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A note on the scheduling with two families of jobs. (English) Zbl 1123.90040
Summary: K. R. Baker and J. C. Smith [J. Sched. 6, No. 1, 7–16 (2003)] introduced a new model of scheduling in which there are two or more distinct families of jobs pursuing different objectives. Their contributions include two polynomial-time dynamic programming recursions, respectively, for the single machine scheduling with two families of jobs to minimize a positive combination of total weighted completion time, or maximum lateness, of the first family of jobs and maximum lateness of the second family of jobs. Unfortunately, these dynamic programming recursions are incorrect. In this paper, we solve the same problems by an $O\left({n}_{1}{n}_{2}\left({n}_{1}+{n}_{2}\right)\right)$ time algorithm.
##### MSC:
 90B35 Scheduling theory, deterministic 90C60 Abstract computational complexity for mathematical programming problems
##### References:
 [1] Baker, K. R. and J. C. Smith, ”A multiple-criterion model for machine scheduling,” Journal of Scheduling, 6, 7–16, (2003). · Zbl 1154.90406 · doi:10.1023/A:1022231419049