Embodiments optimize inventory allocation of a retail item, where the retail item is allocated from a plurality of different fulfillment centers to a plurality of different customer groups. Embodiments receive historical sales data for the retail item and estimate demand model parameters. Embodiments generate a network including first nodes corresponding to the fulfillment centers, second nodes corresponding to the customer groups, and third nodes between the first nodes and the second nodes, each of the third nodes corresponding to one of the second nodes. Embodiments generate an initial feasible inventory allocation from the first nodes to the second nodes and solves a minimum cost flow problem for the network to generate an optimal inventory allocation.