SENSITIVITY ANALYSIS OF LIST SCHEDULING HEURISTICS

When jobs have to be processed on a set of identical parallel machines so as to minimize the makespan of the schedule, list scheduling rules form a popular class of heuristics. The order in which jobs appear on the list is assumed here to be determined by the relative size of the ir processing times; well-known special cases are the LPT rule and the SPT rule, in which the jobs are ordered according to non-increasing a nd non-decreasing processing time respectively. When all processing ti mes are exactly known, a given list scheduling rule will generate a un ique assignment of jobs to machines. However, when there exists a prio ri uncertainty with respect to one of the processing times, then there will be, in general, several possibilities for the assignment that wi ll be generated once the processing time is known. This number of poss ible assignments may be viewed as a measure of the sensitivity of the list scheduling rule that is applied. We derive bounds on the maximum number of possible assignments for several list scheduling heuristics, and we also study the makespan associated with these assignments. In this way we obtain analytical support for the intuitively plausible no tion that the sensitivity of a list scheduling rule increases with the quality of the schedule produced.