An Unrelated Parallel Processing with Weighted jobs and Setup times scheduling prolem is studied. We consider a parallel processing in which a group of processors(machines) perform a single operation on jobs of a number of different job types. The processing time of each job depends on both the job and the machine, and each job has a weight. In addition each machine requires significant setup time between processing jobs of different job types. The performance measure is to minimize total weighted flow time in order to meet the job importance and to minimize in-process inventory. We present a 0-1 Mixed Integer Programming model as an optimizing algorithm. We also present a simple heuristic algorithm. Computational results for the optimal and the heuristic algorithm are reported and the results show that the simple heuristic is quite effective and efficient.