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The stable allocation (or ordinal transportation) problem. (English)
Math. Oper. Res. 27, No. 3, 485-503 (2002).
Summary: The stable allocation problem generalizes the 0,1 stable matching problems (one-to-one, one-to-many, and many-to-many) to the allocation of real valued hours or quantities. A strongly polynomial algorithm proves the existence of “stable allocations." The set of stable allocations is shown to be a distributive lattice in general, but in the “nondegenerate" case it is a complete linear order. Indeed, in the generic case, when a problem is “strongly nondegenerate", there exists a single stable allocation. A simple algorithm finds “row-optimal" and “column-optimal" stable allocations, given any stable allocation. When a problem is nondegenerate it finds all stable allocations. A corrected version has been printed in ibid. 27, No. 4, 485‒503 (2002).
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