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Maximization Problems in Single Machine Scheduling

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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.

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Authors and Affiliations

  1. Ecole des Mines de Nancy, Parc de Saurupt, MACSI team of INRIA-Lorraine and LORIA-INPL, 54042, Nancy Cedex, France

    Mohamed Ali Aloulou & Marie-Claude Portmann

  2. Faculty of Economics, Belarus State University, K. Marxa 31, 220050, Minsk, Belarus

    Mikhail Y. Kovalyov

Authors
  1. Mohamed Ali Aloulou
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  2. Mikhail Y. Kovalyov
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  3. Marie-Claude Portmann
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Aloulou, M.A., Kovalyov, M.Y. & Portmann, MC. Maximization Problems in Single Machine Scheduling. Annals of Operations Research 129, 21–32 (2004). https://doi.org/10.1023/B:ANOR.0000030679.25466.02

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  • DOI: https://doi.org/10.1023/B:ANOR.0000030679.25466.02

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