The increased use of secondary (i.e., recycled) and renewable resources will likely be key toward achieving sustainable materials use. Unfortunately, these strategies share a common barrier to economical implementation - increased quality variation compared to their primary and synthetic counterparts. Current deterministic process-planning models overestimate the economic impact of this increased variation. This paper shows that for a range of industries from biomaterials to inorganics, managing variation through a chance-constrained (CC) model enables increased use of such variable raw materials, or heterogeneous feedstocks (hF), over conventional, deterministic models. An abstract, analytical model and a quantitative model applied to an industrial case of aluminum recycling were used to explore the limits and benefits of the CC formulation. The results indicate that the CC solution can reduce cost and increase potential hF use across a broad range of production conditions through raw materials diversification. These benefits increase where the hFs exhibit mean quality performance close to that of the more homogeneous feedstocks (often the primary and synthetic materials) or have large quality variability. In terms of operational context, the relative performance grows as intolerance for batch error increases and as the opportunity to diversify the raw material portfolio increases.