A submodular optimization approach to bicriteria scheduling problems with controllable processing times on parallel machines

Akiyoshi Shioura, Natalia V. Shakhlevich, Vitaly A. Strusevich

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

In this paper, we present a general methodology for designing polynomial-time algorithms for bicriteria scheduling problems on parallel machines with controllable processing times. For each considered problem, the two criteria are the makespan and the total compression cost, and the solution is delivered in the form of the break points of the efficient frontier. We reformulate the scheduling problems in terms of optimization over submodular polyhedra and give efficient procedures for computing the corresponding rank functions. As a result, for two of the considered problems we obtain the first polynomial-time algorithms, while for the third problem we considerably improve the known running time.

Original languageEnglish
Pages (from-to)186-204
Number of pages19
JournalSIAM Journal on Discrete Mathematics
Volume27
Issue number1
DOIs
Publication statusPublished - 2013

Keywords

  • Bicriteria problems
  • Controllable processing times
  • Parallel machine scheduling
  • Submodular optimization

ASJC Scopus subject areas

  • Mathematics(all)

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