, Volume 57, Issue 4, pp 769–795 | Cite as

Fully Polynomial Approximation Schemes for a Symmetric Quadratic Knapsack Problem and its Scheduling Applications



We design a fully polynomial-time approximation scheme (FPTAS) for a knapsack problem to minimize a symmetric quadratic function. We demonstrate how the designed FPTAS can be adopted for several single machine scheduling problems to minimize the sum of the weighted completion times. The applications presented in this paper include problems with a single machine non-availability interval (for both the non-resumable and the resumable scenarios) and a problem of planning a single machine maintenance period; the latter problem is closely related to a single machine scheduling problem with two competing agents. The running time of each presented FPTAS is strongly polynomial.


Quadratic knapsack Single machine scheduling Total weighted completion time Availability constraints Scheduling agents FPTAS 


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© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Institut für Statistik und Operations ResearchUniversität GrazGrazAustria
  2. 2.School of Computing and Mathematical SciencesUniversity of Greenwich, Old Royal Naval CollegeLondonUK

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