An O(n4) algorithm for preemptive scheduling of a single machine to minimize the number of late jobs

Authors:
Philippe Baptiste
Affiliations:
UMR CNRS 6599, HEUDIASYC, Université de Technologie de Compiègne, Centre de Recherches de Royallieu, Rue Personne de Roberval, BP 20.529, 60205 Compiègne Cedex, France11Corresponden ...
Venue:
Operations Research Letters
Year:
1999

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Abstract

We study the problem of minimizing, in the preemptive case, the number of late jobs on a single machine (1|pmtn,r"j|@?U"j). This problem can be solved by Lawler's algorithm [E.L. Lawler, Ann. Oper. Res. 26 (1990) 125-133] whose time and space complexities are respectively O(n^5) and O(n^3). We propose a new dynamic programming algorithm whose complexities are respectively O(n^4) and O(n^2).