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Minimizing worst-case and average-case makespan over scenarios

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We consider scheduling problems over scenarios where the goal is to find a single assignment of the jobs to the machines which performs well over all scenarios in an explicitly given set. Each scenario is a subset of jobs that must be executed in that scenario. The two objectives that we consider are minimizing the maximum makespan over all scenarios and minimizing the sum of the makespans of all scenarios. For both versions, we give several approximation algorithms and lower bounds on their approximability. We also consider some (easier) special cases. Combinatorial optimization problems under scenarios in general, and scheduling problems under scenarios in particular, have seen only limited research attention so far. With this paper, we make a step in this interesting research direction.

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  1. An alternative way of viewing the scenarios would be that every scenario specifies a |J|-tuple of processing times, where the processing time of job j in any scenario \(S_i\) equals either \(p_j\) or 0.


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Correspondence to Suzanne van der Ster.

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Feuerstein, E., Marchetti-Spaccamela, A., Schalekamp, F. et al. Minimizing worst-case and average-case makespan over scenarios. J Sched 20, 545–555 (2017).

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