We formulate the omni-channel fulfillment problem as an online optimization problem. We propose a novel algorithm for this problem based on the primal-dual schema. Our algorithm is robust: it does not require explicit demand forecasts. This is an important practical advantage in the apparel-retail setting where demand is volatile and unpredictable. We provide a performance analysis establishing that our algorithm admits optimal performance guarantees in the face of adversarial demand.
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We describe a large-scale implementation of our algorithm at Urban Outfitters, Inc. This implementation processes on average eighteen thousand customer orders a day, and as many as one hundred thousand orders on peak demand days. We estimate conservatively that the system has saved at least six million dollars annually relative to an incumbent industry standard fulfillment optimization implementation. This saving is achieved through optimal order-fulfillment decisions that simultaneously increase turn and lower shipping costs.