Resource-Constrained Scheduling | Worksheet 3/10

Question 1

A project has 6 tasks with the following requirements: - T1: Duration 4 days, Requires 3 resources - T2: Duration 5 days, Requires 1 resources - T3: Duration 2 days, Requires 3 resources - T4: Duration 2 days, Requires 2 resources - T5: Duration 5 days, Requires 3 resources - T6: Duration 3 days, Requires 2 resources Dependencies: - T2 must be completed before T3 - T4 must be completed before T5 - 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, 3 resources
- T2: 5 days, 1 resources
- T3: 2 days, 3 resources
- T4: 2 days, 2 resources
- T5: 5 days, 3 resources
- T6: 3 days, 2 resources

2. Available resources: 5 per day

3. Dependencies considered

4. Optimal schedule:
Days 0-4: T1 (3 resources)
Days 0-2: T4 (2 resources)
Days 2-7: T5 (3 resources)
Days 2-7: T2 (1 resources)
Days 7-9: T3 (3 resources)
Days 7-10: T6 (2 resources)

5. Total time: 9 days

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

Question 2

A project has 6 tasks with the following requirements: - T1: Duration 5 days, Requires 1 resources - T2: Duration 2 days, Requires 2 resources - T3: Duration 3 days, Requires 1 resources - T4: Duration 4 days, Requires 3 resources - T5: Duration 2 days, Requires 2 resources - T6: Duration 4 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: 2 days, 2 resources
- T3: 3 days, 1 resources
- T4: 4 days, 3 resources
- T5: 2 days, 2 resources
- T6: 4 days, 3 resources

2. Available resources: 4 per day

3. Dependencies considered

4. Optimal schedule:
Days 0-2: T2 (2 resources)
Days 0-2: T5 (2 resources)
Days 2-6: T6 (3 resources)
Days 2-7: T1 (1 resources)
Days 6-9: T3 (1 resources)
Days 9-13: T4 (3 resources)

5. Total time: 13 days

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

Question 3

A project has 5 tasks with the following requirements: - T1: Duration 3 days, Requires 1 resources - T2: Duration 3 days, Requires 2 resources - T3: Duration 4 days, Requires 2 resources - T4: Duration 4 days, Requires 1 resources - T5: Duration 2 days, Requires 2 resources Dependencies: - T3 must be completed before T4 - 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: 3 days, 1 resources
- T2: 3 days, 2 resources
- T3: 4 days, 2 resources
- T4: 4 days, 1 resources
- T5: 2 days, 2 resources

2. Available resources: 4 per day

3. Dependencies considered

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

5. Total time: 6 days

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

Question 4

A project has 6 tasks with the following requirements: - T1: Duration 2 days, Requires 3 resources - T2: Duration 5 days, Requires 2 resources - T3: Duration 5 days, Requires 2 resources - T4: Duration 5 days, Requires 1 resources - T5: Duration 3 days, Requires 2 resources - T6: Duration 5 days, Requires 3 resources Dependencies: - T3 must be completed before T4 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, 3 resources
- T2: 5 days, 2 resources
- T3: 5 days, 2 resources
- T4: 5 days, 1 resources
- T5: 3 days, 2 resources
- T6: 5 days, 3 resources

2. Available resources: 5 per day

3. Dependencies considered

4. Optimal schedule:
Days 0-2: T1 (3 resources)
Days 0-5: T2 (2 resources)
Days 2-7: T6 (3 resources)
Days 2-7: T3 (2 resources)
Days 7-10: T5 (2 resources)
Days 7-12: T4 (1 resources)

5. Total time: 10 days

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

Question 5

A project has 7 tasks with the following requirements: - T1: Duration 2 days, Requires 2 resources - T2: Duration 3 days, Requires 2 resources - T3: Duration 3 days, Requires 2 resources - T4: Duration 5 days, Requires 2 resources - T5: Duration 4 days, Requires 1 resources - T6: Duration 2 days, Requires 3 resources - T7: Duration 5 days, Requires 1 resources Dependencies: - T1 must be completed before T2 - T4 must be completed before T5 - T6 must be completed before T7 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, 2 resources
- T2: 3 days, 2 resources
- T3: 3 days, 2 resources
- T4: 5 days, 2 resources
- T5: 4 days, 1 resources
- T6: 2 days, 3 resources
- T7: 5 days, 1 resources

