A single machine scheduling problem to minimize total early work

Yoav Ben-Yehoshua, Gur Mosheiov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


We study a single machine scheduling problem, where the objective is minimum total early work. In this setting, a job is penalized according to the duration of the parts of the job completed prior to its due-date. First we prove that the problem is NP-hard. Then, based on a number of properties of an optimal schedule, we introduce a pseudo-polynomial dynamic programming algorithm, verifying NP-hardness in the ordinary sense. Our numerical tests indicate that the dynamic programming solves problems of hundreds of jobs in very reasonable time.

Original languageAmerican English
Pages (from-to)115-118
Number of pages4
JournalComputers and Operations Research
StatePublished - Sep 2016

Bibliographical note

Funding Information:
This research was supported by the Israel Science Foundation (Grant no. 1286/14 ). The second author was supported in part by the Recanati Fund of The School of Business Administration, and Charles I. Rosen Chair of Management, The Hebrew University of Jerusalem, Israel.

Publisher Copyright:
© 2016 Elsevier Ltd. All rights reserved.


  • Dynamic programming
  • Scheduling
  • Single machine
  • Total early work


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