The performance of a shared memory multiprocessor system is very sensitive to process scheduling. w can enhance the performance of a whole system as well as of an individual process by taking the multiprocessor characteristics into account in the design of the process scheduler. In this paper, we proposed a general purpose scheduler for a shared memory multiprocessor, called the Two-Level Multi-Scan (TLMS) process scheduler, that considers the processor affinity loosely and decreases the interference among multiple processors greatly. The TLMS scheduler is composed of a local scheduler at each processor and a semi-global scheduler that balances the load among processors. In particular, the semi-global scheduler tries to minimize priority inversion, which is an important factor of the system performance. The TLMS scheduler also tries to reduce the number of resources to be shared and improves the processor utilization. to meet these requirements, th semi-global scheduler interacts with the operation of the local scheduler when a need arises, thus the name is loose processor-affinity. We also show that the proposed scheduling technique can be extended for other types of resources making it a general purpose resource management queue.