Production Line Scheduling | Worksheet 7/10

Question 1

A production line needs to manufacture: - Product A: 1 units (each takes 1 hours) - Product C: 2 units (each takes 3 hours) - Product B: 3 units (each takes 4 hours) - Product D: 3 units (each takes 2 hours) Setup time required when switching products: - P->P: 3 hour What is the minimum total time if production starts with Product C?

Step-by-step solution:

Production Sequencing with Setup Times:
1. Calculate total production time (without setup):
- Product A: 1 x 1 = 1 hours
- Product C: 2 x 3 = 6 hours
- Product B: 3 x 4 = 12 hours
- Product D: 3 x 2 = 6 hours
- Base production time: 25 hours

2. Minimize setup time by batching:
- Optimal sequence: Product C -> Product C -> Product A -> Product B -> Product B -> Product B -> Product D -> Product D -> Product D
3. Total with setups:
- Product C: 3 hours
- Product C: 3 hours (no setup)
- Setup Product C→Product A: 3 hour + Product A: 1 hours
- Setup Product A→Product B: 3 hour + Product B: 4 hours
- Product B: 4 hours (no setup)
- Product B: 4 hours (no setup)
- Setup Product B→Product D: 3 hour + Product D: 2 hours
- Product D: 2 hours (no setup)
- Product D: 2 hours (no setup)

Total: 34 hours

Key Strategy: Batch identical products together to minimize setup changes.

Question 2

A production line needs to manufacture: - Product A: 2 units (each takes 3 hours) - Product B: 3 units (each takes 4 hours) - Product C: 2 units (each takes 4 hours) - Product D: 1 units (each takes 1 hours) Setup time required when switching products: - P->P: 2 hour What is the minimum total time if production starts with Product D?

Step-by-step solution:

Production Sequencing with Setup Times:
1. Calculate total production time (without setup):
- Product A: 2 x 3 = 6 hours
- Product B: 3 x 4 = 12 hours
- Product C: 2 x 4 = 8 hours
- Product D: 1 x 1 = 1 hours
- Base production time: 27 hours

2. Minimize setup time by batching:
- Optimal sequence: Product D -> Product A -> Product A -> Product B -> Product B -> Product B -> Product C -> Product C
3. Total with setups:
- Product D: 1 hours
- Setup Product D→Product A: 2 hour + Product A: 3 hours
- Product A: 3 hours (no setup)
- Setup Product A→Product B: 2 hour + Product B: 4 hours
- Product B: 4 hours (no setup)
- Product B: 4 hours (no setup)
- Setup Product B→Product C: 2 hour + Product C: 4 hours
- Product C: 4 hours (no setup)

Total: 33 hours

Key Strategy: Batch identical products together to minimize setup changes.

Question 3

A production line needs to manufacture: - Product B: 1 units (each takes 1 hours) - Product D: 2 units (each takes 4 hours) - Product C: 1 units (each takes 2 hours) Setup time required when switching products: - P->P: 1 hour What is the minimum total time if production starts with Product B?

Step-by-step solution:

Production Sequencing with Setup Times:
1. Calculate total production time (without setup):
- Product B: 1 x 1 = 1 hours
- Product D: 2 x 4 = 8 hours
- Product C: 1 x 2 = 2 hours
- Base production time: 11 hours

2. Minimize setup time by batching:
- Optimal sequence: Product B -> Product D -> Product D -> Product C
3. Total with setups:
- Product B: 1 hours
- Setup Product B→Product D: 1 hour + Product D: 4 hours
- Product D: 4 hours (no setup)
- Setup Product D→Product C: 1 hour + Product C: 2 hours

Total: 13 hours

Key Strategy: Batch identical products together to minimize setup changes.

Question 4

A production line needs to manufacture: - Product B: 2 units (each takes 1 hours) - Product A: 3 units (each takes 4 hours) - Product D: 2 units (each takes 2 hours) Setup time required when switching products: - P->P: 3 hour What is the minimum total time if production starts with Product D?

