Problem:
You are a team of project managers working on a construction project. The goal is to optimize the project schedule to minimize completion time while adhering to resource constraints and minimizing costs associated with resource usage. The project involves multiple tasks with different durations, dependencies, and resource requirements. Data:
- Tasks: 1. Excavation (Duration: 5 days, Resource: 2 workers, Cost: $500 per day) 2. Foundation (Duration: 7 days, Resource: 3 workers, Cost: $700 per day) 3. Framing (Duration: 10 days, Resource: 4 workers, Cost: $900 per day) 4 Roofing (Duration: 5 days, Resource: 2 workers, Cost: $600 per day) 5. Electrical Wiring (Duration: 8 days, Resource: 3 workers, Cost: $800 per day) 6. Plumbing (Duration: 6 days, Resource: 2 workers, Cost: $700 per day) 7. Insulation (Duration: 4 days, Resource: 1 worker, Cost: $400 per day) 8. Drywall (Duration: 7 days, Resource: 3 workers, Cost: $750 per day) 9. Painting (Duration: 5 days, Resource: 2 workers, Cost: $650 per day)
- Task Dependencies:
- Excavation must be completed before Foundation. Foundation must be completed before Framing. Roofing can only start after Framing. Electrical Wiring and Plumbing can start once Framing is done. Insulation and Drywall can start once Roofing is