:
Days 0-5: T5 (3 resources)
Days 5-9: T1 (2 resources)
Days 5-10: T3 (2 resources)
Days 9-12: T2 (1 resources)

5. Total time: 12 days

Key Strategy: Identify task combinations that fit within resource limits.

Question 5

A project has 7 tasks with the following requirements: - T1: Duration 4 days, Requires 3 resources - T2: Duration 2 days, Requires 2 resources - T3: Duration 3 days, Requires 3 resources - T4: Duration 2 days, Requires 3 resources - T5: Duration 4 days, Requires 1 resources - T6: Duration 2 days, Requires 2 resources - T7: Duration 5 days, Requires 1 resources Dependencies: - T4 must be completed before T5 Maximum 4 resources are available at any time. What is the minimum project completion time?
Step-by-step solution:

Resource-Constrained Scheduling:
1. List all tasks with resource requirements:
- T1: 4 days, 3 resources
- T2: 2 days, 2 resources
- T3: 3 days, 3 resources
- T4: 2 days, 3 resources
- T5: 4 days, 1 resources
- T6: 2 days, 2 resources
- T7: 5 days, 1 resources

2. Available resources: 4 per day

3. Dependencies considered

4. Optimal schedule:
Days 0-4: T1 (3 resources)
Days 0-5: T7 (1 resources)
Days 4-7: T3 (3 resources)
Days 7-9: T4 (3 resources)
Days 9-11: T2 (2 resources)
Days 9-11: T6 (2 resources)
Days 11-15: T5 (1 resources)

5. Total time: 15 days

Key Strategy: Identify task combinations that fit within resource limits.

Question 6

A project has 5 tasks with the following requirements: - T1: Duration 5 days, Requires 1 resources - T2: Duration 2 days, Requires 2 resources - T3: Duration 4 days, Requires 2 resources - T4: Duration 2 days, Requires 2 resources - T5: Duration 4 days, Requires 2 resources Dependencies: - T2 must be completed before T3 Maximum 6 resources are available at any time. What is the minimum project completion time?
Step-by-step solution:

Resource-Constrained Scheduling:
1. List all tasks with resource requirements:
- T1: 5 days, 1 resources
- T2: 2 days, 2 resources
- T3: 4 days, 2 resources
- T4: 2 days, 2 resources
- T5: 4 days, 2 resources

2. Available resources: 6 per day

3. Dependencies considered

4. Optimal schedule:
Days 0-2: T2 (2 resources)
Days 0-2: T4 (2 resources)
Days 0-4: T5 (2 resources)
Days 2-6: T3 (2 resources)
Days 2-7: T1 (1 resources)

5. Total time: 6 days

Key Strategy: Identify task combinations that fit within resource limits.

Question 7

A project has 6 tasks with the following requirements: - T1: Duration 4 days, Requires 3 resources - T2: Duration 2 days, Requires 1 resources - T3: Duration 4 days, Requires 2 resources - T4: Duration 2 days, Requires 2 resources - T5: Duration 3 days, Requires 1 resources - T6: Duration 4 days, Requires 2 resources Dependencies: - T2 must be completed before T3 - T5 must be completed before T6 Maximum 6 resources are available at any time. What is the minimum project completion time?
Step-by-step solution:

Resource-Constrained Scheduling:
1. List all tasks with resource requirements:
- T1: 4 days, 3 resources
- T2: 2 days, 1 resources
- T3: 4 days, 2 resources
- T4: 2 days, 2 resources
- T5: 3 days, 1 resources
- T6: 4 days, 2 resources

2. Available resources: 6 per day

3. Dependencies considered

4. Optimal schedule:
Days 0-4: T1 (3 resources)
Days 0-2: T4 (2 resources)
Days 0-2: T2 (1 resources)
Days 2-6: T3 (2 resources)
Days 2-5: T5 (1 resources)
Days 5-9: T6 (2 resources)

5. Total time: 9 days

Key Strategy: Identify task combinations that fit within resource limits.

