Question 1
A production line needs to manufacture:
- Product B: 2 units (each takes 3 hours)
- Product C: 1 units (each takes 4 hours)
- Product A: 1 units (each takes 3 hours)
- Product D: 3 units (each takes 3 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 B: 2 x 3 = 6 hours
- Product C: 1 x 4 = 4 hours
- Product A: 1 x 3 = 3 hours
- Product D: 3 x 3 = 9 hours
- Base production time: 22 hours
2. Minimize setup time by batching:
- Optimal sequence: Product D -> Product D -> Product D -> Product B -> Product B -> Product C -> Product A
3. Total with setups:
- Product D: 3 hours
- Product D: 3 hours (no setup)
- Product D: 3 hours (no setup)
- Setup Product D→Product B: 2 hour + Product B: 3 hours
- Product B: 3 hours (no setup)
- Setup Product B→Product C: 2 hour + Product C: 4 hours
- Setup Product C→Product A: 2 hour + Product A: 3 hours
Total: 28 hours
Key Strategy: Batch identical products together to minimize setup changes.
Production Sequencing with Setup Times:
1. Calculate total production time (without setup):
- Product B: 2 x 3 = 6 hours
- Product C: 1 x 4 = 4 hours
- Product A: 1 x 3 = 3 hours
- Product D: 3 x 3 = 9 hours
- Base production time: 22 hours
2. Minimize setup time by batching:
- Optimal sequence: Product D -> Product D -> Product D -> Product B -> Product B -> Product C -> Product A
3. Total with setups:
- Product D: 3 hours
- Product D: 3 hours (no setup)
- Product D: 3 hours (no setup)
- Setup Product D→Product B: 2 hour + Product B: 3 hours
- Product B: 3 hours (no setup)
- Setup Product B→Product C: 2 hour + Product C: 4 hours
- Setup Product C→Product A: 2 hour + Product A: 3 hours
Total: 28 hours
Key Strategy: Batch identical products together to minimize setup changes.