Allocation Games: Addressing the Ill-Posed Nature of Allocation in Life-Cycle Inventories

Allocation is required when a life cycle contains multi-functional processes. One approach to allocation is to partition the embodied resources in proportion to a criterion, such as product mass or cost. Many practitioners apply multiple partitioning criteria to avoid choosing one arbitrarily. However, life cycle results from different allocation methods frequently contradict each other, making it difficult or impossible for the practitioner to draw any meaningful conclusions from the study. Using the matrix notation for life-cycle inventory data, we show that an inventory that requires allocation leads to an ill-posed problem: an inventory based on allocation is one of an infinite number of inventories that are highly dependent upon allocation methods. This insight is applied to comparative life-cycle assessment (LCA), in which products with the same function but different life cycles are compared. Recently, there have been several studies that applied multiple allocation methods and found that different products were preferred under different methods. We develop the Comprehensive Allocation Investigation Strategy (CAIS) to examine any given inventory under all possible allocation decisions, enabling us to detect comparisons that are not robust to allocation, even when the comparison appears robust under conventional partitioning methods. While CAIS does not solve the ill-posed problem, it provides a systematic way to parametrize and examine the effects of partitioning allocation. The practical usefulness of this approach is demonstrated with two case studies. The first compares ethanol produced from corn stover hydrolysis, corn stover gasification, and corn grain fermentation. This comparison was not robust to allocation. The second case study compares 1,3-propanediol (PDO) produced from fossil fuels and from biomass, which was found to be a robust comparison.