In this article the objective is to evaluate the performance of a WSPT (weighted shortest processing time) rule for scheduling n independent jobs where the resources to process these jobs vary over time and a job can be processed by several processors simultaneously. This problem was raised by Baker and Nuttle. A linear-programming (LP) model is formulated to obtain a lower bound on the minimum value of the weighted completion times. The purpose of the model is to provide a basis for evaluating the WSPT heuristic. 1000 experiments were performed using different resource profiles to test the performance of WSPT. Using WSPT, the weighted completion times were found to be, on the average, 0.2% away from their LP lower bounds.
