This data article describes an instance dataset motivated by the problem of scheduling a project with diverging material flows. Such material flows are released during the execution of the project and are subject to limited processing and storage capacities. Typical examples are nuclear dismantling or other deconstruction/demolition projects, where large amounts of material must be classified, scanned for hazardousness, and processed accordingly. The problem setting is mathematically described as a resource-constrained project scheduling problem with cumulative resources (RCPSP/c). The RCPSP/c deals with finding a project schedule with minimal makespan that satisfies temporal, renewable resource, and cumulative resource constraints. In total, the dataset comprises 192 artificially generated instances that are suitable for testing models and solution methods. In addition, we provide our best found solution for each instance and different modeling variants (e.g., for two types of objective functions). These solutions were computed by heuristic solution methods. The dataset serves as a benchmark for researchers evaluating the performance of solution methods for the RCPSP/c or the more general problem class with resources that can be produced and consumed.