On a cardinality-constrained transportation problem with market choice

It is well-known that the intersection of the matching polytope with a cardinality constraint is integral (Schrijver, 2003)? 8. In this note, we prove a similar result for the polytope corresponding to the transportation problem with market choice (TPMC) (introduced in Damci-Kurt et?al. (2015)) when the demands are in the set { 1 , 2 } . This result generalizes the result regarding the matching polytope. The result in this note implies that some special classes of minimum weight perfect matching problem with a cardinality constraint on a subset of edges can be solved in polynomial time.