An approximation algorithm for the two identical parallel machine problem under machine availability constraints

Anh H.G. Nguyen, Gwo Ji Sheen, Ying-Chieh Yeh

Research output: Contribution to journalArticlepeer-review

Abstract

This study addresses the scheduling problem of two identical parallel machines with the objective of minimizing the total completion time under the machine availability constraints. To the best of our knowledge, this study is the first to develop a fully polynomial-time approximation scheme (FPTAS), a solution method which has been neglected in past studies, to solve the studied problem. The FPTAS, which is based on a dynamic programming algorithm is developed by applying a trimming-the-state-space approach. Theoretical proofs of the error bound and the time complexity for the proposed FPTAS are also provided. The computational results indicate that the proposed FPTAS performs more efficiently than a dynamic programming algorithm in terms of both run time and problem size. The error bound of the FPTAS is demonstrated to be within the pre-specified error bound.

Original languageEnglish
JournalJournal of Industrial and Production Engineering
DOIs
StateAccepted/In press - 2022

Keywords

  • Parallel machine scheduling
  • dynamic programming algorithm
  • fully polynomial-time approximation scheme
  • machine availability constraints
  • trimming-the-state-space approach

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