An FPTAS for scheduling a two-machine flowshop with one unavailability interval

Chi To Ng, Mikhail Y. Kovalyov

Research output: Journal article publicationJournal articleAcademic researchpeer-review

27 Citations (Scopus)


We study a deterministic two-machine flowshop scheduling problem with an assumption that one of the two machines is not available in a specified time period. This period can be due to a breakdown, preventive maintenance, or processing unfinished jobs from a previous planning horizon. The problem is known to be NP-hard. Pseudopolynomial dynamic programming algorithms and heuristics with worst case error bounds are given in the literature to solve the problem. They are different for the cases when the unavailability interval is for the first or second machine. The existence of a fully polynomial time approximation scheme (FPTAS) was formulated as an open conjecture in the literature. In this paper, we show that the two cases of the problem under study are equivalent to similar partition type problems. Then we derive a generic FPTAS for the latter problems with O(n5/ε4) time complexity.
Original languageEnglish
Pages (from-to)307-315
Number of pages9
JournalNaval Research Logistics
Issue number3
Publication statusPublished - 1 Jan 2004


  • Flowshop scheduling
  • Fully polynomial time approximation scheme
  • Machine availability

ASJC Scopus subject areas

  • Modelling and Simulation
  • Ocean Engineering
  • Management Science and Operations Research


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