Erratum: The Stable Allocation (or Ordinal Transportation) Problem

An incorrect version of this paper was printed in Mathematics of Operations Research, Vol. 27, No. 3, August 2002, pp. 485–503. The paper is reprinted correctly below. 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.