Abstract
The papers 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 2 n + 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( nmax m, log n) time. Basing on this algorithm, a procedure for finding an ε-approximation of the efficient frontier is proposed.
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