Scheduling of uniform parallel machines with s-precedence constraints

This paper considers a problem of scheduling s-precedence constrained jobs on machines in parallel which have different speeds. The objective is to minimize the weighted 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. An LP-based heuristic procedure is derived for the problem. Numerical experiments are conducted to show that the derived heuristic finds effective solutions.