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Annals of Operations Research

, Volume 26, Issue 1, pp 125–133 | Cite as

A dynamic programming algorithm for preemptive scheduling of a single machine to minimize the number of late jobs

  • E. L. Lawler
Single-Machine Scheduling

Abstract

The scheduling problem 1|pmtn, r j w j U j calls forn jobs with arbitrary release dates and due dates to be preemptively scheduled for processing by a single machine, with the objective of minimizing the sum of the weights of the late jobs. A dynamic programming algorithm for this problem is described. Time and space bounds for the algorithm are, respectively,O(nk2W2) andO(k2W), wherek is the number of distinct release dates andW is the sum of the integer job weights. Thus, for the problem 1|pmtn, r j U j , in which the objective is simply to minimize the number of late jobs, the pseudopolynomial time bound becomes polynomial, i.e.O(n3k2).

Keywords

Schedule Problem Dynamic Programming Release Date Single Machine Programming Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© J.C. Baltzer AG, Scientific Publishing Company 1990

Authors and Affiliations

  • E. L. Lawler
    • 1
  1. 1.Computer Science DivisionUniversity of CaliforniaBerkeleyUSA

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