Fast approximation algorithms for bi-criteria scheduling with machine assignment costs

Kangbok Lee, Joseph Y.T. Leung, Zhao Hong Jia, Wenhua Li, Michael L. Pinedo*, Bertrand M.T. Lin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


We consider parallel machine scheduling problems where the processing of the jobs on the machines involves two types of objectives. The first type is one of two classical objective functions in scheduling theory: either the total completion time or the makespan. The second type involves an actual cost associated with the processing of a specific job on a given machine; each job-machine combination may have a different cost. Two bi-criteria scheduling problems are considered: (1) minimize the maximum machine cost subject to the total completion time being at its minimum, and (2) minimize the total machine cost subject to the makespan being at its minimum. Since both problems are strongly NP-hard, we propose fast heuristics and establish their worst-case performance bounds.

Original languageEnglish
Pages (from-to)54-64
Number of pages11
JournalEuropean Journal of Operational Research
Issue number1
StatePublished - 1 Oct 2014


  • Bi-criteria scheduling
  • Heuristics
  • Makespan
  • Maximum machine cost
  • Total completion time
  • Total machine cost

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