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Roughly speaking, the problem deals with scheduling jobs that consume non-renewable resources\u2014each job has individual resource demands. The goal is to minimize the makespan. We focus on the single-machine case without preemption: from time to time, the resources of the machine are (partially) replenished, thus allowing for meeting a necessary precondition for processing further jobs. We initiate a systematic exploration of the parameterized computational complexity landscape of <jats:sc>Material Consumption Scheduling<\/jats:sc>, providing parameterized tractability as well as intractability results. Doing so, we mainly investigate how parameters related to the resource supplies influence the problem\u2019s computational complexity. 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