The problem of finding a schedule with the lowest makespan in the class of all flowtime-optimal schedules for parallel identical machines is an NP-hard problem. Several approximation algorithms have been suggested for this problem. We focus on algorithms that are fast and easy to implement, rather than on more involved algorithms that might provide tighter approximation bounds. A set of approaches for proving conjectured bounds on performance ratios for such algorithms is outlined. These approaches are used to examine Coffman and Sethi's conjecture for a worst-case bound on the ratio of the makespan of the schedule generated by the LD algorithm to the makespan of the optimal schedule. A significant reduction is achieved in the size of a hypothesised minimal counterexample to this conjecture.

The problem of finding a schedule with the lowest makespan in the class of all flowtime-optimal schedules for parallel identical machines is an NP-hard problem. Several approximation algorithms have been suggested for this problem. We focus on algorithms that are fast and easy to implement, rather than on more involved algorithms that might provide tighter approximation bounds. A set of approaches for proving conjectured bounds on performance ratios for such algorithms is outlined. These approaches are used to examine Coffman and Sethi's conjecture for a worst-case bound on the ratio of the makespan of the schedule generated by the LD algorithm to the makespan of the optimal schedule. A significant reduction is achieved in the size of a hypothesised minimal counterexample to this conjecture.