Scheduling of parallel identical machines to maximize the weighted number of just-in-time jobs

Kunihiko Hiraishi, Eugene Levner, Milan Vlach

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49 Scopus citations


We study the problem of nonpreemptively scheduling n jobs on m identical machines in parallel to maximize the weighted number of jobs that are completed exactly at their due dates. We show that this problem is solvable in polynomial time even if positive set-up times are allowed. Moreover, we show that if due date tolerances are permitted, then already the single-machine case is NP-hard even if all set-up times are zero and all weights are the same. Most of the literature in the field of deterministic scheduling deals with regular measures of performance, that is with minimizing objective functions that are nondecreasing in job completion times. With the growing interest in just-in-time production, the demand for research into problems with regular performance measures has considerably increased (see Baker and Scudder, Oper Res 38(1) (1990) 22). This note provides an efficient algorithm for finding nonpreemptive schedules that are optimal with respect to a special type of irregular performance measures in the case of identical machines in parallel.

Original languageEnglish
Pages (from-to)841-848
Number of pages8
JournalComputers and Operations Research
Issue number7
StatePublished - Jun 2002
Externally publishedYes

Bibliographical note

Funding Information:
The second author gratefully acknowledges the partial support of JSPS of Japan and the MOS of Israel (grant no. 8951-2-98).


  • Irregular objective
  • Just-in-time
  • Parallel machines
  • Polynomial algorithm
  • Scheduling
  • Set-up times


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