2. Available resources: 4 per day

3. Dependencies considered

4. Optimal schedule:
Days 0-2: T6 (3 resources)
Days 2-4: T1 (2 resources)
Days 2-5: T3 (2 resources)
Days 4-7: T2 (2 resources)
Days 4-9: T4 (2 resources)
Days 7-12: T7 (1 resources)

5. Total time: 12 days

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

Question 6

A project has 6 tasks with the following requirements: - T1: Duration 2 days, Requires 2 resources - T2: Duration 4 days, Requires 2 resources - T3: Duration 4 days, Requires 3 resources - T4: Duration 4 days, Requires 1 resources - T5: Duration 3 days, Requires 3 resources - T6: Duration 4 days, Requires 1 resources Dependencies: - T1 must be completed before T2 - T4 must be completed before T5 - 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, 2 resources
- T2: 4 days, 2 resources
- T3: 4 days, 3 resources
- T4: 4 days, 1 resources
- T5: 3 days, 3 resources
- T6: 4 days, 1 resources

2. Available resources: 6 per day

3. Dependencies considered

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

5. Total time: 6 days

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

Question 7

A project has 7 tasks with the following requirements: - T1: Duration 4 days, Requires 1 resources - T2: Duration 4 days, Requires 2 resources - T3: Duration 2 days, Requires 2 resources - T4: Duration 5 days, Requires 2 resources - T5: Duration 5 days, Requires 1 resources - T6: Duration 3 days, Requires 1 resources - T7: Duration 5 days, Requires 3 resources Dependencies: - T1 must be completed before T2 - T2 must be completed before T3 - T3 must be completed before T4 - T6 must be completed before T7 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, 1 resources
- T2: 4 days, 2 resources
- T3: 2 days, 2 resources
- T4: 5 days, 2 resources
- T5: 5 days, 1 resources
- T6: 3 days, 1 resources
- T7: 5 days, 3 resources

2. Available resources: 5 per day

3. Dependencies considered

4. Optimal schedule:
Days 0-4: T1 (1 resources)
Days 0-5: T5 (1 resources)
Days 0-3: T6 (1 resources)
Days 3-8: T7 (3 resources)

5. Total time: 8 days

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

Question 8

A project has 5 tasks with the following requirements: - T1: Duration 2 days, Requires 3 resources - T2: Duration 3 days, Requires 1 resources - T3: Duration 4 days, Requires 1 resources - T4: Duration 4 days, Requires 2 resources - T5: Duration 4 days, Requires 1 resources Dependencies: - T1 must be completed before T2 - T3 must be completed before T4 - T4 must be completed before T5 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, 3 resources
- T2: 3 days, 1 resources
- T3: 4 days, 1 resources
- T4: 4 days, 2 resources
- T5: 4 days, 1 resources

2. Available resources: 6 per day

3. Dependencies considered

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

5. Total time: 5 days

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

Question 9

A project has 6 tasks with the following requirements: - T1: Duration 4 days, Requires 1 resources - T2: Duration 2 days, Requires 1 resources - T3: Duration 5 days, Requires 2 resources - T4: Duration 3 days, Requires 2 resources - T5: Duration 2 days, Requires 2 resources - T6: Duration 2 days, Requires 3 resources 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, 1 resources
- T2: 2 days, 1 resources
- T3: 5 days, 2 resources
- T4: 3 days, 2 resources
- T5: 2 days, 2 resources
- T6: 2 days, 3 resources

2. Available resources: 6 per day

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

5. Total time: 4 days

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

Question 10

A project has 6 tasks with the following requirements: - T1: Duration 4 days, Requires 2 resources - T2: Duration 4 days, Requires 2 resources - T3: Duration 4 days, Requires 1 resources - T4: Duration 2 days, Requires 2 resources - T5: Duration 4 days, Requires 1 resources - T6: 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: 4 days, 2 resources
- T2: 4 days, 2 resources
- T3: 4 days, 1 resources
- T4: 2 days, 2 resources
- T5: 4 days, 1 resources
- T6: 2 days, 1 resources