Step-by-step solution:

Production Sequencing with Setup Times:
1. Calculate total production time (without setup):
- Product B: 2 x 1 = 2 hours
- Product A: 3 x 4 = 12 hours
- Product D: 2 x 2 = 4 hours
- Base production time: 18 hours

2. Minimize setup time by batching:
- Optimal sequence: Product D -> Product D -> Product B -> Product B -> Product A -> Product A -> Product A
3. Total with setups:
- Product D: 2 hours
- Product D: 2 hours (no setup)
- Setup Product D→Product B: 3 hour + Product B: 1 hours
- Product B: 1 hours (no setup)
- Setup Product B→Product A: 3 hour + Product A: 4 hours
- Product A: 4 hours (no setup)
- Product A: 4 hours (no setup)

Total: 24 hours

Key Strategy: Batch identical products together to minimize setup changes.

Question 5

A production line needs to manufacture: - Product B: 3 units (each takes 2 hours) - Product A: 1 units (each takes 1 hours) - Product C: 2 units (each takes 4 hours) - Product D: 2 units (each takes 2 hours) Setup time required when switching products: - P->P: 3 hour What is the minimum total time if production starts with Product C?

Step-by-step solution:

Production Sequencing with Setup Times:
1. Calculate total production time (without setup):
- Product B: 3 x 2 = 6 hours
- Product A: 1 x 1 = 1 hours
- Product C: 2 x 4 = 8 hours
- Product D: 2 x 2 = 4 hours
- Base production time: 19 hours

2. Minimize setup time by batching:
- Optimal sequence: Product C -> Product C -> Product B -> Product B -> Product B -> Product A -> Product D -> Product D
3. Total with setups:
- Product C: 4 hours
- Product C: 4 hours (no setup)
- Setup Product C→Product B: 3 hour + Product B: 2 hours
- Product B: 2 hours (no setup)
- Product B: 2 hours (no setup)
- Setup Product B→Product A: 3 hour + Product A: 1 hours
- Setup Product A→Product D: 3 hour + Product D: 2 hours
- Product D: 2 hours (no setup)

Total: 28 hours

Key Strategy: Batch identical products together to minimize setup changes.

Question 6

A production line needs to manufacture: - Product D: 1 units (each takes 2 hours) - Product A: 2 units (each takes 2 hours) - Product B: 2 units (each takes 4 hours) - Product C: 3 units (each takes 1 hours) Setup time required when switching products: - P->P: 2 hour What is the minimum total time if production starts with Product A?

Step-by-step solution:

Production Sequencing with Setup Times:
1. Calculate total production time (without setup):
- Product D: 1 x 2 = 2 hours
- Product A: 2 x 2 = 4 hours
- Product B: 2 x 4 = 8 hours
- Product C: 3 x 1 = 3 hours
- Base production time: 17 hours

2. Minimize setup time by batching:
- Optimal sequence: Product A -> Product A -> Product D -> Product B -> Product B -> Product C -> Product C -> Product C
3. Total with setups:
- Product A: 2 hours
- Product A: 2 hours (no setup)
- Setup Product A→Product D: 2 hour + Product D: 2 hours
- Setup Product D→Product B: 2 hour + Product B: 4 hours
- Product B: 4 hours (no setup)
- Setup Product B→Product C: 2 hour + Product C: 1 hours
- Product C: 1 hours (no setup)
- Product C: 1 hours (no setup)

Total: 23 hours

Key Strategy: Batch identical products together to minimize setup changes.

Question 7

A production line needs to manufacture: - Product D: 2 units (each takes 3 hours) - Product A: 1 units (each takes 1 hours) - Product C: 2 units (each takes 1 hours) - Product B: 1 units (each takes 2 hours) Setup time required when switching products: - P->P: 1 hour What is the minimum total time if production starts with Product D?