Question 8

A project has 7 tasks with the following requirements: - T1: Duration 3 days, Requires 2 resources - T2: Duration 5 days, Requires 2 resources - T3: Duration 2 days, Requires 2 resources - T4: Duration 3 days, Requires 3 resources - T5: Duration 5 days, Requires 1 resources - T6: Duration 2 days, Requires 2 resources - T7: Duration 5 days, Requires 1 resources Dependencies: - T1 must be completed before T2 Maximum 4 resources are available at any time. What is the minimum project completion time?
Step-by-step solution:

Resource-Constrained Scheduling:
1. List all tasks with resource requirements:
- T1: 3 days, 2 resources
- T2: 5 days, 2 resources
- T3: 2 days, 2 resources
- T4: 3 days, 3 resources
- T5: 5 days, 1 resources
- T6: 2 days, 2 resources
- T7: 5 days, 1 resources

2. Available resources: 4 per day

3. Dependencies considered

4. Optimal schedule:
Days 0-3: T4 (3 resources)
Days 0-5: T5 (1 resources)
Days 3-6: T1 (2 resources)
Days 3-5: T3 (2 resources)
Days 5-7: T6 (2 resources)
Days 5-10: T7 (1 resources)

5. Total time: 7 days

Key Strategy: Identify task combinations that fit within resource limits.

Question 9

A project has 6 tasks with the following requirements: - T1: Duration 5 days, Requires 1 resources - T2: Duration 4 days, Requires 3 resources - T3: Duration 4 days, Requires 2 resources - T4: Duration 5 days, Requires 3 resources - T5: Duration 5 days, Requires 3 resources - T6: Duration 5 days, Requires 3 resources Dependencies: - T3 must be completed before T4 - T5 must be completed before T6 Maximum 4 resources are available at any time. What is the minimum project completion time?
Step-by-step solution:

Resource-Constrained Scheduling:
1. List all tasks with resource requirements:
- T1: 5 days, 1 resources
- T2: 4 days, 3 resources
- T3: 4 days, 2 resources
- T4: 5 days, 3 resources
- T5: 5 days, 3 resources
- T6: 5 days, 3 resources

2. Available resources: 4 per day

3. Dependencies considered

4. Optimal schedule:
Days 0-4: T2 (3 resources)
Days 0-5: T1 (1 resources)
Days 4-9: T5 (3 resources)
Days 9-14: T6 (3 resources)
Days 14-18: T3 (2 resources)
Days 18-23: T4 (3 resources)

5. Total time: 23 days

Key Strategy: Identify task combinations that fit within resource limits.

Question 10

A project has 7 tasks with the following requirements: - T1: Duration 2 days, Requires 1 resources - T2: Duration 2 days, Requires 2 resources - T3: Duration 2 days, Requires 1 resources - T4: Duration 4 days, Requires 1 resources - T5: Duration 2 days, Requires 2 resources - T6: Duration 4 days, Requires 1 resources - T7: Duration 4 days, Requires 1 resources Dependencies: - T1 must be completed before T2 - T3 must be completed before T4 Maximum 6 resources are available at any time. What is the minimum project completion time?
Step-by-step solution:

Resource-Constrained Scheduling:
1. List all tasks with resource requirements:
- T1: 2 days, 1 resources
- T2: 2 days, 2 resources
- T3: 2 days, 1 resources
- T4: 4 days, 1 resources
- T5: 2 days, 2 resources
- T6: 4 days, 1 resources
- T7: 4 days, 1 resources

2. Available resources: 6 per day

3. Dependencies considered

4. Optimal schedule:
Days 0-2: T5 (2 resources)
Days 0-2: T1 (1 resources)
Days 0-2: T3 (1 resources)
Days 0-4: T6 (1 resources)
Days 0-4: T7 (1 resources)
Days 2-4: T2 (2 resources)
Days 2-6: T4 (1 resources)

5. Total time: 4 days

Key Strategy: Identify task combinations that fit within resource limits.

