Allocation in life cycle inventory (LCI) analysis is one of the long-standing methodological issues in life cycle assessment (LCA). Discussion on allocation among LCA researchers has taken place almost in complete isolation from the series of closely related discussions from the 1960s in the field of input−output economics, regarding the supply and use framework. This article aims at developing a coherent mathematical framework for allocation in LCA by connecting the parallel developments of the LCA and the input−output communities. In doing so, the article shows that the partitioning method in LCA is equivalent to the industry-technology model in input−output economics, and system expansion in LCA is equivalent to the by-product-technology model in input−output output economics. Furthermore, we argue that the commodity-technology model and the by-product-technology model, which have been considered as two different models in input−output economics for more than 40 years, are essentially equivalent when it comes to practical applications. It is shown that the matrix-based approach used for system expansion successfully solves the endless regression problem that has been raised in LCA literature. A numerical example is introduced to demonstrate the use of allocation models. The relationship of these approaches with consequential and attributional LCA models is also discussed.