Shortest-processing-time order (${\min }_{\sigma }{\sum }_{j=1}^n(n-j+1)t_{\sigma (j)}$)

On one server with all jobs initially available, nonnegative fixed durations and no sequence-dependent setup, a nondecreasing-duration order minimizes the sum of completion times. Swapping adjacent durations $a>b$ reduces their combined contribution by $a-b$ and changes no later completion time, because their total duration is unchanged. Repeated adjacent exchanges remove every inversion. The sum of pre-service waiting times has the same optimum, differing by the fixed total duration.