One-machine scheduling for minimizing total flow time with release dates

The one-machine scheduling problem of minimizing total flow time with different release dates is addressed. This problem is equivalent to the problems of minimizing total completion time, total job lateness, and mean number of jobs in the shop, and it is NP-hard. A necessary and sufficient condition is proved for local optimality and can be considered as a priority rule. Based on this condition, a subset containing all the optimal schedules is defined. Any schedule in this subset verifies some dominance properties proved by other researchers. The author also proposes some efficient heuristic algorithms using the proven condition to build a schedule belonging to this subset. The algorithm performances are provided