On dividing an amount according to individual claims or liabilities
Mathematics of Operations Research
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Towards equitable distributions via proportional equity constraints
Mathematical Programming: Series A and B
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The standard problem of rationing a single over-demanded commodity has a natural bipartite extension with multiple types of a one-dimensional commodity (e.g., stored in different locations), and each agent can only consume some types of the commodity (e.g., has only access to a subset of locations). We define the new standard loss calibrated rationing methods, that equalize across agents the ratio of shares to (calibrated) losses (demand minus share). We extend them to bipartite methods that (1) are not affected by the elimination of an edge and the corresponding flow (Consistency), and (2) treat resource types with identical connectivity as a single type. They are essentially the only standard methods with a bipartite extension meeting the two properties above. Most of the parametric methods discussed in the literature do not admit such extension.