Parallel machine scheduling with s-precedence constraints

For s-precedence constraints, job i cannot start processing until all jobs that precede i start. This is different from the standard definition of a precedence relation where i cannot start until all prior jobs complete. While not discussed in the scheduling literature, s-precedence constraints have wide applicability in real-world settings such as first-come, first-served processing systems. This article considers a deterministic scheduling problem where jobs with s-precedence relations are processed by multiple identical parallel machines. The objective is to minimize the makespan. The problem is shown to be intractable. A heuristic procedure is developed and tight worst-case bounds on the relative error are derived. Finally, computational experiments show that the proposed heuristic provides effective solutions.