2. Available resources: 5 per day

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

5. Total time: 6 days

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

Question 11

A project has 5 tasks with the following requirements: - T1: Duration 4 days, Requires 2 resources - T2: Duration 3 days, Requires 2 resources - T3: Duration 3 days, Requires 1 resources - T4: Duration 5 days, Requires 1 resources - T5: Duration 5 days, Requires 3 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, 2 resources
- T2: 3 days, 2 resources
- T3: 3 days, 1 resources
- T4: 5 days, 1 resources
- T5: 5 days, 3 resources

2. Available resources: 4 per day

3. Dependencies considered

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

5. Total time: 6 days

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

Question 12

A project has 6 tasks with the following requirements: - T1: Duration 4 days, Requires 1 resources - T2: Duration 3 days, Requires 2 resources - T3: Duration 4 days, Requires 2 resources - T4: Duration 2 days, Requires 1 resources - T5: Duration 4 days, Requires 1 resources - T6: Duration 4 days, Requires 3 resources Dependencies: - T2 must be completed before T3 - T3 must be completed before T4 - T4 must be completed before T5 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, 1 resources
- T2: 3 days, 2 resources
- T3: 4 days, 2 resources
- T4: 2 days, 1 resources
- T5: 4 days, 1 resources
- T6: 4 days, 3 resources

2. Available resources: 6 per day

3. Dependencies considered

4. Optimal schedule:
Days 0-4: T6 (3 resources)
Days 0-3: T2 (2 resources)
Days 0-4: T1 (1 resources)
Days 3-7: T3 (2 resources)
Days 7-9: T4 (1 resources)
Days 9-13: T5 (1 resources)

5. Total time: 13 days

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

Question 13

A project has 7 tasks with the following requirements: - T1: Duration 2 days, Requires 3 resources - T2: Duration 3 days, Requires 2 resources - T3: Duration 4 days, Requires 1 resources - T4: Duration 2 days, Requires 2 resources - T5: Duration 4 days, Requires 1 resources - T6: Duration 4 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 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, 3 resources
- T2: 3 days, 2 resources
- T3: 4 days, 1 resources
- T4: 2 days, 2 resources
- T5: 4 days, 1 resources
- T6: 4 days, 2 resources
- T7: 4 days, 2 resources

2. Available resources: 6 per day

3. Dependencies considered

4. Optimal schedule:
Days 0-2: T1 (3 resources)
Days 0-2: T4 (2 resources)
Days 0-4: T5 (1 resources)
Days 2-5: T2 (2 resources)
Days 2-6: T6 (2 resources)
Days 2-6: T7 (2 resources)
Days 5-9: T3 (1 resources)

5. Total time: 9 days

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

Question 14

A project has 7 tasks with the following requirements: - T1: Duration 4 days, Requires 3 resources - T2: Duration 4 days, Requires 3 resources - T3: Duration 2 days, Requires 3 resources - T4: Duration 3 days, Requires 2 resources - T5: Duration 3 days, Requires 2 resources - T6: Duration 3 days, Requires 1 resources - T7: Duration 5 days, Requires 3 resources Dependencies: - T2 must be completed before T3 - T5 must be completed before T6 - T6 must be completed before T7 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: 4 days, 3 resources
- T3: 2 days, 3 resources
- T4: 3 days, 2 resources
- T5: 3 days, 2 resources
- T6: 3 days, 1 resources
- T7: 5 days, 3 resources

2. Available resources: 6 per day

3. Dependencies considered

4. Optimal schedule:
Days 0-4: T1 (3 resources)
Days 0-4: T2 (3 resources)
Days 4-6: T3 (3 resources)
Days 4-7: T4 (2 resources)
Days 6-9: T5 (2 resources)
Days 9-12: T6 (1 resources)
Days 12-17: T7 (3 resources)

5. Total time: 17 days

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

Question 15

A project has 6 tasks with the following requirements: - T1: Duration 3 days, Requires 2 resources - T2: Duration 2 days, Requires 2 resources - T3: Duration 5 days, Requires 1 resources - T4: Duration 3 days, Requires 3 resources - T5: Duration 4 days, Requires 3 resources - T6: Duration 3 days, Requires 3 resources Dependencies: - T4 must be completed before T5 - 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: 3 days, 2 resources
- T2: 2 days, 2 resources
- T3: 5 days, 1 resources
- T4: 3 days, 3 resources
- T5: 4 days, 3 resources
- T6: 3 days, 3 resources

