Scheduling a single machine with parallel batching to minimize makespan and total rejection cost

Cheng He, Joseph Y.T. Leung, Kangbok Lee, Michael L. Pinedo

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

We consider the problem of scheduling a set of n jobs on a single machine with parallel batching and with rejection being allowed. Two bi-criteria problems are considered: (a) minimize the makespan subject to the constraint that the total rejection cost does not exceed a given threshold, and (b) minimize the total rejection cost subject to the constraint that the makespan does not exceed a given threshold. For the case of a batching machine with infinite capacity (i.e., the batch size allowed on the machine is larger than or equal to the number of jobs), we assume that the jobs have release dates. We present an O(n2)-time 2-approximation algorithm for problem (a) and, in addition, we present dynamic programming algorithms and fully polynomial-time approximation schemes for both problems (a) and (b). For the case of a batching machine with finite capacity (i.e., the batch size allowed on the machine is less than the number of jobs), we assume that the jobs have identical release dates. We propose approximation algorithms for (a) and present dynamic programming algorithms and fully polynomial-time approximation schemes for both problems (a) and (b).

Original languageEnglish (US)
Pages (from-to)150-163
Number of pages14
JournalDiscrete Applied Mathematics
Volume204
DOIs
StatePublished - May 11 2016

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Keywords

  • Approximation algorithms
  • Batching machine scheduling
  • Dynamic programming
  • FPTAS
  • Makespan
  • Rejection

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