Unified Theory of Allocations and Constructs in Life Cycle Assessment and Input-Output Analysis

The treatment of coproducts is one of the most persistent methodological challenges for both input-output (IO) analysis and life cycle assessment (LCA). The two fields have developed distinct modeling traditions to artificially extract independent Leontief production functions (technological recipes) for products of multioutput activities; whereas IO operates in terms of system-wide models named constructs, LCA practitioners usually use allocations or system expansion on a process-by-process basis. Recently, there have been renewed efforts to connect these two modeling traditions on the basis of their underlying assumptions. A formal description of a unified framework for the treatment of coproducts is still lacking, however. The present article strives to fill this gap. From a single generalized allocation equation, we derive all practical LCA allocations and IO constructs. This approach extends previous studies by arranging the different models in a formal taxonomic tree, clarifying the relation between the different LCA allocation and IO construct models. This framework also clarifies the relation of certain models to classical system expansion. We then analyze the properties of these models when combined with different types of inventories and make recommendations for best practice in inventory compilation.