International Journal of Fuzzy Logic and Intelligent Systems

Korean Institute of Intelligent Systems (한국지능시스템학회)
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A Term-based Language for Resource-Constrained Project Scheduling and its Complexity Analysis

  • Kutzner, Arne (Department of Information Systems, Hanyang University) ;
  • Kim, Pok-Son (Department of Mathematics, Kookmin University)
  • Received : 2011.10.06
  • Accepted : 2012.03.10
  • Published : 2012.03.25
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Abstract

We define a language $\mathcal{RS}$, a subclass of the scheduling language $\mathcal{RS}V$ (resource constrained project scheduling with variant processes). $\mathcal{RS}$ involves the determination of the starting times for ground activities of a project satisfying precedence and resource constraints, in order to minimize the total project duration. In $\mathcal{RS}$ ground activities and two structural symbols (operators) 'seq' and 'pll' are used to construct activity-terms representing scheduling problems. We consider three different variants for formalizing the $\mathcal{RS}$-scheduling problem, the optimizing variant, the number variant and the decision variant. Using the decision variant we show that the problem $\mathcal{RS}$ is $\mathcal{NP}$-complete. Further we show that the optimizing variant (or number variant) of the $\mathcal{RS}$-problem is computable in polynomial time iff the decision variant is computable in polynomial time.

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References

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