Step-by-step solution:

Production Sequencing with Setup Times:
1. Calculate total production time (without setup):
- Product D: 2 x 3 = 6 hours
- Product A: 1 x 1 = 1 hours
- Product C: 2 x 1 = 2 hours
- Product B: 1 x 2 = 2 hours
- Base production time: 11 hours

2. Minimize setup time by batching:
- Optimal sequence: Product D -> Product D -> Product A -> Product C -> Product C -> Product B
3. Total with setups:
- Product D: 3 hours
- Product D: 3 hours (no setup)
- Setup Product D→Product A: 1 hour + Product A: 1 hours
- Setup Product A→Product C: 1 hour + Product C: 1 hours
- Product C: 1 hours (no setup)
- Setup Product C→Product B: 1 hour + Product B: 2 hours

Total: 14 hours

Key Strategy: Batch identical products together to minimize setup changes.

Question 8

A production line needs to manufacture: - Product B: 1 units (each takes 4 hours) - Product D: 1 units (each takes 3 hours) - Product C: 1 units (each takes 4 hours) - Product A: 2 units (each takes 4 hours) Setup time required when switching products: - P->P: 3 hour What is the minimum total time if production starts with Product C?

Step-by-step solution:

Production Sequencing with Setup Times:
1. Calculate total production time (without setup):
- Product B: 1 x 4 = 4 hours
- Product D: 1 x 3 = 3 hours
- Product C: 1 x 4 = 4 hours
- Product A: 2 x 4 = 8 hours
- Base production time: 19 hours

2. Minimize setup time by batching:
- Optimal sequence: Product C -> Product B -> Product D -> Product A -> Product A
3. Total with setups:
- Product C: 4 hours
- Setup Product C→Product B: 3 hour + Product B: 4 hours
- Setup Product B→Product D: 3 hour + Product D: 3 hours
- Setup Product D→Product A: 3 hour + Product A: 4 hours
- Product A: 4 hours (no setup)

Total: 28 hours

Key Strategy: Batch identical products together to minimize setup changes.

Question 9

A production line needs to manufacture: - Product B: 2 units (each takes 3 hours) - Product D: 1 units (each takes 2 hours) - Product C: 3 units (each takes 4 hours) - Product A: 1 units (each takes 1 hours) Setup time required when switching products: - P->P: 2 hour What is the minimum total time if production starts with Product C?

Step-by-step solution:

Production Sequencing with Setup Times:
1. Calculate total production time (without setup):
- Product B: 2 x 3 = 6 hours
- Product D: 1 x 2 = 2 hours
- Product C: 3 x 4 = 12 hours
- Product A: 1 x 1 = 1 hours
- Base production time: 21 hours

2. Minimize setup time by batching:
- Optimal sequence: Product C -> Product C -> Product C -> Product B -> Product B -> Product D -> Product A
3. Total with setups:
- Product C: 4 hours
- Product C: 4 hours (no setup)
- Product C: 4 hours (no setup)
- Setup Product C→Product B: 2 hour + Product B: 3 hours
- Product B: 3 hours (no setup)
- Setup Product B→Product D: 2 hour + Product D: 2 hours
- Setup Product D→Product A: 2 hour + Product A: 1 hours

Total: 27 hours

Key Strategy: Batch identical products together to minimize setup changes.

Question 10

A production line needs to manufacture: - Product B: 1 units (each takes 4 hours) - Product A: 1 units (each takes 3 hours) - Product C: 1 units (each takes 4 hours) - Product D: 1 units (each takes 3 hours) Setup time required when switching products: - P->P: 1 hour What is the minimum total time if production starts with Product B?

Step-by-step solution:

Production Sequencing with Setup Times:
1. Calculate total production time (without setup):
- Product B: 1 x 4 = 4 hours
- Product A: 1 x 3 = 3 hours
- Product C: 1 x 4 = 4 hours
- Product D: 1 x 3 = 3 hours
- Base production time: 14 hours

2. Minimize setup time by batching:
- Optimal sequence: Product B -> Product A -> Product C -> Product D
3. Total with setups:
- Product B: 4 hours
- Setup Product B→Product A: 1 hour + Product A: 3 hours
- Setup Product A→Product C: 1 hour + Product C: 4 hours
- Setup Product C→Product D: 1 hour + Product D: 3 hours

Total: 17 hours

Key Strategy: Batch identical products together to minimize setup changes.