Question 11

A project has 7 tasks with the following requirements: - T1: Duration 2 days, Requires 1 resources - T2: Duration 4 days, Requires 1 resources - T3: Duration 5 days, Requires 3 resources - T4: Duration 3 days, Requires 2 resources - T5: Duration 2 days, Requires 1 resources - T6: Duration 2 days, Requires 2 resources - T7: Duration 2 days, Requires 1 resources Dependencies: - T3 must be completed before T4 Maximum 6 resources are available at any time. What is the minimum project completion time?
Step-by-step solution:

Resource-Constrained Scheduling:
1. List all tasks with resource requirements:
- T1: 2 days, 1 resources
- T2: 4 days, 1 resources
- T3: 5 days, 3 resources
- T4: 3 days, 2 resources
- T5: 2 days, 1 resources
- T6: 2 days, 2 resources
- T7: 2 days, 1 resources

2. Available resources: 6 per day

3. Dependencies considered

4. Optimal schedule:
Days 0-5: T3 (3 resources)
Days 0-2: T6 (2 resources)
Days 0-2: T1 (1 resources)
Days 2-6: T2 (1 resources)
Days 2-4: T5 (1 resources)
Days 2-4: T7 (1 resources)

5. Total time: 4 days

Key Strategy: Identify task combinations that fit within resource limits.

Question 12

A project has 6 tasks with the following requirements: - T1: Duration 3 days, Requires 2 resources - T2: Duration 4 days, Requires 3 resources - T3: Duration 2 days, Requires 1 resources - T4: Duration 3 days, Requires 3 resources - T5: Duration 2 days, Requires 1 resources - T6: Duration 3 days, Requires 3 resources Maximum 4 resources are available at any time. What is the minimum project completion time?
Step-by-step solution:

Resource-Constrained Scheduling:
1. List all tasks with resource requirements:
- T1: 3 days, 2 resources
- T2: 4 days, 3 resources
- T3: 2 days, 1 resources
- T4: 3 days, 3 resources
- T5: 2 days, 1 resources
- T6: 3 days, 3 resources

2. Available resources: 4 per day

4. Optimal schedule:
Days 0-4: T2 (3 resources)
Days 0-2: T3 (1 resources)
Days 2-5: T4 (3 resources)
Days 2-4: T5 (1 resources)
Days 4-7: T6 (3 resources)
Days 7-10: T1 (2 resources)

5. Total time: 10 days

Key Strategy: Identify task combinations that fit within resource limits.

Question 13

A project has 6 tasks with the following requirements: - T1: Duration 5 days, Requires 2 resources - T2: Duration 3 days, Requires 2 resources - T3: Duration 4 days, Requires 1 resources - T4: Duration 5 days, Requires 1 resources - T5: Duration 5 days, Requires 2 resources - T6: Duration 2 days, Requires 3 resources Dependencies: - T3 must be completed before T4 - T4 must be completed before T5 Maximum 5 resources are available at any time. What is the minimum project completion time?
Step-by-step solution:

Resource-Constrained Scheduling:
1. List all tasks with resource requirements:
- T1: 5 days, 2 resources
- T2: 3 days, 2 resources
- T3: 4 days, 1 resources
- T4: 5 days, 1 resources
- T5: 5 days, 2 resources
- T6: 2 days, 3 resources

2. Available resources: 5 per day

3. Dependencies considered

4. Optimal schedule:
Days 0-2: T6 (3 resources)
Days 0-5: T1 (2 resources)
Days 2-5: T2 (2 resources)
Days 2-6: T3 (1 resources)

5. Total time: 5 days

Key Strategy: Identify task combinations that fit within resource limits.

