Single machine scheduling with general time-dependent deterioration, position-dependent learning and past-sequence-dependent setup times

Xue Huang, Gang Li, Yunzhang Huo, Ping Ji

Research output: Journal article publicationJournal articleAcademic researchpeer-review

14 Citations (Scopus)

Abstract

The paper deals with single machine scheduling problems with setup time considerations where the actual processing time of a job is not only a non-decreasing function of the total normal processing times of the jobs already processed, but also a non-increasing function of the job's position in the sequence. The setup times are proportional to the length of the already processed jobs, i.e., the setup times are past-sequence-dependent (p-s-d). We consider the following objective functions: the makespan, the total completion time, the sum of the δth (δ ≥ 0) power of job completion times, the total weighted completion time and the maximum lateness. We show that the makespan minimization problem, the total completion time minimization problem and the sum of the δ th (δ ≥ 0) power of job completion times minimization problem can be solved by the smallest (normal) processing time first (SPT) rule, respectively. We also show that the total weighted completion time minimization problem and the maximum lateness minimization problem can be solved in polynomial time under certain conditions.
Original languageEnglish
Pages (from-to)1793-1804
Number of pages12
JournalOptimization Letters
Volume7
Issue number8
DOIs
Publication statusPublished - 1 Dec 2013

Keywords

  • Deteriorating jobs
  • Learning effect
  • Scheduling
  • Setup times
  • Single machine

ASJC Scopus subject areas

  • Control and Optimization

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