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Acta Informatica

, Volume 36, Issue 9–10, pp 673–692 | Cite as

Single machine scheduling with deadlines and increasing rates of processing times

  • T.C.E. Cheng
  • Q. Ding
Original articles

Abstract.

The makespan, flow time and maximum lateness problems of scheduling a set of tasks with deadlines and increasing rates of processing times on a single machine are considered in this paper. We first show that, when the increasing rates of processing time are identical, the makespan problem is equivalent to the corresponding flow time problem. Both problems are solvable in \(O(n^5)\) time by a dynamic programming algorithm. As an application of the dynamic programming algorithm, we demonstrate that the corresponding maximum lateness problem can be solved in \(O(n^6\log n)\) time. We then show that the general makespan problem is strongly NP-complete. Thus, both the corresponding flow time problem and maximum lateness problem are also strongly NP-complete.

Keywords

Processing Time Dynamic Programming Flow Time 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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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • T.C.E. Cheng
    • 1
  • Q. Ding
    • 1
  1. 1.The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, (e-mail: mscheng@polyu.edu.hk) HK

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