Question 14

A project has 6 tasks with the following requirements: - T1: Duration 2 days, Requires 1 resources - T2: Duration 5 days, Requires 3 resources - T3: Duration 3 days, Requires 1 resources - T4: Duration 4 days, Requires 3 resources - T5: Duration 5 days, Requires 3 resources - T6: Duration 4 days, Requires 2 resources Dependencies: - T3 must be completed before T4 - T5 must be completed before T6 Maximum 6 resources are available at any time. What is the minimum project completion time?
Step-by-step solution:

Resource-Constrained Scheduling:
1. List all tasks with resource requirements:
- T1: 2 days, 1 resources
- T2: 5 days, 3 resources
- T3: 3 days, 1 resources
- T4: 4 days, 3 resources
- T5: 5 days, 3 resources
- T6: 4 days, 2 resources

2. Available resources: 6 per day

3. Dependencies considered

4. Optimal schedule:
Days 0-5: T2 (3 resources)
Days 0-5: T5 (3 resources)
Days 5-9: T6 (2 resources)
Days 5-7: T1 (1 resources)
Days 5-8: T3 (1 resources)

5. Total time: 7 days

Key Strategy: Identify task combinations that fit within resource limits.

Question 15

A project has 5 tasks with the following requirements: - T1: Duration 4 days, Requires 3 resources - T2: Duration 3 days, Requires 1 resources - T3: Duration 3 days, Requires 2 resources - T4: Duration 3 days, Requires 2 resources - T5: Duration 4 days, Requires 1 resources Dependencies: - T2 must be completed before T3 Maximum 4 resources are available at any time. What is the minimum project completion time?
Step-by-step solution:

Resource-Constrained Scheduling:
1. List all tasks with resource requirements:
- T1: 4 days, 3 resources
- T2: 3 days, 1 resources
- T3: 3 days, 2 resources
- T4: 3 days, 2 resources
- T5: 4 days, 1 resources

2. Available resources: 4 per day

3. Dependencies considered

4. Optimal schedule:
Days 0-4: T1 (3 resources)
Days 0-3: T2 (1 resources)
Days 3-6: T3 (2 resources)
Days 3-6: T4 (2 resources)
Days 6-10: T5 (1 resources)

5. Total time: 10 days

Key Strategy: Identify task combinations that fit within resource limits.

Question 16

A project has 6 tasks with the following requirements: - T1: Duration 2 days, Requires 1 resources - T2: Duration 4 days, Requires 3 resources - T3: Duration 3 days, Requires 3 resources - T4: Duration 3 days, Requires 2 resources - T5: Duration 3 days, Requires 3 resources - T6: Duration 2 days, Requires 2 resources Dependencies: - T1 must be completed before T2 - T2 must be completed before T3 Maximum 5 resources are available at any time. What is the minimum project completion time?
Step-by-step solution:

Resource-Constrained Scheduling:
1. List all tasks with resource requirements:
- T1: 2 days, 1 resources
- T2: 4 days, 3 resources
- T3: 3 days, 3 resources
- T4: 3 days, 2 resources
- T5: 3 days, 3 resources
- T6: 2 days, 2 resources

2. Available resources: 5 per day

3. Dependencies considered

4. Optimal schedule:
Days 0-3: T5 (3 resources)
Days 0-3: T4 (2 resources)
Days 3-5: T6 (2 resources)
Days 3-5: T1 (1 resources)
Days 5-9: T2 (3 resources)
Days 9-12: T3 (3 resources)

5. Total time: 12 days

Key Strategy: Identify task combinations that fit within resource limits.

Question 17

A project has 5 tasks with the following requirements: - T1: Duration 3 days, Requires 1 resources - T2: Duration 2 days, Requires 1 resources - T3: Duration 5 days, Requires 3 resources - T4: Duration 3 days, Requires 1 resources - T5: Duration 5 days, Requires 1 resources Dependencies: - T4 must be completed before T5 Maximum 5 resources are available at any time. What is the minimum project completion time?
Step-by-step solution:

Resource-Constrained Scheduling:
1. List all tasks with resource requirements:
- T1: 3 days, 1 resources
- T2: 2 days, 1 resources
- T3: 5 days, 3 resources
- T4: 3 days, 1 resources
- T5: 5 days, 1 resources

2. Available resources: 5 per day

3. Dependencies considered

4. Optimal schedule:
Days 0-5: T3 (3 resources)
Days 0-3: T1 (1 resources)
Days 0-2: T2 (1 resources)
Days 2-5: T4 (1 resources)
Days 5-10: T5 (1 resources)

5. Total time: 10 days

Key Strategy: Identify task combinations that fit within resource limits.

