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A proof for the longest‐job‐first policy in one‐machine scheduling
Author(s) -
Cheng T. C. E.,
Kahlbacher H. G.
Publication year - 1991
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/1520-6750(199110)38:5<715::aid-nav3220380506>3.0.co;2-6
Subject(s) - tardiness , mathematical optimization , sequence (biology) , due date , computer science , job shop scheduling , scheduling (production processes) , mathematics , schedule , biology , genetics , operating system
We consider a one‐machine scheduling problem with earliness and tardiness penalties. All jobs are assigned a common due date and the objective is to minimize the total penalty due to job earliness and tardiness. We are interested in finding the optimal combination of the common due‐date value and the job sequence. Despite the fact that this problem in general is very hard to solve, we prove that there exists at least a common property for all optimal solutions: The first job in an optimal sequence is one of the longest jobs. We also prove that this property holds for a general class of unimodal penalty functions.