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

Evgeny Gafarov (), Alexander Lazarev and Frank Werner ()

Annals of Operations Research, 2014, vol. 213, issue 1, 115-130

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

Keywords: Project scheduling; Makespan; Lower bounds; Upper bounds (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10479-012-1106-5

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