Question 18

A project has 6 tasks with the following requirements: - T1: Duration 4 days, Requires 1 resources - T2: Duration 5 days, Requires 2 resources - T3: Duration 2 days, Requires 3 resources - T4: Duration 3 days, Requires 3 resources - T5: Duration 4 days, Requires 1 resources - T6: Duration 5 days, Requires 3 resources Maximum 4 resources are available at any time. What is the minimum project completion time?
Step-by-step solution:

Resource-Constrained Scheduling:
1. List all tasks with resource requirements:
- T1: 4 days, 1 resources
- T2: 5 days, 2 resources
- T3: 2 days, 3 resources
- T4: 3 days, 3 resources
- T5: 4 days, 1 resources
- T6: 5 days, 3 resources

2. Available resources: 4 per day

4. Optimal schedule:
Days 0-2: T3 (3 resources)
Days 0-4: T1 (1 resources)
Days 2-5: T4 (3 resources)
Days 2-6: T5 (1 resources)
Days 5-10: T6 (3 resources)
Days 10-15: T2 (2 resources)

5. Total time: 15 days

Key Strategy: Identify task combinations that fit within resource limits.

Question 19

A project has 6 tasks with the following requirements: - T1: Duration 4 days, Requires 2 resources - T2: Duration 3 days, Requires 1 resources - T3: Duration 2 days, Requires 1 resources - T4: Duration 3 days, Requires 2 resources - T5: Duration 4 days, Requires 2 resources - T6: Duration 3 days, Requires 3 resources Dependencies: - T2 must be completed before T3 - T5 must be completed before T6 Maximum 5 resources are available at any time. What is the minimum project completion time?
Step-by-step solution:

Resource-Constrained Scheduling:
1. List all tasks with resource requirements:
- T1: 4 days, 2 resources
- T2: 3 days, 1 resources
- T3: 2 days, 1 resources
- T4: 3 days, 2 resources
- T5: 4 days, 2 resources
- T6: 3 days, 3 resources

2. Available resources: 5 per day

3. Dependencies considered

4. Optimal schedule:
Days 0-4: T1 (2 resources)
Days 0-3: T4 (2 resources)
Days 0-3: T2 (1 resources)
Days 3-7: T5 (2 resources)
Days 3-5: T3 (1 resources)

5. Total time: 5 days

Key Strategy: Identify task combinations that fit within resource limits.

Question 20

A project has 7 tasks with the following requirements: - T1: Duration 2 days, Requires 1 resources - T2: Duration 2 days, Requires 3 resources - T3: Duration 5 days, Requires 2 resources - T4: Duration 2 days, Requires 1 resources - T5: Duration 2 days, Requires 1 resources - T6: Duration 5 days, Requires 2 resources - T7: Duration 4 days, Requires 2 resources Dependencies: - T1 must be completed before T2 - T2 must be completed before T3 Maximum 4 resources are available at any time. What is the minimum project completion time?
Step-by-step solution:

Resource-Constrained Scheduling:
1. List all tasks with resource requirements:
- T1: 2 days, 1 resources
- T2: 2 days, 3 resources
- T3: 5 days, 2 resources
- T4: 2 days, 1 resources
- T5: 2 days, 1 resources
- T6: 5 days, 2 resources
- T7: 4 days, 2 resources

2. Available resources: 4 per day

3. Dependencies considered

4. Optimal schedule:
Days 0-5: T6 (2 resources)
Days 0-4: T7 (2 resources)
Days 4-6: T1 (1 resources)
Days 4-6: T4 (1 resources)
Days 4-6: T5 (1 resources)
Days 6-8: T2 (3 resources)
Days 8-13: T3 (2 resources)

5. Total time: 13 days

Key Strategy: Identify task combinations that fit within resource limits.
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