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.