The NP-hard problem MATERIAL CONSUMPTION SCHEDULING and related problems have been thoroughly studied since the 1980’s. Roughly speaking, the problem deals with scheduling jobs that consume non-renewable resources—each 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 MATERIAL CONSUMPTION SCHEDULING, providing parameterized tractability as well as intractability results. Doing so, we mainly investigate how parameters related to the resource supplies influence the problem’s computational complexity. This leads to a deepened understanding of this fundamental scheduling problem.