2. Available resources: 4 per day

3. Dependencies considered

4. Optimal schedule:
Days 0-3: T4 (3 resources)
Days 0-5: T3 (1 resources)
Days 3-7: T5 (3 resources)
Days 7-10: T6 (3 resources)
Days 10-13: T1 (2 resources)
Days 10-12: T2 (2 resources)

5. Total time: 12 days

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

Question 16

A project has 6 tasks with the following requirements: - T1: Duration 5 days, Requires 3 resources - T2: Duration 2 days, Requires 1 resources - T3: Duration 5 days, Requires 2 resources - T4: Duration 5 days, Requires 2 resources - T5: Duration 5 days, Requires 1 resources - T6: Duration 2 days, Requires 3 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: 5 days, 3 resources
- T2: 2 days, 1 resources
- T3: 5 days, 2 resources
- T4: 5 days, 2 resources
- T5: 5 days, 1 resources
- T6: 2 days, 3 resources

2. Available resources: 5 per day

4. Optimal schedule:
Days 0-5: T1 (3 resources)
Days 0-5: T3 (2 resources)
Days 5-7: T6 (3 resources)
Days 5-10: T4 (2 resources)
Days 7-9: T2 (1 resources)
Days 7-12: T5 (1 resources)

5. Total time: 9 days

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

Question 17

A project has 6 tasks with the following requirements: - T1: Duration 3 days, Requires 1 resources - T2: Duration 4 days, Requires 2 resources - T3: Duration 5 days, Requires 1 resources - T4: Duration 3 days, Requires 3 resources - T5: Duration 3 days, Requires 1 resources - T6: Duration 5 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: 4 days, 2 resources
- T3: 5 days, 1 resources
- T4: 3 days, 3 resources
- T5: 3 days, 1 resources
- T6: 5 days, 1 resources

2. Available resources: 5 per day

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

5. Total time: 6 days

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

Question 18

A project has 5 tasks with the following requirements: - T1: Duration 5 days, Requires 3 resources - T2: Duration 4 days, Requires 1 resources - T3: Duration 3 days, Requires 1 resources - T4: Duration 3 days, Requires 2 resources - T5: Duration 4 days, Requires 3 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: 5 days, 3 resources
- T2: 4 days, 1 resources
- T3: 3 days, 1 resources
- T4: 3 days, 2 resources
- T5: 4 days, 3 resources

2. Available resources: 4 per day

3. Dependencies considered

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

5. Total time: 10 days

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

Question 19

A project has 6 tasks with the following requirements: - T1: Duration 2 days, Requires 1 resources - T2: Duration 4 days, Requires 1 resources - T3: Duration 5 days, Requires 1 resources - T4: Duration 2 days, Requires 3 resources - T5: Duration 5 days, Requires 3 resources - T6: Duration 2 days, Requires 3 resources Dependencies: - T1 must be completed before T2 - 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: 4 days, 1 resources
- T3: 5 days, 1 resources
- T4: 2 days, 3 resources
- T5: 5 days, 3 resources
- T6: 2 days, 3 resources

2. Available resources: 6 per day

3. Dependencies considered

4. Optimal schedule:
Days 0-2: T4 (3 resources)
Days 0-5: T5 (3 resources)
Days 2-4: T1 (1 resources)
Days 2-7: T3 (1 resources)
Days 4-8: T2 (1 resources)

5. Total time: 8 days

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

Question 20

A project has 5 tasks with the following requirements: - T1: Duration 5 days, Requires 1 resources - T2: Duration 5 days, Requires 2 resources - T3: Duration 4 days, Requires 1 resources - T4: Duration 4 days, Requires 3 resources - T5: Duration 3 days, Requires 3 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: 5 days, 1 resources
- T2: 5 days, 2 resources
- T3: 4 days, 1 resources
- T4: 4 days, 3 resources
- T5: 3 days, 3 resources

2. Available resources: 5 per day

4. Optimal schedule:
Days 0-4: T4 (3 resources)
Days 0-5: T2 (2 resources)
Days 4-7: T5 (3 resources)
Days 4-9: T1 (1 resources)
Days 4-8: T3 (1 resources)

5. Total time: 7 days

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

Master Resource-Constrained Scheduling - Beginner Level Problems Resource-Constrained Scheduling BEGINNER

What you'll learn in this worksheet: