Preemptive Scheduling of Two Uniform Machines to Minimize the Number of Late Jobs

E. L. Lawler and C. U. Martel
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E. L. Lawler: University of California, Berkeley, California
C. U. Martel: University of California, Davis, California

Operations Research, 1989, vol. 37, issue 2, 314-318

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 (search for similar items in EconPapers)
Date: 1989
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Citations: View citations in EconPapers (12)

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