Minimizing total completion time with linear deterioration: A new lower bound

Matan Atsmony, Gur Mosheiov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We study scheduling problems in which the job processing times are linearly deteriorating. Each job has a constant (job-independent) basic processing time and a job-dependent deterioration rate. The objective function is minimum total completion time. The machine settings considered are: single machine and parallel identical machines. The complexity status of these problems has been an open question for the last three decades. We introduce a new lower bound on the optimal total completion time, which is shown numerically (through a comparison to the results obtained by a simple heuristic) to be extremely accurate for both problems.

Original languageAmerican English
Article number107867
JournalComputers and Industrial Engineering
StatePublished - Jan 2022

Bibliographical note

Funding Information:
This research was funded by the Israel Science Foundation (grant No. 2505/19) and by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project Number 452470135. It was also supported by the Recanati Fund of The School of Business Administration, and by Charles I. Rosen Chair of Management, The Hebrew University of Jerusalem , Israel.

Publisher Copyright:
© 2021 Elsevier Ltd


  • Heuristic
  • Linear deterioration
  • Lower bound
  • Scheduling
  • Total completion time


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