Scheduling of tasks with effectiveness precedence constraints

We formally present the problem of scheduling tasks with effectiveness precedence relationships in order to achieve the minimum total weighted completion time. We provide the problem formulation and define the scope of the problem considered. We present computational complexity results for this problem and an approximation algorithm for it. We prove the theoretical performance of our algorithm and demonstrate its efficiency and practical performance through computational testing, which includes a comparison to the optimal results obtained with an integer programming formulation.