Just-in-time scheduling with controllable processing times on parallel machines

Yaron Leyvand, Dvir Shabtay, George Steiner, Liron Yedidsion

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


We study scheduling problems with controllable processing times on parallel machines. Our objectives are to maximize the weighted number of jobs that are completed exactly at their due date and to minimize the total resource allocation cost. We consider four different models for treating the two criteria. We prove that three of these problems are mathcal{NP} -hard even on a single machine, but somewhat surprisingly, the problem of maximizing an integrated objective function can be solved in polynomial time even for the general case of a fixed number of unrelated parallel machines. For the three mathcal{NP} -hard versions of the problem, with a fixed number of machines and a discrete resource type, we provide a pseudo-polynomial time optimization algorithm, which is converted to a fully polynomial time approximation scheme.

Original languageEnglish
Pages (from-to)347-368
Number of pages22
JournalJournal of Combinatorial Optimization
Issue number3
StatePublished - 1 Apr 2010


  • Controllable processing times
  • Fixed interval scheduling
  • Just-in-time scheduling
  • Resource allocation
  • Unrelated parallel machines

ASJC Scopus subject areas

  • Computer Science Applications
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Theory and Mathematics
  • Applied Mathematics


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