Question 11

A production line needs to manufacture: - Product B: 3 units (each takes 1 hours) - Product C: 1 units (each takes 2 hours) - Product A: 2 units (each takes 3 hours) - Product D: 2 units (each takes 1 hours) Setup time required when switching products: - P->P: 1 hour What is the minimum total time if production starts with Product C?

Step-by-step solution:

Production Sequencing with Setup Times:
1. Calculate total production time (without setup):
- Product B: 3 x 1 = 3 hours
- Product C: 1 x 2 = 2 hours
- Product A: 2 x 3 = 6 hours
- Product D: 2 x 1 = 2 hours
- Base production time: 13 hours

2. Minimize setup time by batching:
- Optimal sequence: Product C -> Product B -> Product B -> Product B -> Product A -> Product A -> Product D -> Product D
3. Total with setups:
- Product C: 2 hours
- Setup Product C→Product B: 1 hour + Product B: 1 hours
- Product B: 1 hours (no setup)
- Product B: 1 hours (no setup)
- Setup Product B→Product A: 1 hour + Product A: 3 hours
- Product A: 3 hours (no setup)
- Setup Product A→Product D: 1 hour + Product D: 1 hours
- Product D: 1 hours (no setup)

Total: 16 hours

Key Strategy: Batch identical products together to minimize setup changes.

Question 12

A production line needs to manufacture: - Product B: 1 units (each takes 1 hours) - Product D: 2 units (each takes 1 hours) - Product C: 3 units (each takes 2 hours) - Product A: 1 units (each takes 1 hours) Setup time required when switching products: - P->P: 3 hour What is the minimum total time if production starts with Product B?

Step-by-step solution:

Production Sequencing with Setup Times:
1. Calculate total production time (without setup):
- Product B: 1 x 1 = 1 hours
- Product D: 2 x 1 = 2 hours
- Product C: 3 x 2 = 6 hours
- Product A: 1 x 1 = 1 hours
- Base production time: 10 hours

2. Minimize setup time by batching:
- Optimal sequence: Product B -> Product D -> Product D -> Product C -> Product C -> Product C -> Product A
3. Total with setups:
- Product B: 1 hours
- Setup Product B→Product D: 3 hour + Product D: 1 hours
- Product D: 1 hours (no setup)
- Setup Product D→Product C: 3 hour + Product C: 2 hours
- Product C: 2 hours (no setup)
- Product C: 2 hours (no setup)
- Setup Product C→Product A: 3 hour + Product A: 1 hours

Total: 19 hours

Key Strategy: Batch identical products together to minimize setup changes.

Question 13

A production line needs to manufacture: - Product C: 1 units (each takes 1 hours) - Product D: 3 units (each takes 1 hours) - Product A: 1 units (each takes 1 hours) - Product B: 2 units (each takes 1 hours) Setup time required when switching products: - P->P: 3 hour What is the minimum total time if production starts with Product A?

Step-by-step solution:

Production Sequencing with Setup Times:
1. Calculate total production time (without setup):
- Product C: 1 x 1 = 1 hours
- Product D: 3 x 1 = 3 hours
- Product A: 1 x 1 = 1 hours
- Product B: 2 x 1 = 2 hours
- Base production time: 7 hours

2. Minimize setup time by batching:
- Optimal sequence: Product A -> Product C -> Product D -> Product D -> Product D -> Product B -> Product B
3. Total with setups:
- Product A: 1 hours
- Setup Product A→Product C: 3 hour + Product C: 1 hours
- Setup Product C→Product D: 3 hour + Product D: 1 hours
- Product D: 1 hours (no setup)
- Product D: 1 hours (no setup)
- Setup Product D→Product B: 3 hour + Product B: 1 hours
- Product B: 1 hours (no setup)

Total: 16 hours

Key Strategy: Batch identical products together to minimize setup changes.

Question 14

A production line needs to manufacture: - Product B: 1 units (each takes 2 hours) - Product D: 2 units (each takes 2 hours) - Product A: 3 units (each takes 3 hours) Setup time required when switching products: - P->P: 3 hour What is the minimum total time if production starts with Product A?

