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Maximization Problems in Single Machine Scheduling

Author

Listed:
  • Mohamed Aloulou
  • Mikhail Kovalyov
  • Marie-Claude Portmann

Abstract

Problems of scheduling n jobs on a single machine to maximize regular objective functions are studied. Precedence constraints may be given on the set of jobs and the jobs may have different release times. Schedules of interest are only those for which the jobs cannot be shifted to start earlier without changing job sequence or violating release times or precedence constraints. Solutions to the maximization problems provide an information about how poorly such schedules can perform. The most general problem of maximizing maximum cost is shown to be reducible to n similar problems of scheduling n−1 jobs available at the same time. It is solved in O(mn+n 2 ) time, where m is the number of arcs in the precedence graph. When all release times are equal to zero, the problem of maximizing the total weighted completion time or the weighted number of late jobs is equivalent to its minimization counterpart with precedence constraints reversed with respect to the original ones. If there are no precedence constraints, the problem of maximizing arbitrary regular function reduces to n similar problems of scheduling n−1 jobs available at the same time. Copyright Kluwer Academic Publishers 2004

Suggested Citation

  • Mohamed Aloulou & Mikhail Kovalyov & Marie-Claude Portmann, 2004. "Maximization Problems in Single Machine Scheduling," Annals of Operations Research, Springer, vol. 129(1), pages 21-32, July.
    • Handle: RePEc:spr:annopr:v:129:y:2004:i:1:p:21-32:10.1023/b:anor.0000030679.25466.02
    DOI: 10.1023/B:ANOR.0000030679.25466.02
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    Cited by:

    1. Evgeny Gafarov & Alexander Lazarev & Frank Werner, 2012. "Transforming a pseudo-polynomial algorithm for the single machine total tardiness maximization problem into a polynomial one," Annals of Operations Research, Springer, vol. 196(1), pages 247-261, July.
    2. Evgeny Gafarov & Alexander Lazarev & Frank Werner, 2013. "Single machine total tardiness maximization problems: complexity and algorithms," Annals of Operations Research, Springer, vol. 207(1), pages 121-136, August.
    3. Xin Chen & Sergey Kovalev & Małgorzata Sterna & Jacek Błażewicz, 2021. "Mirror scheduling problems with early work and late work criteria," Journal of Scheduling, Springer, vol. 24(5), pages 483-487, October.
    4. Sergey Kovalev, 2015. "Maximizing total tardiness on a single machine in $$O(n^2)$$ O ( n 2 ) time via a reduction to half-product minimization," Annals of Operations Research, Springer, vol. 235(1), pages 815-819, December.

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