We study an inventory optimization problem for a retailer that faces stochastic online and in-store demand in a selling season of fixed length. The retailer has to decide the order-up-to inventory levels and an order fulfillment policy that optimizes the expected total costs. We propose a technique that combines the framework of Turing-Good sampling and stochastic optimization. Our algorithm obtains an average of 6.2% total cost reduction compared to a state-of-the-art algorithm. The cost decrease is obtained by reserving more inventory, thereby reducing the lost sales costs and reducing fulfillment costs. The algorithm we propose is especially beneficial for shorter time horizons and higher in-store demand.