A Multivariate Complexity Analysis of the Material Consumption Scheduling Problem

The NP-hard MATERIAL CONSUMPTION SCHEDULING PROBLEM and related problems have been thoroughly studied since the 1980’s. Roughly speaking, the problem deals with minimizing the makespan when scheduling jobs that consume non-renewable resources. We focus on the singlemachine case without preemption: from time to time, the resources of the machine are (partially) replenished, thus allowing for meeting a necessary pre-condition for processing further jobs, each of which having individual resource demands. We initiate a systematic exploration of the parameterized computational complexity landscape of the problem, providing parameterized tractability as well as intractability results. Doing so, we mainly investigate how parameters related to the resource supplies influence the computational complexity. Thereby, we get a deepened understanding of this fundamental scheduling problem.

Authors

• Matthias Bentert Technische Universität Berlin
• Robert Bredereck Institut für Informatik, TU Clausthal
• Péter Györgyi
• Andrzej Kaczmarczyk AGH University
• Rolf Niedermeier Technische Universität Berlin

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