Scheduling with a weight-modifying activity to minimize the total weighted completion time

Bertrand M.T. Lin*, Shu Wei Liu, Gur Mosheiov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

This paper considers a single-machine scheduling problem to minimize the total weighted completion time with a weight modifying activity, after which the job weights are discounted by a given factor. The problem is known to be ordinary NP-hard. We propose two mixed integer linear programs (MILPs) and a dynamic programming algorithm to optimally solve the problem. Optimality properties are established and then formulated as pruning constraints to improve the problem-solving efficiency of the MILPs. Special cases are discussed and shown to be solvable by polynomial time algorithms. Complexity status of the studied problem with several instance characteristics is shown. Computational experiments indicate that the optimality properties can reduce the computing efforts and that one of the proposed MILPs can solve instances of 200 jobs in a few seconds.

Original languageAmerican English
Article number103115
JournalOmega (United Kingdom)
Volume128
DOIs
StatePublished - Oct 2024

Bibliographical note

Publisher Copyright:
© 2024 Elsevier Ltd

Keywords

  • Dynamic programming
  • Mixed integer linear programming
  • Single-machine scheduling
  • Weight modifying activity

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