Technical Note

Journal of Scheduling

, Volume 8, Issue 6, pp 537-542

A note on the scheduling with two families of jobs

  • J. J. YuanAffiliated withDepartment of Mathematics, Zhengzhou University Email author 
  • , W. P. ShangAffiliated withDepartment of Mathematics, Zhengzhou University
  • , Q. FengAffiliated withDepartment of Mathematics, Zhengzhou University

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Abstract

Baker and Smith [J. Scheduling, 6, 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(n 1 n 2(n 1 + n 2)) time algorithm.