Model the problem by defining variables for start/end times of jobs on each machine, then express precedence constraints as inequalities (e.g., `end_time ≥ start_time + duration`).

Introduce auxiliary variables to represent machine availability (e.g., `machine_idle_time ≥ previous_job_end_time`) and link them to job scheduling constraints.

Transform the inequalities into a graph where nodes represent events (job starts/ends) and edges encode constraints, then apply the Bellman-Ford algorithm to detect feasible schedules or identify conflicts.