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Approximability results for the resource-constrained project scheduling problem with a single type of resources

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  • Evgeny Gafarov
  • Alexander Lazarev
  • Frank Werner

Abstract

In this paper, we consider the well-known resource-constrained project scheduling problem. We give some arguments that already a special case of this problem with a single type of resources is not approximable in polynomial time with an approximation ratio bounded by a constant. We prove that there exist instances for which the optimal makespan values for the non-preemptive and the preemptive problems have a ratio of O(logn), where n is the number of jobs. This means that there exist instances for which the lower bound of Mingozzi et al. has a bad relative error of O(logn), and the calculation of this bound is an NP-hard problem. In addition, we give a proof that there exists a type of instances for which known approximation algorithms with polynomial time complexity have an approximation ratio of at least equal to $O(\sqrt{n})$ , and known lower bounds have a relative error of at least equal to O(logn). This type of instances corresponds to the single machine parallel-batch scheduling problem 1|p−batch,b=∞|C max . Copyright Springer Science+Business Media, LLC 2014

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  • Evgeny Gafarov & Alexander Lazarev & Frank Werner, 2014. "Approximability results for the resource-constrained project scheduling problem with a single type of resources," Annals of Operations Research, Springer, vol. 213(1), pages 115-130, February.
    • Handle: RePEc:spr:annopr:v:213:y:2014:i:1:p:115-130:10.1007/s10479-012-1106-5
    DOI: 10.1007/s10479-012-1106-5
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    1. Demeulemeester, Erik L. & Herroelen, Willy S., 1996. "An efficient optimal solution procedure for the preemptive resource-constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 90(2), pages 334-348, April.
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    10. Hartmann, Sönke & Kolisch, R., 2000. "Experimental evaluation of state-of-the-art heuristics for the resource-constrained project scheduling problem," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 11180, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
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    Cited by:

    1. Péter Györgyi & Tamás Kis, 2015. "Approximability of scheduling problems with resource consuming jobs," Annals of Operations Research, Springer, vol. 235(1), pages 319-336, December.
    2. Zdeněk Hanzálek & Přemysl Šůcha, 2017. "Time symmetry of resource constrained project scheduling with general temporal constraints and take-give resources," Annals of Operations Research, Springer, vol. 248(1), pages 209-237, January.

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