Open AccessNote—A Note on Shwimer's Theorem A
Author(s) -
Werner Dinkelbach,
Otto Rosenberg
Publication year - 1977
Publication title -
management science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.954
H-Index - 255
eISSN - 1526-5501
pISSN - 0025-1909
DOI - 10.1287/mnsc.23.6.660
Subject(s) - tardiness , sequence (biology) , mathematical optimization , scheduling (production processes) , computer science , mathematics , job shop scheduling , mathematical economics , schedule , biology , genetics , operating system
In 1972 Joel Shwimer published some interesting research "on the n-job, one-machine, sequence-independent scheduling problem with tardiness penalties ... where the goal is to minimize the total penalty costs resulting from the tardiness of the jobs" (Shwimer, J. 1972. On the n-job, one-machine, sequence-independent scheduling problem with tardiness penalties: a branch-bound solution. Management Sci. 18 (6) B301-B313.). The proposed algorithm is essentially based on his Theorem A. Unfortunately the given proof of Theorem A contains an inconsistency. In this note we present a different proof of the mentioned theorem.