Improving the preemptive bound for the one-machine dynamic total completion time scheduling problem

We consider the single machine dynamic total completion time scheduling problem. This problem is known to be NP-hard in the strong sense. The currently best available lower bound for the problem is known to be the optimal solution value of the corresponding preemptive problem which can be computed in O(n log n) time. We propose an improvement on this bound by exploiting the properties of the preemptive solution. The proposed improvement reduces by approximately 44% on the average the gap between the preemptive solution value and the optimal solution value.