Preemptive Scheduling of Two Uniform Machines to Minimize the Number of Late Jobs
Operations Research · 1989 · Volume 37 · Issue 2
Abstract
Suppose that n jobs, each with a specified processing requirement and due date, are to be preemptively scheduled for processing by a number of parallel machines, with the objective of maximizing the number of jobs that are completed by their due dates. It is known that this scheduling problem is NP-hard, even for identical machines, if the number of machines is variable, that is, specified as part of the problem instance. However, if the machine environment consists of a fixed set of uniform machines, the problem can be solved in polynomial time. An O ( n 3 ) algorithm is presented for the special case of two uniform machines. The running time of this algorithm becomes O ( Wn 2 ), where W is the sum of the job weights, for the more general problem in which it is desired to minimize the weighted number of late jobs. A fully polynomial approximation scheme is also presented for the weighted case.
Keywords
computers: preemptive scheduling of uniform processors, dynamic programming: application, production/scheduling: deterministic scheduling
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