Scheduling of parallel machines to minimize total completion time subject to s-precedence constraints

This paper considers a deterministic scheduling problem where multiple jobs with s-precedence relations are processed on multiple identical parallel machines. The objective is to minimize the total completion time. The s-precedence relation between two jobs i and j represents the situation where job j is constrained from processing until job i starts processing, which is different from the standard definition of a precedence relation where j cannot start until i completes. The s-precedence relation has wide applicability in the real world such as first-come-first-served processing systems. The problem is shown to be intractable, for which a heuristic procedure is derived. Numerical experiments are conducted to show that the derived heuristic provides effective solutions.