Step-by-step solution:

Production Sequencing with Setup Times:
1. Calculate total production time (without setup):
- Product B: 1 x 2 = 2 hours
- Product D: 2 x 2 = 4 hours
- Product A: 3 x 3 = 9 hours
- Base production time: 15 hours

2. Minimize setup time by batching:
- Optimal sequence: Product A -> Product A -> Product A -> Product B -> Product D -> Product D
3. Total with setups:
- Product A: 3 hours
- Product A: 3 hours (no setup)
- Product A: 3 hours (no setup)
- Setup Product A→Product B: 3 hour + Product B: 2 hours
- Setup Product B→Product D: 3 hour + Product D: 2 hours
- Product D: 2 hours (no setup)

Total: 21 hours

Key Strategy: Batch identical products together to minimize setup changes.

Question 15

A production line needs to manufacture: - Product B: 2 units (each takes 1 hours) - Product C: 1 units (each takes 3 hours) - Product A: 2 units (each takes 2 hours) - Product D: 1 units (each takes 2 hours) Setup time required when switching products: - P->P: 3 hour What is the minimum total time if production starts with Product A?

Step-by-step solution:

Production Sequencing with Setup Times:
1. Calculate total production time (without setup):
- Product B: 2 x 1 = 2 hours
- Product C: 1 x 3 = 3 hours
- Product A: 2 x 2 = 4 hours
- Product D: 1 x 2 = 2 hours
- Base production time: 11 hours

2. Minimize setup time by batching:
- Optimal sequence: Product A -> Product A -> Product B -> Product B -> Product C -> Product D
3. Total with setups:
- Product A: 2 hours
- Product A: 2 hours (no setup)
- Setup Product A→Product B: 3 hour + Product B: 1 hours
- Product B: 1 hours (no setup)
- Setup Product B→Product C: 3 hour + Product C: 3 hours
- Setup Product C→Product D: 3 hour + Product D: 2 hours

Total: 20 hours

Key Strategy: Batch identical products together to minimize setup changes.

Question 16

A production line needs to manufacture: - Product D: 3 units (each takes 3 hours) - Product A: 2 units (each takes 2 hours) - Product C: 3 units (each takes 1 hours) Setup time required when switching products: - P->P: 3 hour What is the minimum total time if production starts with Product D?

Step-by-step solution:

Production Sequencing with Setup Times:
1. Calculate total production time (without setup):
- Product D: 3 x 3 = 9 hours
- Product A: 2 x 2 = 4 hours
- Product C: 3 x 1 = 3 hours
- Base production time: 16 hours

2. Minimize setup time by batching:
- Optimal sequence: Product D -> Product D -> Product D -> Product A -> Product A -> Product C -> Product C -> Product C
3. Total with setups:
- Product D: 3 hours
- Product D: 3 hours (no setup)
- Product D: 3 hours (no setup)
- Setup Product D→Product A: 3 hour + Product A: 2 hours
- Product A: 2 hours (no setup)
- Setup Product A→Product C: 3 hour + Product C: 1 hours
- Product C: 1 hours (no setup)
- Product C: 1 hours (no setup)

Total: 22 hours

Key Strategy: Batch identical products together to minimize setup changes.

Question 17

A production line needs to manufacture: - Product D: 2 units (each takes 3 hours) - Product A: 1 units (each takes 4 hours) - Product C: 1 units (each takes 4 hours) - Product B: 2 units (each takes 3 hours) Setup time required when switching products: - P->P: 3 hour What is the minimum total time if production starts with Product D?

Step-by-step solution:

Production Sequencing with Setup Times:
1. Calculate total production time (without setup):
- Product D: 2 x 3 = 6 hours
- Product A: 1 x 4 = 4 hours
- Product C: 1 x 4 = 4 hours
- Product B: 2 x 3 = 6 hours
- Base production time: 20 hours

2. Minimize setup time by batching:
- Optimal sequence: Product D -> Product D -> Product A -> Product C -> Product B -> Product B
3. Total with setups:
- Product D: 3 hours
- Product D: 3 hours (no setup)
- Setup Product D→Product A: 3 hour + Product A: 4 hours
- Setup Product A→Product C: 3 hour + Product C: 4 hours
- Setup Product C→Product B: 3 hour + Product B: 3 hours
- Product B: 3 hours (no setup)

Total: 29 hours

Key Strategy: Batch identical products together to minimize setup changes.

