Two-machine flow-shop scheduling with rejection

Dvir Shabtay, Nufar Gasper

Research output: Contribution to journalArticlepeer-review

35 Scopus citations


We study a scheduling problem with rejection on a set of two machines in a flow-shop scheduling system. We evaluate the quality of a solution by two criteria: the first is the makespan and the second is the total rejection cost. We show that the problem of minimizing the makespan plus total rejection cost is NP-hard and for its solution we provide two different approximation algorithms, a pseudo-polynomial time optimization algorithm and a fully polynomial time approximation scheme (FPTAS). We also study the problem of finding the entire set of Pareto-optimal points (this problem is NP-hard due to the NP-hardness of the same problem variation on a single machine [20]). We show that this problem can be solved in pseudo-polynomial time. Moreover, we show how we can provide an FPTAS that, given that there exists a Pareto optimal schedule with a total rejection cost of at most R and a makespan of at most K, finds a solution with a total rejection cost of at most (1ε)R and a makespan value of at most (1ε)K. This is done by defining a set of auxiliary problems and providing an FPTAS algorithm to each one of them.

Original languageEnglish
Pages (from-to)1087-1096
Number of pages10
JournalComputers and Operations Research
Issue number5
StatePublished - 1 May 2012


  • Approximation algorithm
  • Bicriteria optimization
  • Flow-shop scheduling
  • NP - hard
  • Pseudo-polynomial time algorithm
  • Scheduling with rejection

ASJC Scopus subject areas

  • General Computer Science
  • Modeling and Simulation
  • Management Science and Operations Research


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