The Stable Allocation (or Ordinal Transportation) Problem

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.