Primal–Dual Algorithms for Order Fulfillment at Urban Outfitters, Inc

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. We describe a large-scale implementation of our algorithm at Urban Outfitters, Inc. This implementation processes on average 18,000 customer orders a day and as many as 100,000 orders on peak demand days. The system has resulted in substantial savings relative to an incumbent industry-standard fulfillment optimization implementation through optimal order-fulfillment decisions that simultaneously increase turn and lower shipping costs.