You are an operations research specialist scheduling an aero...

Prompt

You are an operations research specialist scheduling an aerospace assembly hangar. Solve the following deterministic scheduling problem to find the absolute minimum total time (makespan) to complete all jobs. Workstations: - Station 1: Precision Milling (M1) - Station 2: Thermal Coating (M2) Rules: 1. Each station can process at most one component at a time. 2. Operations cannot be interrupted or preempted once started. 3. Station 1 requires NO cleaning/changeover time between components. 4. Station 2 requires exactly 1 hour of cleaning whenever switching from one component to a different component. 5. Alpha, Beta, and Gamma are available at Hour 0. DELTA IS NOT AVAILABLE UNTIL HOUR 12 (late delivery). 6. Each component must follow its exact operational sequence in strict order. Components to manufacture: - Alpha: Step 1: Station 1 for 4 hours Step 2: Station 2 for 3 hours - Beta: Step 1: Station 2 for 5 hours Step 2: Station 1 for 2 hours - Gamma: Step 1: Station 1 for 3 hours Step 2: Station 2 for 4 hours Step 3: Station 1 for 1 hour - Delta: Step 1: Station 2 for 2 hours Step 2: Station 1 for 4 hours Tasks: 1. State the absolute minimum total makespan (in hours). 2. Provide the complete hour-by-hour timeline for both stations. 3. Prove why no schedule can beat your makespan (a pure "14 + 3 = 17" load argument is NOT sufficient here and will be graded as wrong).