Sequencing jobs in a one-machine shop using the Shortest Processing Time (SPT) rule minimizes flow time and average number of jobs in the system. SPT sequencing picks up jobs with the least processing time first, achieving objectives such as minimizing mean waiting time and mean number of tasks waiting as in-process inventory. Other sequencing rules like Earliest Due Date (EDD), First Come First Serve (FCFS), and Critical Ratio (CR) have different objectives and may not achieve the same results as SPT.