Journal of Heuristics

, Volume 24, Issue 2, pp 173–203 | Cite as

Reduction criteria, upper bounds, and a dynamic programming based heuristic for the max–min \(k_i\)-partitioning problem

  • Alexander Lawrinenko
  • Stefan Schwerdfeger
  • Rico WalterEmail author


This paper addresses the max–min \(k_i\)-partitioning problem that asks for an assignment of n jobs to m parallel machines so that the minimum machine completion time is maximized and the number of jobs on each machine does not exceed a machine-dependent cardinality limit \(k_i\) \((i=1,\ldots ,m)\). We propose different preprocessing as well as lifting procedures and derive several upper bound arguments. Furthermore, we introduce suited construction heuristics as well as an effective dynamic programming based improvement procedure. Results of a comprehensive computational study on a large set of randomly generated instances indicate that our algorithm quickly finds (near-)optimal solutions.


Parallel machines Cardinality limits Preprocessing Upper bounds Dynamic programming 


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  • Alexander Lawrinenko
    • 1
  • Stefan Schwerdfeger
    • 1
  • Rico Walter
    • 1
    Email author
  1. 1.Chair for Management ScienceFriedrich-Schiller-University JenaJenaGermany

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