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

Abstract

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.

Fully integrated modelling for sustainability assessment of resource recovery from waste

“…Their mathematics are discussed further below. It should be noted that allocations present major issues when TCs are not physically-based, and results of LCA are highly sensitive to practitioners' assumptions (Reap et al, 2008), particularly when system expansion is used to estimate avoided impacts due to processes' secondary products (Hanes et al, 2015). In our cases, avoidable issues around assigning responsibility remain.…”

“…Moreover, they may determine where in the lifecycle of products waste reduction interventions are applied and at what actors they are aimed (households, businesses, etc.). Such values may also affect the design of sustainability assessments more broadly via the choices made when selecting methods, metrics, system boundaries, and allocation coefficients for secondary products (Hanes et al, 2015;Sala et al, 2013b). For example, the monetising of environmental and social impacts in ECBA (Kallis et al, 2013;McCauley, 2006;Millward-Hopkins, 2016) is a contentious approach that opponents have argued is fundamentally incompatible with sustainability science (Anderson et al, 2015).…”

“…The transfer coefficients for type 1 metrics can be based upon metric values from any another layer-i.e. a partition allocation (Hanes et al, 2015)-provided that value is conserved over the process in the other layer. This highlights a problem with allocating, say, carbon emissions by (relative) market prices, as the latter can be destroyed by a process, while the former should be conserved.…”

A pseudo-statistical approach to treat choice uncertainty: the example of partitioning allocation methods

“…To provide a solution for the system of linear equations of an LCA (Heijungs and Suh 2002), the use of the least-squares technique has been investigated (Marvuglia et al 2010;Cruze et al 2014). In this sense, particularly Cruze et al (2014) favor avoiding allocation over partitioning regardless of the principle arguing that, Bsince the number of solutions to choose from is infinite, even consensus… would not necessarily lend validity to an LCA study.M ore recently, the study by Hanes et al (2015) developed an analytical approach dealing with the choice of allocation method: the Comprehensive Allocation Investigation Strategy (CAIS). This approach considers all possible combinations of partitioning methods in a comparative LCA; therefore, it systematically explores the allocation space of various systems.…”

“…Besides the analytical method of Hanes et al (2015), there is the statistical approach of Andrianandraina et al (2015). They apply local and global sensitivity analyses to determine the influence of uncertainty in unit process data and methodological and modeling parameters to the total uncertainty in LCA results.…”