Question 18

A production line needs to manufacture: - Product A: 2 units (each takes 4 hours) - Product D: 3 units (each takes 3 hours) - Product C: 3 units (each takes 1 hours) Setup time required when switching products: - P->P: 2 hour What is the minimum total time if production starts with Product A?

Step-by-step solution:

Production Sequencing with Setup Times:
1. Calculate total production time (without setup):
- Product A: 2 x 4 = 8 hours
- Product D: 3 x 3 = 9 hours
- Product C: 3 x 1 = 3 hours
- Base production time: 20 hours

2. Minimize setup time by batching:
- Optimal sequence: Product A -> Product A -> Product D -> Product D -> Product D -> Product C -> Product C -> Product C
3. Total with setups:
- Product A: 4 hours
- Product A: 4 hours (no setup)
- Setup Product A→Product D: 2 hour + Product D: 3 hours
- Product D: 3 hours (no setup)
- Product D: 3 hours (no setup)
- Setup Product D→Product C: 2 hour + Product C: 1 hours
- Product C: 1 hours (no setup)
- Product C: 1 hours (no setup)

Total: 24 hours

Key Strategy: Batch identical products together to minimize setup changes.

Question 19

A production line needs to manufacture: - Product A: 2 units (each takes 4 hours) - Product B: 1 units (each takes 4 hours) - Product D: 3 units (each takes 4 hours) - Product C: 3 units (each takes 1 hours) Setup time required when switching products: - P->P: 1 hour What is the minimum total time if production starts with Product A?

Step-by-step solution:

Production Sequencing with Setup Times:
1. Calculate total production time (without setup):
- Product A: 2 x 4 = 8 hours
- Product B: 1 x 4 = 4 hours
- Product D: 3 x 4 = 12 hours
- Product C: 3 x 1 = 3 hours
- Base production time: 27 hours

2. Minimize setup time by batching:
- Optimal sequence: Product A -> Product A -> Product B -> Product D -> Product D -> Product D -> Product C -> Product C -> Product C
3. Total with setups:
- Product A: 4 hours
- Product A: 4 hours (no setup)
- Setup Product A→Product B: 1 hour + Product B: 4 hours
- Setup Product B→Product D: 1 hour + Product D: 4 hours
- Product D: 4 hours (no setup)
- Product D: 4 hours (no setup)
- Setup Product D→Product C: 1 hour + Product C: 1 hours
- Product C: 1 hours (no setup)
- Product C: 1 hours (no setup)

Total: 30 hours

Key Strategy: Batch identical products together to minimize setup changes.

Question 20

A production line needs to manufacture: - Product D: 3 units (each takes 2 hours) - Product C: 2 units (each takes 1 hours) - Product B: 1 units (each takes 4 hours) Setup time required when switching products: - P->P: 3 hour What is the minimum total time if production starts with Product C?

Step-by-step solution:

Production Sequencing with Setup Times:
1. Calculate total production time (without setup):
- Product D: 3 x 2 = 6 hours
- Product C: 2 x 1 = 2 hours
- Product B: 1 x 4 = 4 hours
- Base production time: 12 hours

2. Minimize setup time by batching:
- Optimal sequence: Product C -> Product C -> Product D -> Product D -> Product D -> Product B
3. Total with setups:
- Product C: 1 hours
- Product C: 1 hours (no setup)
- Setup Product C→Product D: 3 hour + Product D: 2 hours
- Product D: 2 hours (no setup)
- Product D: 2 hours (no setup)
- Setup Product D→Product B: 3 hour + Product B: 4 hours

Total: 18 hours

Key Strategy: Batch identical products together to minimize setup changes.

Master Production Line Scheduling - Intermediate-Advanced Level Problems Production Line Scheduling INTERMEDIATE ADVANCED

What you'll learn in this worksheet: