We study the i.i.d. online bipartite matching problem, a dynamic version of the classical model where one side of the bipartition is fixed and known in advance, while nodes from the other side appear one at a time as i.i.d. realizations of a uniform distribution, and must immediately be matched or discarded. We consider various relaxations of the polyhedral set of achievable matching probabilities, introduce valid inequalities, and discuss when they are facet-defining. We also show how several of these relaxations correspond to ranking policies and their time-dependent generalizations. We finally present a computational study of these relaxations and policies to determine their empirical performance.
Stewart School of Industrial and Systems Engineering, April, 2016