A BICRITERION APPROACH TO PREEMPTIVE SCHEDULING OF PARALLEL MACHINES WITH CONTROLLABLE JOB PROCESSING TIMES

The paper deals with a bicriterion approach to preemptive scheduling of m parallel machines for jobs having processing costs which are linear functions of variable processing times. One of the objective functions is a completion time and the other, a processing cost. In the case of identical machines, an O(n(2)) greedy algorithm is given which generates all breakpoints of a piecewise linear efficient frontier; it is shown that in the problem with n jobs there are at most 2n + 1 breakpoints, which is a tight bound. For uniform machines, an algorithm is provided which solves a problem of least processing cost under limited completion time in O(n max {m, log n}) time. Basing on this algorithm, a procedure for finding an epsilon-approximation of the efficient frontier is proposed.